Probability density estimators, their properties and applications

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21340%2F23%3A00365477" target="_blank" >RIV/68407700:21340/23:00365477 - isvavai.cz</a>

Result on the web

—

DOI - Digital Object Identifier

—

Result language

angličtina

Original language name

Probability density estimators, their properties and applications

Original language description

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.

Czech name

—

Czech description

—

Type

O - Miscellaneous

CEP classification

—

OECD FORD branch

10103 - Statistics and probability

Project

Result was created during the realization of more than one project. More information in the Projects tab.

Continuities

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

Publication year

2023

Confidentiality

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