- 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.