Nonlinear constrained and saturated control of power electronics and electromechanical systems

Power electronic converters are extensively adopted for the solution of timely issues, such as power quality improvement in industrial plants, energy management in hybrid electrical systems, and control of electrical generators for renewables. Beside nonlinearity, this systems are typically characterized by hard constraints on the control inputs, and sometimes the state variables. In this respect, control laws able to handle input saturation are crucial to formally characterize the systems stability and performance properties. From a practical viewpoint, a proper saturation management allows to extend the systems transient and steady-state operating ranges, improving their reliability and availability. The main topic of this thesis concern saturated control methodologies, based on modern approaches, applied to power electronics and electromechanical systems. The pursued objective is to provide formal results under any saturation scenario, overcoming the drawbacks of the classic solution commonly applied to cope with saturation of power converters, and enhancing performance. For this purpose two main approaches are exploited and extended to deal with power electronic applications: modern anti-windup strategies, providing formal results and systematic design rules for the anti-windup compensator, devoted to handle control saturation, and “one step” saturated feedback design techniques, relying on a suitable characterization of the saturation nonlinearity and less conservative extensions of standard absolute stability theory results. The first part of the thesis is devoted to present and develop a novel general anti-windup scheme, which is then specifically applied to a class of power converters adopted for power quality enhancement in industrial plants. In the second part a polytopic differential inclusion representation of saturation nonlinearity is presented and extended to deal with a class of multiple input power converters, used to manage hybrid electrical energy sources. The third part regards adaptive observers design for robust estimation of the parameters required for high performance control of power systems.

Biomimetic bilayer membranes made from polymers and lipids

Amphiphile Blockcopolymere sind in der Lage in Wasser Morphologien auszubilden, die analog sind zur hydrophil-hydrophob-hydrophil-Struktur von natürlichen Lipiddoppelschichten. In dieser Arbeit wird zum ersten Mal die Präparation und Charakterisierung von oberflächengestützten Polymerdoppelschichten aus Polybutadien-b-Polyethylenoxid (PB-PEO) beschrieben. Für die Herstellung dieser Strukturen wurden zwei unterschiedliche Präparationsstrategien verfolgt. Der erste Weg besteht aus einer zweistufigen Methode, bei der im ersten Schritt organisierte Monoschichten mittels Langmuir-Blodgett-Transfer auf Gold übertragen und kovalent angebunden werden. Im zweiten Schritt werden hydrophobe Wechselwirkungen ausgenutzt, um über Langmuir-Schaefer-Transfer eine weitere Schicht aufzubringen. Somit wurden homogene Architekturen erzeugt, die oberflächengestützten Lipiddoppelschichten gleichen. Als alternativer, einstufiger Ansatz zur Herstellung von Polymerdoppelschichten wurde das Spreiten von Polymervesikeln auf Gold verfolgt. Auch hierdurch ließen sich Doppelschichtstrukturen mit einer vollständigen Oberflächenbedeckung erzeugen. Die hergestellten Polymerdoppelschichten besitzen eine Dicke von 11-14 nm, die von der Präparationsmethode abhängt. Die Polymerstrukturen weisen bei Trocknung für 1.5 h eine Stabilität gegenüber Luft auf. Bei längeren Trocknungszeiten von ca. 12 h kommt es zu einer Reorganisation der Oberfläche. Dies deutet darauf hin, dass Wasser dazu notwendig ist die Strukturen auf lange Sicht zu stabilisieren. Um die Biokompatibilität der Polymerschichten nachzuweisen, wurden die Wechselwirkungen mit dem membranaktiven Peptid Polymyxin B und dem Transmembranprotein α-Haemolysin gezeigt. Mobilität ist ein wichtiger Faktor für die korrekte Funktion vieler Transmembranproteine. Um die laterale Diffusionsdynamik innerhalb der künstlichen Strukturen zu untersuchen, wurde die Mobilität eines integralen Modellpeptids und von fluoreszierenden Membransonden gemessen. Es konnte mit einzelmolekülempfindlichen Techniken gezeigt werden, dass das α-helikale Peptid und die kleinen Fluoreszenzfarbstoffe frei im hydrophoben Kern der Polymerdoppelschicht diffundieren können. Die Diffusion von beiden Spezies scheint stark von der Fluidität der Polymermatrix beeinflusst zu sein. Ein weiterer Teil dieser Arbeit widmet sich der Entwicklung eines angemessenen, lipidbasierten Referenzsystems für zukünftige Proteinuntersuchungen. Hierzu wurde eine neue Methode zu Herstellung von peptidgestützten Lipiddoppelschichtmembranen entwickelt. Dies wurde durch kovalente Befestigung eines Thiopeptids an einen Goldfilm und darauffolgende Anbindung eines Lipids erreicht. Zur Ausbildung der Lipiddoppelschicht auf dem Lipopeptidunterbau wurder der Rapid Solvent Exchange verwendet. Die Ausbildung der Lipiddoppelschicht wurde sowohl auf microskopischer als auch auf makroskopischer Ebene nachgewiesen. Im letzten Schritt wurde die Anwendbarkeit des Modelsystems für elektrochemische Messungen durch den funktionalen Einbau des Ionentransporters Valinomycin unter Beweis gestellt.

Physiologische Veränderungen bei der Thylakoidmembranbiogenese und die Funktionsweise des Nukleotidaustauschfaktors GrpE in Cyanobakterien

Bei Wachstum im Dunkeln zeigten sich rudimentäre Thylakoidstrukturen, wobei nach dem Transfer ins Licht ein vollständiges Thylakoidmembransystem erneut ausgebildet wurde. Parallel stieg, der Chlorophyllgehalt pro Zelle und das Verhältnis von Phycobilisomen zu Chlorophyll verschob sich erneut auf die Seite des Chlorophylls. Das bei Wachstum im Dunkeln als Monomer vorliegende PS II, war nicht funktional. Nach dem Transfer ins Licht, war nach etwa acht bis zwölf Stunden ein aktives PS II zu detektieren. Das PS I lag nach der Inkubation im Dunkeln, in geringerer Konzentration aber aktiv als Trimer in den Zellen vor.rnZwei Typ I Signalpeptidasen aus Synechocystis sp. PCC 6803 zeigten Unterschiede im Bezug auf ihre intrazelluläre Lokalisation. Für die Untersuchungen der Lokalisation konnte ein neues System der Fluoreszenzmikroskopie entwickelt und erfolgreich eingesetzt werden. Das LepB1 zeigte einen (auto-) proteolytischen Abbau. Für Untersuchungen zur katalytischen Aktivität wurden Vorläuferproteine als Substrate für LepB2 identifiziert.rnDie Funktionsweise der GrpE-Proteine aus verwandten Cyanobakterien zeigt Unterschiede. Bei beiden GrpE-Proteinen erfolgt der reversible Übergang von einem Dimer hin zu einem Monomer innerhalb eines physiologisch relevanten Temperaturbereichs in einem Schritt. Bei dem Protein aus Synechocystis sp. ist der N-Terminus und bei dem Protein aus dem thermophilen Bakterium Thermosynechococcus der C-Terminus für die Dimerisierung essentiell. rn

Nanocapsules for self-healing materials

Im Rahmen dieser Arbeit wurden neue Ansätze für das Konzept der kapselbasierten Selbstheilungsmaterialien untersucht. Die Verkapselung von Selbstheilungsreagenzien in funktionellen Nanokapseln wurde dabei mittels drei verschiedener Herstellungsmethoden in Miniemulsion durchgeführt. Zunächst wurde die Synthese von Kern-Schale-Partikeln mit verkapselten Monomeren für die Ringöffnungs-Metathese-Polymerisation über freie radikalische Polymerisation in Miniemulsionstropfen beschrieben. Durch orthogonale Reaktionen wurden dabei verschiedene chemische Funktionalisierungen in die Schale eingebracht. Die Rolle des Tensides, das Verhältnis von Kernmaterial zu Monomer sowie die Variation der Lösungsmittelqualität hatte dabei einen Einfluss auf die Struktur der Kolloide. Die Heilungsreagenzien blieben auch nach der Verkapselung aktiv, was durch erfolgreich durchgeführte Selbstheilungsexperimente gezeigt werden konnte. Im zweiten Abschnitt wurde die Synthese von Silica-Nanocontainern für Selbstheilungsmaterialien über Hydrolyse und Polykondensation von Alkoxysilanen an der Grenzfläche der Miniemulsionstropfen beschrieben. Dieser Ansatz ermöglichte die effiziente Verkapselung sowohl von Monomeren als auch von Lösungen der Katalysatoren für die Metathese-Polymerisation in einem Einstufenprozess. Die Größe der Kapseln, die Dicke der Schale und der Feststoffgehalt der Dispersionen konnte dabei in einem weiten Bereich variiert werden. Anhand von erfolgreich durchgeführten Selbstheilungsreaktionen, die über Thermogravimetrie und 13C-NMR-Spektroskopie verfolgt wurden, konnte gezeigt werden, dass die Selbstheilungsreagenzien nach der Verkapselung aktiv blieben. Das dritte Konzept behandelte die Herstellung von polymeren Nanokapseln mittels Emulsions-Lösungsmittelverdampfungstechnik, welche eine milde Methode zur Verkapselung darstellt. Es wurde eine allgemeine und einfache Vorgehensweise beschrieben, in der Selbstheilungsreagenzien in polymeren Nanokapseln unter Verwendung von kommerziell erhältlichen Polymeren als Schalenmaterial verkapselt wurden. Zudem wurden Copolymere aus Styrol und verschiedenen hydrophilen Monomeren über freie radikalische Polymerisation sowie über polymeranaloge Reaktionen hergestellt. Diese statistischen Copolymere waren ebenso wie Blockcopolymere zur Herstellung von wohldefinierten Kern-Schale-Nanopartikeln mittels Emulsions-Lösungsmittelverdampfungsprozess geeignet. rnrnDes Weiteren wurde ein neues Konzept für die Synthese von pH-responsiven Nanokapseln aus tensidfreien Emulsionen unter Verwendung von Copolymeren aus Styrol und Trimethylsilylmethacrylat beschrieben. Der vorgeschlagene synthetische Ansatz ermöglicht dabei die erste Synthese von Nanokapseln über den Emulsions-Lösungsmittelverdampfungsprozess in Abwesenheit eines Tensides. Eine vollständig reversible Aggregation ermöglichte eine leichte Trennung der Nanokapseln von der kontinuierlichen Phase sowie eine Erhöhung der Konzentration der Nanokapseldispersionen auf das bis zu fünffache. Darüber hinaus war es möglich, Selbstheilungsreagenzien in stabilem Zustand zu verkapseln. Abschließend wurde die elektrochemische Abscheidung von mit Monomer gefüllten Nanokapseln in eine Zinkschicht zur Anwendung im Korrosionsschutz behandelt.

Twitter data analysis for financial markets

Over the time, Twitter has become a fundamental source of information for news. As a one step forward, researchers have tried to analyse if the tweets contain predictive power. In the past, in financial field, a lot of research has been done to propose a function which takes as input all the tweets for a particular stock or index s, analyse them and predict the stock or index price of s. In this work, we take an alternative approach: using the stock price and tweet information, we investigate following questions. 1. Is there any relation between the amount of tweets being generated and the stocks being exchanged? 2. Is there any relation between the sentiment of the tweets and stock prices? 3. What is the structure of the graph that describes the relationships between users?

Polymer nanoparticles : their functionalization for biomedical applications and dynamics near an electrode

In this work, a method for the functionalization of biocompatible, poly(lactic acid)-based nanoparticles with charged moieties or fluorescent labels is presented. Therefore, a miniemulsion solvent evaporation procedure is used in which prepolymerized poly(L-lactic acid) is used together with a previously synthesized copolymer of methacrylic acid or a polymerizable dye, respectively, and an oligo(lactic acid) macromonomer. Alternatively, the copolymerization has been carried out in one step with the miniemulsion solvent evaporation. The increased stability in salty solutions of the carboxyl-modified nanoparticles compared to nanoparticles consisting of poly(lactic acid) only has been shown in light scattering experiments. The properties of the nanoparticles that were prepared with the separately synthesized copolymer were almost identical to those in which the copolymerization and particle fabrication were carried out simultaneously. During the characterization of the fluorescently labeled nanoparticles, the focus was on the stable bonding between the fluorescent dye and the rest of the polymer chain to ensure that none of it is released from the particles, even after longer storage time or during lengthy experiments. In a fluorescence correlation spectroscopy experiment, it could be shown that even after two weeks, no dye has been released into the solvent. Besides biomedical research for which the above described, functionalized nanoparticles were optimized, nanoparticles also play a role in coating technology. One possibility to fabricate coatings is the electrophoretic deposition of particles. In this process, the mobility of nanoparticles near electrode interfaces plays a crucial role. In this thesis, the nanoparticle mobility has been investigated with resonance enhanced dynamic light scattering (REDLS). A new setup has been developed in which the evanescent electromagnetic eld of a surface plasmon that propagates along the gold-sample interface has been used as incident beam for the dynamic light scattering experiment. The gold layer that is necessary for the excitation of the plasmon doubles as an electrode. Due to the penetration depth of the surface plasmon into the sample layer that is limited to ca. 200 nm, insights on the voltage- and frequency dependent mobility of the nanoparticles near the electrode could be gained. Additionally, simultaneous measurements at four different scattering angles can be carried out with this setup, therefore the investigation of samples undergoing changes is feasible. The results were discussed in context with the mechanisms of electrophoretic deposition.

Stationary states in random walks on networks

In this thesis we dealt with the problem of describing a transportation network in which the objects in movement were subject to both finite transportation capacity and finite accomodation capacity. The movements across such a system are realistically of a simultaneous nature which poses some challenges when formulating a mathematical description. We tried to derive such a general modellization from one posed on a simplified problem based on asyncronicity in particle transitions. We did so considering one-step processes based on the assumption that the system could be describable through discrete time Markov processes with finite state space. After describing the pre-established dynamics in terms of master equations we determined stationary states for the considered processes. Numerical simulations then led to the conclusion that a general system naturally evolves toward a congestion state when its particle transition simultaneously and we consider one single constraint in the form of network node capacity. Moreover the congested nodes of a system tend to be located in adjacent spots in the network, thus forming local clusters of congested nodes.

Surgical hip dislocation for osteochondral transplantation as a salvage procedure for a femoral head impaction fracture

Obturator anterior hip dislocation is very rare. Poor results are described in patients with additional large transchondral fractures and treatment of these injuries remains challenging. Appropriate treatment recommendations are missing in the literature. This case report introduces surgical hip dislocation for osteochondral autograft transplantation with graft harvest from the nonweightbearing area of the head-neck junction as a salvage procedure in a large femoral head defect. We report the treatment and outcome of a 48-year-old man who sustained an anterior dislocation of the left hip after a motorcycle accident. After initial closed reduction in the emergency room, imaging analysis revealed a large osteochondral defect of the femoral head within the weightbearing area (10 × 20 mm, depth: 5 mm). The hip was exposed with a surgical hip dislocation using a trochanteric osteotomy. An osteochondral autograft was harvested from a nonweightbearing area of the femoral head and transferred into the defect. The patient was prospectively examined clinically and radiologically. Two years postoperatively, the patient was free of pain and complaints. The function of the injured hip was comparable to that of the contralateral, healthy hip and showed satisfying radiologic results. Surgical hip dislocation with a trochanteric flip osteotomy is a simple, one-step technique that allows full inspection of the hip to treat osteochondral femoral defects by osteochondral transplantation. The presented technique, used as a salvage procedure in a large femoral head defect, yielded good clinical and satisfying radiologic outcomes at the midterm.

High-throughput procedure for tick surveys of tick-borne encephalitis virus and its application in a national surveillance study in Switzerland

Tick-borne encephalitis (TBE), a viral infection of the central nervous system, is endemic in many Eurasian countries. In Switzerland, TBE risk areas have been characterized by geographic mapping of clinical cases. Since mass vaccination should significantly decrease the number of TBE cases, alternative methods for exposure risk assessment are required. We established a new PCR-based test for the detection of TBE virus (TBEV) in ticks. The protocol involves an automated, high-throughput nucleic acid extraction method (QIAsymphony SP system) and a one-step duplex real-time reverse transcription-PCR (RT-PCR) assay for the detection of European subtype TBEV, including an internal process control. High usability, reproducibility, and equivalent performance for virus concentrations down to 5 x 10(3) viral genome equivalents/microl favor the automated protocol compared to the modified guanidinium thiocyanate-phenol-chloroform extraction procedure. The real-time RT-PCR allows fast, sensitive (limit of detection, 10 RNA copies/microl), and specific (no false-positive test results for other TBEV subtypes, other flaviviruses, or other tick-transmitted pathogens) detection of European subtype TBEV. The new detection method was applied in a national surveillance study, in which 62,343 Ixodes ricinus ticks were screened for the presence of TBE virus. A total of 38 foci of endemicity could be identified, with a mean virus prevalence of 0.46%. The foci do not fully agree with those defined by disease mapping. Therefore, the proposed molecular test procedure constitutes a prerequisite for an appropriate TBE surveillance. Our data are a unique complement of human TBE disease case mapping in Switzerland.

Immobilization and characterization of recombinant esterase enzyme on chitosan nanoparticles

Immobilization of biologically important molecules on myriad nano-sized materials has attracted great attention. Through this study, thermophilic esterase enzyme was obtained using recombinant DNA technology and purified applying one-step His-Select HF nickel affinity gel. The synthesis of chitosan was achieved from chitin by deacetylation process and degree of deacetylation was calculated as 89% by elemental analysis. Chitosan nanoparticles were prepared based on the ionic gelation of chitosan with tripolyphosphate anions. The physicochemical properties of the chitosan and chitosan nanoparticles were determined by several methods including SEM (Scanning Electron Microscopy), FT-IR (Fourier Transform Infrared Spectroscopy) and DLS (Dynamic Light Scattering). The morphology of chitosan nanoparticles was spherical and the nanospheres’ average diameter was 75.3 nm. The purified recombinant esterase was immobilized efficiently by physical adsorption onto chitosan nanoparticles and effects of various immobilization conditions were investigated in details to develope highly cost-effective esterase as a biocatalyst to be utilized in biotechnological purposes. The optimal conditions of immobilization were determined as follows; 1.0 mg/mL of recombinant esterase was immobilized on 1.5 mg chitosan nanoparticles for 30 min at 60°C, pH 7.0 under 100 rpm stirring speed. Under optimized conditions, immobilized recombinant esterase activity yield was 88.5%. The physicochemical characterization of enzyme immobilized chitosan nanoparticles was analyzed by SEM, FT-IR and AFM (Atomic Force Microscopy).

Measuring Correlation Between HIV Sequence Variation and Disease Stage of HIV-Infected Individuals

With a virus such as Human Immunodeficiency Virus (HIV) that has infected millions of people worldwide, and with many unaware that they are infected, it becomes vital to understand how the virus works and how it functions at the molecular level. Because there currently is no vaccine and no way to eradicate the virus from an infected person, any information about how the virus interacts with its host greatly increases the chances of understanding how HIV works and brings scientists one step closer to being able to combat such a destructive virus. Thousands of HIV viruses have been sequenced and are available in many online databases for public use. Attributes that are linked to each sequence include the viral load within the host and how sick the patient is currently. Being able to predict the stage of infection for someone is a valuable resource, as it could potentially aid in treatment options and proper medication use. Our approach of analyzing region-specific amino acid composition for select genes has been able to predict patient disease state up to an accuracy of 85.4%. Moreover, we output a set of classification rules based on the sequence that may prove useful for diagnosing the expected clinical outcome of the infected patient.

Squared Extrapolation Methods (SQUAREM): A New Class of Simple and Efficient Numerical Schemes for Accelerating the Convergence of the EM Algorithm

We derive a new class of iterative schemes for accelerating the convergence of the EM algorithm, by exploiting the connection between fixed point iterations and extrapolation methods. First, we present a general formulation of one-step iterative schemes, which are obtained by cycling with the extrapolation methods. We, then square the one-step schemes to obtain the new class of methods, which we call SQUAREM. Squaring a one-step iterative scheme is simply applying it twice within each cycle of the extrapolation method. Here we focus on the first order or rank-one extrapolation methods for two reasons, (1) simplicity, and (2) computational efficiency. In particular, we study two first order extrapolation methods, the reduced rank extrapolation (RRE1) and minimal polynomial extrapolation (MPE1). The convergence of the new schemes, both one-step and squared, is non-monotonic with respect to the residual norm. The first order one-step and SQUAREM schemes are linearly convergent, like the EM algorithm but they have a faster rate of convergence. We demonstrate, through five different examples, the effectiveness of the first order SQUAREM schemes, SqRRE1 and SqMPE1, in accelerating the EM algorithm. The SQUAREM schemes are also shown to be vastly superior to their one-step counterparts, RRE1 and MPE1, in terms of computational efficiency. The proposed extrapolation schemes can fail due to the numerical problems of stagnation and near breakdown. We have developed a new hybrid iterative scheme that combines the RRE1 and MPE1 schemes in such a manner that it overcomes both stagnation and near breakdown. The squared first order hybrid scheme, SqHyb1, emerges as the iterative scheme of choice based on our numerical experiments. It combines the fast convergence of the SqMPE1, while avoiding near breakdowns, with the stability of SqRRE1, while avoiding stagnations. The SQUAREM methods can be incorporated very easily into an existing EM algorithm. They only require the basic EM step for their implementation and do not require any other auxiliary quantities such as the complete data log likelihood, and its gradient or hessian. They are an attractive option in problems with a very large number of parameters, and in problems where the statistical model is complex, the EM algorithm is slow and each EM step is computationally demanding.

Estimation with Interval Censored Data in Longitudinal Studies

In biostatistical applications interest often focuses on the estimation of the distribution of a time-until-event variable T. If one observes whether or not T exceeds an observed monitoring time at a random number of monitoring times, then the data structure is called interval censored data. We extend this data structure by allowing the presence of a possibly time-dependent covariate process that is observed until end of follow up. If one only assumes that the censoring mechanism satisfies coarsening at random, then, by the curve of dimensionality, typically no regular estimators will exist. To fight the curse of dimensionality we follow the approach of Robins and Rotnitzky (1992) by modeling parameters of the censoring mechanism. We model the right-censoring mechanism by modeling the hazard of the follow up time, conditional on T and the covariate process. For the monitoring mechanism we avoid modeling the joint distribution of the monitoring times by only modeling a univariate hazard of the pooled monitoring times, conditional on the follow up time, T, and the covariates process, which can be estimated by treating the pooled sample of monitoring times as i.i.d. In particular, it is assumed that the monitoring times and the right-censoring times only depend on T through the observed covariate process. We introduce inverse probability of censoring weighted (IPCW) estimator of the distribution of T and of smooth functionals thereof which are guaranteed to be consistent and asymptotically normal if we have available correctly specified semiparametric models for the two hazards of the censoring process. Furthermore, given such correctly specified models for these hazards of the censoring process, we propose a one-step estimator which will improve on the IPCW estimator if we correctly specify a lower-dimensional working model for the conditional distribution of T, given the covariate process, that remains consistent and asymptotically normal if this latter working model is misspecified. It is shown that the one-step estimator is efficient if each subject is at most monitored once and the working model contains the truth. In general, it is shown that the one-step estimator optimally uses the surrogate information if the working model contains the truth. It is not optimal in using the interval information provided by the current status indicators at the monitoring times, but simulations in Peterson, van der Laan (1997) show that the efficiency loss is small.

Locally Efficient Estimation with Current Status Data and High Dimensional Covariates

In biostatistical applications, interest often focuses on the estimation of the distribution of time T between two consecutive events. If the initial event time is observed and the subsequent event time is only known to be larger or smaller than an observed monitoring time, then the data is described by the well known singly-censored current status model, also known as interval censored data, case I. We extend this current status model by allowing the presence of a time-dependent process, which is partly observed and allowing C to depend on T through the observed part of this time-dependent process. Because of the high dimension of the covariate process, no globally efficient estimators exist with a good practical performance at moderate sample sizes. We follow the approach of Robins and Rotnitzky (1992) by modeling the censoring variable, given the time-variable and the covariate-process, i.e., the missingness process, under the restriction that it satisfied coarsening at random. We propose a generalization of the simple current status estimator of the distribution of T and of smooth functionals of the distribution of T, which is based on an estimate of the missingness. In this estimator the covariates enter only through the estimate of the missingness process. Due to the coarsening at random assumption, the estimator has the interesting property that if we estimate the missingness process more nonparametrically, then we improve its efficiency. We show that by local estimation of an optimal model or optimal function of the covariates for the missingness process, the generalized current status estimator for smooth functionals become locally efficient; meaning it is efficient if the right model or covariate is consistently estimated and it is consistent and asymptotically normal in general. Estimation of the optimal model requires estimation of the conditional distribution of T, given the covariates. Any (prior) knowledge of this conditional distribution can be used at this stage without any risk of losing root-n consistency. We also propose locally efficient one step estimators. Finally, we show some simulation results.

Locally Efficient Estimation in Censored Data Models: Theory and Examples

In many applications the observed data can be viewed as a censored high dimensional full data random variable X. By the curve of dimensionality it is typically not possible to construct estimators that are asymptotically efficient at every probability distribution in a semiparametric censored data model of such a high dimensional censored data structure. We provide a general method for construction of one-step estimators that are efficient at a chosen submodel of the full-data model, are still well behaved off this submodel and can be chosen to always improve on a given initial estimator. These one-step estimators rely on good estimators of the censoring mechanism and thus will require a parametric or semiparametric model for the censoring mechanism. We present a general theorem that provides a template for proving the desired asymptotic results. We illustrate the general one-step estimation methods by constructing locally efficient one-step estimators of marginal distributions and regression parameters with right-censored data, current status data and bivariate right-censored data, in all models allowing the presence of time-dependent covariates. The conditions of the asymptotics theorem are rigorously verified in one of the examples and the key condition of the general theorem is verified for all examples.