arXiv subjects

Guy Martial Nkiet

Publications and source records attributed to Guy Martial Nkiet.

24 records · Page 2Linked to original sources

arXiv2018

Smoothed functional average variance estimation for dimension reduction

We propose an estimation method that we call functional average variance estimation (FAVE), for estimating the EDR space in functional semiparametric regression model, based on kernel estimates of density and regression. Consistency results are then established for the estimator of the interest operator, and for the directions of EDR space. A simulation study that shows that the proposed approach performs as well as traditional ones is presented.

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arXiv2018

Strong consistency of kernel estimator in a semiparametric regression model

Estimating the effective dimension reduction (EDR) space, related to the semiparametric regression model introduced by Li \cite{sir}, is based on the estimation of the covariance matrix $Λ$ of the conditional expectation of the vector of predictors given the response. An estimator $\widehatΛ_n$ of $Λ$ based on kernel method was introduced by Zhu and Fang \cite{Asymptotics} who then derived, under some conditions, the asymptotic distribution of $\sqrt{n}\left(\widehatΛ_n-Λ\right)$, as $n\rightarrow +\infty$. In this paper, we obtain, under specified conditions, the almost sure convergence of $\widehatΛ_n$ to $Λ$, as $n\rightarrow +\infty$.

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arXiv2018

Robust multiple-set linear canonical analysis based on minimum covariance determinant estimator

By deriving influence functions related to multiple-set linear canonical analysis (MSLCA) we show that the classical version of this analysis, based on empirical covariance operators, is not robust. Then, we introduce a robust version of MSLCA by using the MCD estimator of the covariance operator of the involved random vector. The related influence functions are then derived and are shown to be bounded. Asymptotic properties of the introduced robust MSLCA are obtained and permit to propose a robust test for mutual non-correlation. This test is shown to be robust by studying the related second order influence function under the null hypothesis.

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arXiv2017

Asymptotic theory of multiple-set linear canonical analysis

This paper deals with asymptotics for multiple-set linear canonical analysis (MSLCA). A definition of this analysis, that adapts the classical one to the context of Euclidean random variables, is given and properties of the related canonical coefficients are derived. Then, estimators of the MSLCA's elements, based on empirical covariance operators, are proposed and asymptotics for these estimators are obtained. More precisely, we prove their consistency and we obtain asymptotic normality for the estimator of the operator that gives MSLCA, and also for the estimator of the vector of canonical coefficients. These results are then used to obtain a test for mutual non-correlation between the involved Euclidean random variables.

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arXiv2017

Variable selection in discriminant analysis for mixed variables and several groups

We propose a method for variable selection in discriminant analysis with mixed categorical and continuous variables. This method is based on a criterion that permits to reduce the variable selection problem to a problem of estimating suitable permutation and dimensionality. Then, estimators for these parameters are proposed and the resulting method for selecting variables is shown to be consistent. A simulation study that permits to study several poperties of the proposed approach and to compare it with an existing method is given.

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arXiv2015

Variable selection in multiple regression with random design

We propose a method for variable selection in multiple regression with random predictors. This method is based on a criterion that permits to reduce the variable selection problem to a problem of estimating suitable permutation and dimensionality. Then, estimators for these parameters are proposed and the resulting method for selecting variables is shown to be consistent. A simulation study that permits to gain understanding of the performances of the proposed approach and to compare it with an existing method is given.

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