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Last edited on
Oct 18, 2021 by JJ
.
Thesis:
Master in Mathematics

Author:
Fayez Murad

Title:
Adaptive goodness-of-fit tests in a density model

Supervisor:
Jan JOHANNES

Abstract:
In this Master’s thesis we observe n i.i.d real random variables with unknown density f. We propose to test whether f equals assumed density f0. we introduce a multiple testing procedure based on an estimation of the L2-distance between f and f0. Our procedure is a collection of linear subspace of L2(R), which consist of mixing of spaces and each of these spaces is generated either by constant piecewise functions, scaling functions or trigonometric polynomials. We prove that our test is adaptive, in sense it achieves the optimal rates of testing established by Ingster (2000) over various classes of smooth functions. We will discuss the result of some Monte Carlo simulation to verify our theoretical results and we compare their power with the power of the tests proposed by Kolmogorov and Smirnov.

Reference:
M. Fromont et B. Laurent. Adaptive goodness-of-fit tests in a density model. The Annals of Statistics, 34(2):680–720, 2006.