Non-classical error bounds in the central limit theorem

The classical central limit theorem states the uniform convergence of the distribution functions of the standardized sums of independent and identically distributed square integrable real-valued random variables to the standard normal distribution function. While first versions of the central limit theorem are already due to Moivre (1730) and Laplace (1812), a systematic study of this topic started at the beginning of the last century with the fundamental work of Lyapunov (1900, 1901). Meanwhile, extensions of the central limit theorem are available for a multitude of settings. This includes, e.g., Banach space valued random variables as well as substantial relaxations of the assumptions of independence and identical distributions. Furthermore, explicit error bounds are established and asymptotic expansions are employed to obtain better approximations. Classical error estimates like the famous bound of Berry and Esseen are stated in terms of absolute moments of the random summands and therefore do not reflect a potential closeness of the distributions of the single random summands to a normal distribution. Non-classical approaches take this issue into account by providing error estimates based on, e.g., pseudomoments. The latter field of investigation was initiated by work of Zolotarev in the 1960's and is still in its infancy compared to the development of the classical theory. For example, non-classical error bounds for asymptotic expansions seem not to be available up to now ...

Higher order finite elements and the fictitious domain concept for wave propagation analysis

Magdeburg, Univ., Fak. für Maschinenbau, Diss., 2014

A comparative analysis of Cobb-Douglas model with additive and multiplicative error

This paper dis cusses the fitting of a Cobb-Doug las response curve Yi = αXβi, with additive error, Yi = αXβi + e i, instead of the usual multiplicative error Yi = αXβi (1 + e i). The estimation of the parameters A and B is discussed. An example is given with use of both types of error.

Stability and error analysis for a numerical scheme to approximate elastic flow

Otto-von-Guericke-Universität Magdeburg, Fakultät für Mathematik, Univ., Dissertation, 2015

Credit markets and the propagation of monetary policy shocks

This paper analyzes the propagation of monetary policy shocks through the creation of credit in an economy. Models of the monetary transmission mechanism typically feature responses which last for a few quarters contrary to what the empirical evidence suggests. To propagate the impact of monetary shocks over time, these models introduce adjustment costs by which agents find it optimal to change their decisions slowly. This paper presents another explanation that does not rely on any sort of adjustment costs or stickiness. In our economy, agents own assets and make occupational choices. Banks intermediate between agents demanding and supplying assets. Our interpretation is based on the way banks create credit and how the monetary authority affects the process of financial intermediation through its monetary policy. As the central bank lowers the interest rate by buying government bonds in exchange for reserves, high productive entrepreneurs are able to borrow more resources from low productivity agents. We show that this movement of capital among agents sets in motion a response of the economy that resembles an expansionary phase of the cycle.

Restriction site-associated DNA sequencing, genotyping error estimation and de novo assembly optimization for population genetic inference.

Restriction site-associated DNA sequencing (RADseq) provides researchers with the ability to record genetic polymorphism across thousands of loci for nonmodel organisms, potentially revolutionizing the field of molecular ecology. However, as with other genotyping methods, RADseq is prone to a number of sources of error that may have consequential effects for population genetic inferences, and these have received only limited attention in terms of the estimation and reporting of genotyping error rates. Here we use individual sample replicates, under the expectation of identical genotypes, to quantify genotyping error in the absence of a reference genome. We then use sample replicates to (i) optimize de novo assembly parameters within the program Stacks, by minimizing error and maximizing the retrieval of informative loci; and (ii) quantify error rates for loci, alleles and single-nucleotide polymorphisms. As an empirical example, we use a double-digest RAD data set of a nonmodel plant species, Berberis alpina, collected from high-altitude mountains in Mexico.

Codificación a nivel de paquete para comunicaciones móviles por satélite

Una de les opcions que es contemplen per transmetre continguts multimèdia i proporcionar accés a Internet a grups de usuaris mòbils és fer servir satèl·lits. Les condiciones de propagació del canal mòbil impliquen que d'una manera o altra haurem de garantir la qualitat de servei. Això té fins i tot més importància si tenim en compte que, en el cas d'accés a Internet, no es té la capacitat d'assumir cert percentatge de pèrdua de dades que tenim, per exemple, en la transmissió de so o vídeo (rebaixant la qualitat). Entre les principals alternatives per a aquesta classe d’entorns es troba la inclusió de codificacions a nivell de paquet. El funcionament d'aquesta tècnica es basa en incloure a la transmissió paquets redundants, obtinguts mitjançant un determinat algoritme. El receptor podrà recuperar la informació original que es volia enviar, sempre que hagi rebut una certa quantitat de paquets, similar a la quantitat de paquets originals. A aquest mecanisme se'l coneix com Forward Error Correction (FEC) a nivell de paquet. En aquesta memòria es valoren breument les alternatives existents i s'expliquen algunes de les codificacions per a FEC més importants. A continuació es realitza un estudi compartiu d’algunes d'elles: les variants de LDPC (Low Density Parity Check) conegudes com LDGM (Low Density Generator Matrix), i la codificació Raptor

Stochastic Search Variable Selection in Vector Error Correction Models with an Application to a Model of the UK Macroeconomy

This paper develops methods for Stochastic Search Variable Selection (currently popular with regression and Vector Autoregressive models) for Vector Error Correction models where there are many possible restrictions on the cointegration space. We show how this allows the researcher to begin with a single unrestricted model and either do model selection or model averaging in an automatic and computationally efficient manner. We apply our methods to a large UK macroeconomic model.

Diseño e implementación de un receptor multifrecuencia basado en muestreo paso banda aplicado al sistema Galileo

Este trabajo tiene como objetivo diseñar e implementar un receptor multifrecuencia requerido para aplicaciones Galileo centradas a realizar correcciones de errores y estudios de la ionosfera. Estas características obligan a buscar alternativas respecto los receptores superheterodinos convencionales dado que para éstos los retardos de propagación entre las diferentes bandas de interés son inaceptables. Por ello, se presenta un receptor basado en la técnica de muestreo paso banda, que permite trasladar el espectro mediante el conversor ADC a través de un aliasing intencionado, eliminando así los retardos de propagación entre bandas de interés, dado que todas se albergan en un mismo canal. En este trabajo nos hemos centrado únicamente en las etapas críticas del receptor presentado, siendo éstas la etapa de filtrado y conversión digital. La etapa de filtrado requerirá filtros muy selectivos, ya que el ruido existente fuera de banda se solapará a nuestra banda de interés, degradando la SNR del sistema a medida que tenga más potencia. Esta etapa se ha realizado mediante una estructura duplexora conjuntamente con dos filtros de líneas acopladas. La etapa de conversión se ha realizado fabricando el layout de un conversor comercial, del cual se ha validado el correcto funcionamiento para la aplicación requerida.

Propagation connectivity of random hypergraphs

We study the concept of propagation connectivity on random 3-uniform hypergraphs. This concept is inspired by a simple linear time algorithm for solving instances of certain constraint satisfaction problems. We derive upper and lower bounds for the propagation connectivity threshold, and point out some algorithmic implications.

Restriction site-associated DNA sequencing, genotyping error estimation and de novo assembly optimization for population genetic inference.

Restriction site-associated DNA sequencing (RADseq) provides researchers with the ability to record genetic polymorphism across thousands of loci for nonmodel organisms, potentially revolutionizing the field of molecular ecology. However, as with other genotyping methods, RADseq is prone to a number of sources of error that may have consequential effects for population genetic inferences, and these have received only limited attention in terms of the estimation and reporting of genotyping error rates. Here we use individual sample replicates, under the expectation of identical genotypes, to quantify genotyping error in the absence of a reference genome. We then use sample replicates to (i) optimize de novo assembly parameters within the program Stacks, by minimizing error and maximizing the retrieval of informative loci; and (ii) quantify error rates for loci, alleles and single-nucleotide polymorphisms. As an empirical example, we use a double-digest RAD data set of a nonmodel plant species, Berberis alpina, collected from high-altitude mountains in Mexico.

Nonclassical measurement error with applications to labor and development issues

Zero correlation between measurement error and model error has been assumed in existing panel data models dealing specifically with measurement error. We extend this literature and propose a simple model where one regressor is mismeasured, allowing the measurement error to correlate with model error. Zero correlation between measurement error and model error is a special case in our model where correlated measurement error equals zero. We ask two research questions. First, we wonder if the correlated measurement error can be identified in the context of panel data. Second, we wonder if classical instrumental variables in panel data need to be adjusted when correlation between measurement error and model error cannot be ignored. Under some regularity conditions the answer is yes to both questions. We then propose a two-step estimation corresponding to the two questions. The first step estimates correlated measurement error from a reverse regression; and the second step estimates usual coefficients of interest using adjusted instruments.

Quantificació de l'error comès pels models de níxol ecològic al predir la distribució d'especies generalistes

Report for the scientific sojourn carried out at the University of California at Berkeley, from September to December 2007. Environmental niche modelling (ENM) techniques are powerful tools to predict species potential distributions. In the last ten years, a plethora of novel methodological approaches and modelling techniques have been developed. During three months, I stayed at the University of California, Berkeley, working under the supervision of Dr. David R. Vieites. The aim of our work was to quantify the error committed by these techniques, but also to test how an increase in the sample size affects the resultant predictions. Using MaxEnt software we generated distribution predictive maps, from different sample sizes, of the Eurasian quail (Coturnix coturnix) in the Iberian Peninsula. The quail is a generalist species from a climatic point of view, but an habitat specialist. The resultant distribution maps were compared with the real distribution of the species. This distribution was obtained from recent bird atlases from Spain and Portugal. Results show that ENM techniques can have important errors when predicting the species distribution of generalist species. Moreover, an increase of sample size is not necessary related with a better performance of the models. We conclude that a deep knowledge of the species’ biology and the variables affecting their distribution is crucial for an optimal modelling. The lack of this knowledge can induce to wrong conclusions.

Error estimate and control in the MSFV method for multiphase flow in porous media

n this paper the iterative MSFV method is extended to include the sequential implicit simulation of time dependent problems involving the solution of a system of pressure-saturation equations. To control numerical errors in simulation results, an error estimate, based on the residual of the MSFV approximate pressure field, is introduced. In the initial time steps in simulation iterations are employed until a specified accuracy in pressure is achieved. This initial solution is then used to improve the localization assumption at later time steps. Additional iterations in pressure solution are employed only when the pressure residual becomes larger than a specified threshold value. Efficiency of the strategy and the error control criteria are numerically investigated. This paper also shows that it is possible to derive an a-priori estimate and control based on the allowed pressure-equation residual to guarantee the desired accuracy in saturation calculation.