Probability density estimators, their properties and applications

Kód výsledku v IS VaVaI

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Výsledek na webu

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DOI - Digital Object Identifier

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Jazyk výsledku

angličtina

Název v původním jazyce

Probability density estimators, their properties and applications

Popis výsledku v původním jazyce

The thesis focuses on the minimum distance density estimators b fn of the true density f0 on the real line. Consistency in the L1 norm and in the expected L1 norm is studied. Kolmogorov distance estimator is known to be consistent of the order n^1/2 if the degree of variations of the distribution family D is nite. The same result for Kolmogorov distance estimator is proven under weaker conditions and the L1 consistency results are extended to the Lévy, discrepancy and Cramér - von Mises minimum distance estimator. Further, the generalized Cramér - von Mises distance is dened together with so called Kolmogorov - Cramér distance which includes both Kolmogorov and Cramér - von Mises distance as limiting special cases. We prove consistency and n^-gamma order of consistency in the (expected) L1 norm of both minimum distance estimator based on newly dened distances. Our numerical simulation illustrates the quality of consistency property covered by theoretical results for sample sizes from n = 10 to n = 500. The proportionality constants of the consistency order are approximated from simulated data since they are not given by the proofs of theorems. Dependence of consistency in the L1 norm on "contamination neighbourhood of the true model is studied and, further, the robustness of theses newly dened estimator is investigated for contaminated Normal family. Numerical simulations are used to compare statistical properties of Kolmogorov, Cramér - von Mises, generalized Cramér - von Mises, and Kolmogorov - Cramér estimators and to determine the optimal or preferable choice of parameters of newly dened estimators. Final comparison brings results for robustness and empirical relative eciency of Kolmogorov, Cramér - von Mises, generalized Cramér - von Mises, Kolmogorov - Cramér (with preferable choice of parameters) estimators together with Rényi, Power divergence, and maximum likelihood estimators.

Název v anglickém jazyce

Probability density estimators, their properties and applications

Popis výsledku anglicky

The thesis focuses on the minimum distance density estimators b fn of the true density f0 on the real line. Consistency in the L1 norm and in the expected L1 norm is studied. Kolmogorov distance estimator is known to be consistent of the order n^1/2 if the degree of variations of the distribution family D is nite. The same result for Kolmogorov distance estimator is proven under weaker conditions and the L1 consistency results are extended to the Lévy, discrepancy and Cramér - von Mises minimum distance estimator. Further, the generalized Cramér - von Mises distance is dened together with so called Kolmogorov - Cramér distance which includes both Kolmogorov and Cramér - von Mises distance as limiting special cases. We prove consistency and n^-gamma order of consistency in the (expected) L1 norm of both minimum distance estimator based on newly dened distances. Our numerical simulation illustrates the quality of consistency property covered by theoretical results for sample sizes from n = 10 to n = 500. The proportionality constants of the consistency order are approximated from simulated data since they are not given by the proofs of theorems. Dependence of consistency in the L1 norm on "contamination neighbourhood of the true model is studied and, further, the robustness of theses newly dened estimator is investigated for contaminated Normal family. Numerical simulations are used to compare statistical properties of Kolmogorov, Cramér - von Mises, generalized Cramér - von Mises, and Kolmogorov - Cramér estimators and to determine the optimal or preferable choice of parameters of newly dened estimators. Final comparison brings results for robustness and empirical relative eciency of Kolmogorov, Cramér - von Mises, generalized Cramér - von Mises, Kolmogorov - Cramér (with preferable choice of parameters) estimators together with Rényi, Power divergence, and maximum likelihood estimators.

Druh

O - Ostatní výsledky

CEP obor

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OECD FORD obor

10103 - Statistics and probability

Projekt

Výsledek vznikl pri realizaci vícero projektů. Více informací v záložce Projekty.

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)<br>S - Specificky vyzkum na vysokych skolach

Rok uplatnění

2023

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů