Multivariate wavelet-based density estimation with size-biased data

Q Mathematics

Statistical Methodology Pub Date : 2015-11-01 DOI:10.1016/j.stamet.2015.05.002

Esmaeil Shirazi , Hassan Doosti

引用次数: 12

Abstract

In this paper, we employ wavelet method to propose a multivariate density estimator based on a biased sample. We investigate the asymptotic rate of convergence of the proposed estimator over a large class of densities in the Besov space, $B_{p q}^{s}$ . Moreover, we prove the consistency of our estimator when the expectation of weight function is unknown. This paper is an extension of results in Ramirez and Vidakovic (2010) and Chesneau et al. (2012) to the multivariate case.

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基于多变量小波的尺寸偏倚数据密度估计

本文利用小波变换方法提出了一种基于有偏样本的多元密度估计方法。我们研究了Besov空间(Bpqs)中一大类密度上所提估计量的渐近收敛率。此外，在权函数期望未知的情况下，证明了估计量的相合性。本文将Ramirez and Vidakovic(2010)和Chesneau et al.(2012)的结果推广到多元情况。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Statistical Methodology STATISTICS & PROBABILITY-

CiteScore

0.59

自引率

0.00%

发文量

期刊介绍： Statistical Methodology aims to publish articles of high quality reflecting the varied facets of contemporary statistical theory as well as of significant applications. In addition to helping to stimulate research, the journal intends to bring about interactions among statisticians and scientists in other disciplines broadly interested in statistical methodology. The journal focuses on traditional areas such as statistical inference, multivariate analysis, design of experiments, sampling theory, regression analysis, re-sampling methods, time series, nonparametric statistics, etc., and also gives special emphasis to established as well as emerging applied areas.