Date of Award

2-1-2025

Publication Type

Dissertation

Degree Name

Ph.D.

Department

Economics, Mathematics, and Statistics

Keywords

Conditional quantile; Copulas; Hypothesis testing; Weak convergence

Supervisor

Mohamed Belalia

Rights

info:eu-repo/semantics/openAccess

Abstract

This dissertation explores nonparametric inference in dependence modelling, focusing on hypothesis testing for copulas and conditional quantile estimation. In particular, it proposes nonparametric tests specifically designed for different structures of copula models, as well as tests that utilize copulas as an analytical framework. Additionally, a novel conditional quantile estimator that incorporates mixed covariates and leverages Bernstein polynomials is introduced. Chapter 2 introduced and studied tests of symmetry for bivariate copulas using empirical Bernstein copula process. Three statistics are proposed and their asymptotic properties are established. Besides, a multiplier bootstrap Bernstein version is investigated for implementation purpose. The simulation study demonstrated the superior performance of the Bernstein tests compared to tests based on empirical copulas. Furthermore, in real data applications, these tests consistently yielded similar conclusions across a diverse range of scenarios. In Chapter 3, the empirical Bernstein copula process is utilized to conduct tests for the equality of the dependence structures between two samples. To this end, three tests statistics are proposed, and their asymptotic properties are established under mild regularity conditions. Furthermore, in order to obtain a valid p-value, subsampling and multiplier bootstrap methods are introduced and investigated for the Bernstein based-test statistics. Through a simulation study, it is demonstrated that the Bernstein-based tests significantly outperform the tests based on the empirical copula. Chapter 4 focuses on constructing a Cramér-von Mises test statistic using C-power functions to quantify the degree of independence between the components of a continuous random vector. The asymptotic property and associated multiplier bootstrap of the test statistic are established. The new test outperforms the empirical copula-based competitor according to simulation studies. Chapter 5 presents a novel quantile dependence estimator for mixed covariates, utilizing the Nadaraya–Watson discrete conditional distribution estimator, further refined with Bernstein polynomials for smoothing. The consistency and asymptotic normality of the proposed estimator are established. Also, a simulation study to compare its performance with other existing estimators is carried out.

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