arXiv subjects

Mickael Albertus

Publications and source records attributed to Mickael Albertus.

4 recordsLinked to original sources

arXiv2021

Asymptotic relatively more efficient test with auxiliary information: the case of the $Z$-test and the chi-square test

The main goal of this article is to study how an auxiliary information can be used to improve the efficiency of two famous statistical tests: the $ Z$-test and the chi-square test. Many definitions of auxiliary information can be found in the statistical literature. In this article, the notion of auxiliary information is discussed from a very general point of view and depends on the relevant test. These two statistical tests are modified so that this information is taken into account. It is shown in particular that the efficiency of these new tests is improved in the sense of Pitman's ARE. Some statistical examples illustrate the use of this method.

math.ST↗

arXiv2021

Exponential increase of the power of the independence and homogeneity chi-square tests with auxiliary information

This paper is an extension of the work about the exponential increase of the power of two non-parametric tests: the $ Z $-test and the chi-square goodness-of-fit test. Subject to having auxiliary information, it is possible to improve exponentially relative to the size of the sample the power of the famous chi-square tests of independence and homogeneity. Improving the power of these statistical tests by using auxiliary information makes it possible either to reduce the probability of accepting the null hypothesis under the alternative hypothesis, or to reduce the size of the sample necessary to reach a predefined power. The suggested method is computational and some simple statistical applications are presented to illustrate these results. The framework of this work is non-parametric, so it can be applied to any kind of data and any area using statistics.

math.ST↗

arXiv2019

Raking-ratio empirical process with auxiliary information learning

The raking-ratio method is a statistical and computational method which adjusts the empirical measure to match the true probability of sets of a finite partition. We study the asymptotic behavior of the raking-ratio empirical process indexed by a class of functions when the auxiliary information is given by estimates. We suppose that these estimates result from the learning of the probability of sets of partitions from another sample larger than the sample of the statistician, as in the case of two-stage sampling surveys. Under some metric entropy hypothesis and conditions on the size of the information source sample, we establish the strong approximation of this process and show in this case that the weak convergence is the same as the classical raking-ratio empirical process. We also give possible statistical applications of these results like the strengthening of the $Z$-test and the chi-square goodness of fit test.

math.ST↗

arXiv2018

Auxiliary information : the raking-ratio empirical process

We study the empirical measure associated to a sample of size $n$ and modified by $N$ iterations of the raking-ratio method. This empirical measure is adjusted to match the true probability of sets in a finite partition which changes each step. We establish asymptotic properties of the raking-ratio empirical process indexed by functions as $n\rightarrow +\infty$, for $N$ fixed. We study nonasymptotic properties by using a Gaussian approximation which yields uniform Berry-Esseen type bounds depending on $n, N$ and provides estimates of the uniform quadratic risk reduction. A closed-form expression of the limiting covariance matrices is derived as $N\rightarrow +\infty$. In the two-way contingency table case the limiting process has a simple explicit formula.

math.ST↗