Hilbert Space Valued Signal Plus Noise Models: Analysis of Structural Breaks under High Dimensionality and Temporal Dependence

This thesis is concerned with change point analysis for time series, i.e. with detection of structural breaks in time-ordered, random data. This long-standing research field regained popularity over the last few years and is still undergoing, as statistical analysis in general, a transformation to high-dimensional problems. We focus on the fundamental »change in the mean« problem and provide extensions of the classical non-parametric Darling-Erdős-type cumulative sum (CUSUM) testing and estimation theory within highdimensional Hilbert space settings. In the first part we contribute to (long run) principal component based testing methods for Hilbert space valued time series under a rather broad (abrupt, epidemic, gradual, multiple) change setting and under dependence. For the dependence structure we consider either traditional m-dependence assumptions or more recently developed m-approximability conditions which cover, e.g., MA, AR and ARCH models. We derive Gumbel and Brownian bridge type approximations of the distribution of the test statistic under the null hypothesis of no change and consistency conditions under the alternative. A new formulation of the test statistic using projections on subspaces allows us to simplify the standard proof techniques and to weaken common assumptions on the covariance structure. Furthermore, we propose to adjust the principal components by an implicit estimation of a (possible) change direction. This approach adds flexibility to projection based methods, weakens typical technical conditions and provides better consistency properties under the alternative. In the second part we contribute to estimation methods for common changes in the means of panels of Hilbert space valued time series. We analyze weighted CUSUM estimates within a recently proposed »high-dimensional low sample size (HDLSS)« framework, where the sample size is fixed but the number of panels increases. We derive sharp conditions on »pointwise asymptotic accuracy« or »uniform asymptotic accuracy« of those estimates in terms of the weighting function. Particularly, we prove that a covariance-based correction of Darling-Erdős-type CUSUM estimates is required to guarantee uniform asymptotic accuracy under moderate dependence conditions within panels and that these conditions are fulfilled, e.g., by any MA(1) time series. As a counterexample we show that for AR(1) time series, close to the non-stationary case, the dependence is too strong and uniform asymptotic accuracy cannot be ensured. Finally, we conduct simulations to demonstrate that our results are practically applicable and that our methodological suggestions are advantageous.

Impacto del Programa de Alimentación Escolar en el Trabajo Infantil: Una aproximación desde la toma de decisiones familiares

Esta investigación analiza el impacto del Programa de Alimentación Escolar en el trabajo infantil en Colombia a través de varias técnicas de evaluación de impacto que incluyen emparejamiento simple, emparejamiento genético y emparejamiento con reducción de sesgo. En particular, se encuentra que este programa disminuye la probabilidad de que los escolares trabajen alrededor de un 4%. Además, se explora que el trabajo infantil se reduce gracias a que el programa aumenta la seguridad alimentaria, lo que consecuentemente cambia las decisiones de los hogares y anula la carga laboral en los infantes. Son numerosos los avances en primera infancia llevados a cabo por el Estado, sin embargo, estos resultados sirven de base para construir un marco conceptual en el que se deben rescatar y promover las políticas públicas alimentarias en toda la edad escolar.

Synthetic portfolio for event studies: Estimating the effects of volatility call auctions

We propose a method denoted as synthetic portfolio for event studies in market microstructure that is particularly interesting to use with high frequency data and thinly traded markets. The method is based on Synthetic Control Method and provides a robust data driven method to build a counterfactual for evaluating the effects of the volatility call auctions. We find that SMC could be used if the loss function is defined as the difference between the returns of the asset and the returns of a synthetic portfolio. We apply SCM to test the performance of the volatility call auction as a circuit breaker in the context of an event study. We find that for Colombian Stock Market securities, the asynchronicity of intraday data reduces the analysis to a selected group of stocks, however it is possible to build a tracking portfolio. The realized volatility increases after the auction, indicating that the mechanism is not enhancing the price discovery process.

The Drivers of Wage Inequality Across Europe: A Recentered Influence Function Regression Approach

This study analyzes the impact of individual characteristics as well as occupation and industry on male wage inequality in nine European countries. Unlike previous studies, we consider regression models for five inequality measures and employ the recentered influence function regression method proposed by Firpo et al. (2009) to test directly the influence of covariates on inequality. We conclude that there is heterogeneity in the effects of covariates on inequality across countries and throughout wage distribution. Heterogeneity among countries is more evident in education and experience whereas occupation and industry characteristics as well as holding a supervisory position reveal more similar effects. Our results are compatible with the skill biased technological change, rapid rise in the integration of trade and financial markets as well as explanations related to the increase of the remunerative package of top executives.

Transferability of environmental favourability models in geographic space: The case of the Iberian desman (Galemys pyrenaicus) in Portugal and Spain

Transferring distribution models between different geographical areas may be problematic, as the performance of models outside their original scope is hard to predict. A modelling procedure is needed that gets the gist of the environmental descriptors of a distribution area, without either overfitting to the training data or overestimating the species’ distribution potential.We tested the transferability power of the favourability function, a generalized linear model, on the distribution of the Iberian desman (Galemys pyrenaicus) in the Iberian territories of Portugal and Spain.We also tested the effects of two of the main potential constraints on model transferability: the analysed ranges of the predictor variables, and the completeness of the species distribution data. We modelled 10 km×10km presence/absence data from Portugal and Spain separately, extrapolated each model to the other country, and compared predictions with observations. The Spanish model, despite arguably containing more false absences, showed good predictive ability in Portugal. The Portuguese model, whose predictors ranged between only a subset of the values observed in Spain, overestimated desman distribution when transferred.We discuss possible reasons for this differential model behaviour, and highlight the importance of this kind of models for prediction and conservation applications

Comparison of Photovoltaic panel’s standard and simplified models

Shockley diode equation is basic for single diode model equation, which is overly used for characterizing the photovoltaic cell output and behavior. In the standard equation, it includes series resistance (Rs) and shunt resistance (Rsh) with different types of parameters. Maximum simulation and modeling work done previously, related to single diode photovoltaic cell used this equation. However, there is another form of the standard equation which has not included Series Resistance (Rs) and Shunt Resistance (Rsh) yet, as the Shunt Resistance is much bigger than the load resistance and the load resistance is much bigger than the Series Resistance. For this phenomena, very small power loss occurs within a photovoltaic cell. This research focuses on the comparison of two forms of basic Shockley diode equation. This analysis describes a deep understanding of the photovoltaic cell, as well as gives understanding about Series Resistance (Rs) and Shunt Resistance (Rsh) behavior in the Photovoltaic cell. For making estimation of a real time photovoltaic system, faster calculation is needed. The equation without Series Resistance and Shunt Resistance is appropriate for the real time environment. Error function for both Series resistance (Rs) and Shunt resistances (Rsh) have been analyzed which shows that the total system is not affected by this two parameters' behavior.

Essays in Applied Insurance Economics

The papers included in this thesis deal with a few aspects of insurance economics that have seldom been dealt with in the applied literature. In the first paper I apply for the first time the tools of the economics of crime to study the determinants of frauds, using data on Italian provinces. The contributions to the literature are manifold: -The price of insuring has a positive correlation with the propensity to defraud -Social norms constraint fraudulent behavior, but their strength is curtailed in economic downturns -I apply a simple extension of the Random Coefficient model, which allows for the presence of time invariant covariates and asymmetries in the impact of the regressors. The second paper assesses how the evolution of macro prudential regulation of insurance companies has been reflected in their equity price. I employ a standard event study methodology, deriving the definition of the “control” and “treatment” groups from what is implied by the regulatory framework. The main results are: -Markets care about the evolution of the legislation. Their perception has shifted from a first positive assessment of a possible implicit “too big to fail” subsidy to a more negative one related to its cost in terms of stricter capital requirement -The size of this phenomenon is positively related to leverage, size and on the geographical location of the insurance companies The third paper introduces a novel methodology to forecast non-life insurance premiums and profitability as function of macroeconomic variables, using the simultaneous equation framework traditionally employed macroeconometric models and a simple theoretical model of insurance pricing to derive a long term relationship between premiums, claims expenses and short term rates. The model is shown to provide a better forecast of premiums and profitability compared with the single equation specifications commonly used in applied analysis.

Erythropoietin reduces pathogenic humoral immunity by inhibiting T Follicular Helper cell differentiation and function

A large fraction of organ transplant recipients develop anti-donor antibodies (DSA), with accelerated graft loss and increased mortality. We tested the hypothesis that erythropoietin (EPO) reduces DSA formation by inhibiting T follicular helper (TFH) cells. We measured DSA levels, splenic TFH, TFR cells, germinal center (GC), and class switched B cells, in murine models of allogeneic sensitization, allogeneic transplantation and in parent-to-F1 models of graft versus host disease (GVHD). We quantified the same cell subsets and specific antibodies, upon EPO or vehicle treatment, in wild type mice and animals lacking EPO receptor selectively on T or B cells, immunized with T-independent or T-dependent stimuli. In vitro, we tested the EPO effect on TFH induction. We isolated TFH and TFR cells to perform in vitro assay and clarify their role. EPO reduced DSA levels, GC, class switched B cells, and increased the TFR/TFH ratio in the heart transplanted mice and in two GVHD models. EPO did also reduce TFH and GC B cells in SRBC-immunized mice, while had no effect in TNP-AECM-FICOLL-immunized animals, indicating that EPO inhibits GC B cells by targeting TFH cells. EPO effects were absent in T cells EPOR conditional KO mice, confirming that EPO affects TFH in vivo through EPOR. In vitro, EPO affected TFH induction through an EPO-EPOR-STAT5-dependent pathway. Suppression assay demonstrated that the reduction of IgG antibodies was dependent on TFH cells, sustaining the central role of the subset in this EPO-mediated mechanism. In conclusion, EPO prevents DSA formation in mice through a direct suppression of TFH. Development of DSA is associated with high risk of graft rejection, giving our data a strong rationale for studies testing the hypothesis that EPO administration prevents their formation in organ transplant recipients. Our findings provide a foundation for testing EPO as a treatment of antibody mediated disease processes.

Comprehensive characterization of SDH-deficient GIST using NGS data and iPSC models

Gastrointestinal stromal tumors (GIST) are the most common di tumors of the gastrointestinal tract, arising from the interstitial cells of Cajal (ICCs) or their precursors. The vast majority of GISTs (75–85% of GIST) harbor KIT or PDGFRA mutations. A small percentage of GIST (about 10‐15%) do not harbor any of these driver mutations and have historically been called wild-type (WT). Among them, from 20% to 40% show loss of function of the succinate dehydrogenase complex (SDH), also defined as SDH‐deficient GIST. SDH-deficient GISTs display distinctive clinical and pathological features, and can be sporadic or associated with Carney triad or Carney-Stratakis syndrome. These tumors arise most frequently in the stomach with predilection to distal stomach and antrum, have a multi-nodular growth, display a histological epithelioid phenotype, and present frequent lympho-vascular invasion. Occurrence of lymph node metastases and indolent course are representative features of SDH-deficient GISTs. This subset of GIST is known for the immunohistochemical loss of succinate dehydrogenase subunit B (SDHB), which signals the loss of function of the entire SDH-complex. The overall aim of my PhD project consists of the comprehensive characterization of SDH deficient GIST. Throughout the project, clinical, molecular and cellular characterizations were performed using next-generation sequencing technologies (NGS), that has the potential to allow the identification of molecular patterns useful for the diagnosis and development of novel treatments. Moreover, while there are many different cell lines and preclinical models of KIT/PDGFRA mutant GIST, no reliable cell model of SDH-deficient GIST has currently been developed, which could be used for studies on tumor evolution and in vitro assessments of drug response. Therefore, another aim of this project was to develop a pre-clinical model of SDH deficient GIST using the novel technology of induced pluripotent stem cells (iPSC).

Variational and learning models for image and time series inverse problems

Inverse problems are at the core of many challenging applications. Variational and learning models provide estimated solutions of inverse problems as the outcome of specific reconstruction maps. In the variational approach, the result of the reconstruction map is the solution of a regularized minimization problem encoding information on the acquisition process and prior knowledge on the solution. In the learning approach, the reconstruction map is a parametric function whose parameters are identified by solving a minimization problem depending on a large set of data. In this thesis, we go beyond this apparent dichotomy between variational and learning models and we show they can be harmoniously merged in unified hybrid frameworks preserving their main advantages. We develop several highly efficient methods based on both these model-driven and data-driven strategies, for which we provide a detailed convergence analysis. The arising algorithms are applied to solve inverse problems involving images and time series. For each task, we show the proposed schemes improve the performances of many other existing methods in terms of both computational burden and quality of the solution. In the first part, we focus on gradient-based regularized variational models which are shown to be effective for segmentation purposes and thermal and medical image enhancement. We consider gradient sparsity-promoting regularized models for which we develop different strategies to estimate the regularization strength. Furthermore, we introduce a novel gradient-based Plug-and-Play convergent scheme considering a deep learning based denoiser trained on the gradient domain. In the second part, we address the tasks of natural image deblurring, image and video super resolution microscopy and positioning time series prediction, through deep learning based methods. We boost the performances of supervised, such as trained convolutional and recurrent networks, and unsupervised deep learning strategies, such as Deep Image Prior, by penalizing the losses with handcrafted regularization terms.

Price manipulation: theoretical models and empirical investigation

Understanding why market manipulation is conducted, under which conditions it is the most profitable and investigating the magnitude of these practices are crucial questions for financial regulators. Closing price manipulation induced by derivatives’ expiration is the primary subject of this thesis. The first chapter provides a mathematical framework in continuous time to study the incentive to manipulate a set of securities induced by a derivative position. An agent holding a European-type contingent claim, depending on the price of a basket of underlying securities, is considered. The agent can affect the price of the underlying securities by trading on each of them before expiration. The elements of novelty are at least twofold: (1) a multi-asset market is considered; (2) the problem is solved by means of both classic optimisation and stochastic control techniques. Both linear and option payoffs are considered. In the second chapter an empirical investigation is conducted on the existence of expiration day effects on the UK equity market. Intraday data on FTSE 350 stocks over a six-year period from 2015-2020 are used. The results show that the expiration of index derivatives is associated with a rise in both trading activity and volatility, together with significant price distortions. The expiration of single stock options appears to have little to no impact on the underlying securities. The last chapter examines the existence of patterns in line with closing price manipulation of UK stocks on option expiration days. The main contributions are threefold: (1) this is one of the few empirical studies on manipulation induced by the options market; (2) proprietary equity orderbook and transaction data sets are used to define manipulation proxies, providing a more detailed analysis; (3) the behaviour of proprietary trading firms is studied. Despite the industry concerns, no evidence is found of this type of manipulative behaviour.

Advanced studies on two animal models, murine and fish. RadKI21A626T mouse model: new insights into molecular mechanisms of enteric neuro-epithelial pathology. European sea bass: study of the effects of essential oils in different diets on the gastric system.

My PhD research period was focused on the anatomical, physiological and functional study of the gastrointestinal system on two different animal models. In two different contexts, the purpose of these two lines of research was contribute to understand how a specific genetic mutation or the adoption of a particular dietary supplement can affect gastrointestinal function. Functional gastrointestinal disorders are chronic conditions characterized by symptoms for which no organic cause can be found. Although symptoms are generally mild, a small subset of cases shows severe manifestations. This subset of patients may also have recurrent intestinal sub-occlusive episodes, but in absence of mechanical causes. This condition is referred to as chronic intestinal pseudo-obstruction, a rare, intractable chronic disease. Some mutations have been associated with CIPO. A novel causative RAD21 missense mutation was identified in a large consanguineous family, segregating a recessive form of CIPO. The present thesis was aimed to elucidate the mechanisms leading to neuropathy underlying CIPO via a recently developed conditional KI mouse carrying the RAD21 mutation. The experimental studies are based on the characterization and functional analysis of the conditional KI Rad21A626T mouse model. On the other hand aquaculture is increasing the global supply of foods. The species selected and feeds used affects the nutrients available from aquaculture, with a need to improve feed efficiency, both for economic and environmental reasons, but this will require novel innovative approaches. Nutritional strategies focused on the use of botanicals have attracted interest in animal production. Previous research indicates the positive results of using essential oils (EOs) as natural feed additives for several farmed animals. Therefore, the present study was designed to compare the effects of feed EO supplementation in two different forms (natural and composed of active ingredients obtained by synthesis) on the gastric mucosa in European sea bass.

On the effect of confounding in linear regression models: an approach based on the theory of quadratic forms

The main topic of this thesis is confounding in linear regression models. It arises when a relationship between an observed process, the covariate, and an outcome process, the response, is influenced by an unmeasured process, the confounder, associated with both. Consequently, the estimators for the regression coefficients of the measured covariates might be severely biased, less efficient and characterized by misleading interpretations. Confounding is an issue when the primary target of the work is the estimation of the regression parameters. The central point of the dissertation is the evaluation of the sampling properties of parameter estimators. This work aims to extend the spatial confounding framework to general structured settings and to understand the behaviour of confounding as a function of the data generating process structure parameters in several scenarios focusing on the joint covariate-confounder structure. In line with the spatial statistics literature, our purpose is to quantify the sampling properties of the regression coefficient estimators and, in turn, to identify the most prominent quantities depending on the generative mechanism impacting confounding. Once the sampling properties of the estimator conditionally on the covariate process are derived as ratios of dependent quadratic forms in Gaussian random variables, we provide an analytic expression of the marginal sampling properties of the estimator using Carlson’s R function. Additionally, we propose a representative quantity for the magnitude of confounding as a proxy of the bias, its first-order Laplace approximation. To conclude, we work under several frameworks considering spatial and temporal data with specific assumptions regarding the covariance and cross-covariance functions used to generate the processes involved. This study allows us to claim that the variability of the confounder-covariate interaction and of the covariate plays the most relevant role in determining the principal marker of the magnitude of confounding.

Joint value at risk: a new conditional risk measure

In this PhD thesis a new firm level conditional risk measure is developed. It is named Joint Value at Risk (JVaR) and is defined as a quantile of a conditional distribution of interest, where the conditioning event is a latent upper tail event. It addresses the problem of how risk changes under extreme volatility scenarios. The properties of JVaR are studied based on a stochastic volatility representation of the underlying process. We prove that JVaR is leverage consistent, i.e. it is an increasing function of the dependence parameter in the stochastic representation. A feasible class of nonparametric M-estimators is introduced by exploiting the elicitability of quantiles and the stochastic ordering theory. Consistency and asymptotic normality of the two stage M-estimator are derived, and a simulation study is reported to illustrate its finite-sample properties. Parametric estimation methods are also discussed. The relation with the VaR is exploited to introduce a volatility contribution measure, and a tail risk measure is also proposed. The analysis of the dynamic JVaR is presented based on asymmetric stochastic volatility models. Empirical results with S&P500 data show that accounting for extreme volatility levels is relevant to better characterize the evolution of risk. The work is complemented by a review of the literature, where we provide an overview on quantile risk measures, elicitable functionals and several stochastic orderings.

Enhancing predictive capability of models for solubility and permeability in polymers and composites

The interpretation of phase equilibrium and mass transport phenomena in gas/solvent - polymer system at molten or glassy state is relevant in many industrial applications. Among tools available for the prediction of thermodynamics properties in these systems, at molten/rubbery state, is the group contribution lattice-fluid equation of state (GCLF-EoS), developed by Lee and Danner and ultimately based on Panayiotou and Vera LF theory. On the other side, a thermodynamic approach namely non-equilibrium lattice-fluid (NELF) was proposed by Doghieri and Sarti to consistently extend the description of thermodynamic properties of solute polymer systems obtained through a suitable equilibrium model to the case of non-equilibrium conditions below the glass transition temperature. The first objective of this work is to investigate the phase behaviour in solvent/polymer at glassy state by using NELF model and to develop a predictive tool for gas or vapor solubility that could be applied in several different applications: membrane gas separation, barrier materials for food packaging, polymer-based gas sensors and drug delivery devices. Within the efforts to develop a predictive tool of this kind, a revision of the group contribution method developed by High and Danner for the application of LF model by Panayiotou and Vera is considered, with reference to possible alternatives for the mixing rule for characteristic interaction energy between segments. The work also devotes efforts to the analysis of gas permeability in polymer composite materials as formed by a polymer matrix in which domains are dispersed of a second phase and attention is focused on relation for deviation from Maxwell law as function of arrangement, shape of dispersed domains and loading.