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Strong consistency of kernel method for sliced average variance estimation

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  • Emmanuel De Dieu Nkou

Abstract

In this paper, we consider the kernel method to estimate sliced average variance estimation (SAVE). SAVE is a tool as SIR (sliced inverse regression), recommended to identify and to estimate the central dimension reduction (CDR) subspace. CDR subspace is the intersection of all dimension reduction subspaces which are at the base to describe the conditional distribution of the response Y given a d− dimensional predictor vector X. SAVE and even SIR are used to estimate CDR subspace. Two versions are very popular: slice version and kernel version. In this paper, we are looking at the kernel version. For Kernel SAVE version, two asymptotic properties have been demonstrated in particular: asymptotic normality and convergence in probability. And we know that these two properties, although important, are weak in front of almost sure convergence. However, until now, the strong consistency has not yet been obtained. In this paper, we obtain, under weaker assumptions, this asymptotic property.

Suggested Citation

  • Emmanuel De Dieu Nkou, 2023. "Strong consistency of kernel method for sliced average variance estimation," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 52(21), pages 7586-7600, November.
    • Handle: RePEc:taf:lstaxx:v:52:y:2023:i:21:p:7586-7600
    DOI: 10.1080/03610926.2022.2049821
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