Multivariate wavelet-based density estimation with size-biased data

Esmaeil Shirazi; Hassan Doosti

doi:10.1016/j.stamet.2015.05.002

Multivariate wavelet-based density estimation with size-biased data

Esmaeil Shirazi^*, Hassan Doosti

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

8 Citations (Scopus)

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, Bpqs. 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 etal. (2012) to the multivariate case.

Original language	English
Pages (from-to)	12-19
Number of pages	8
Journal	Statistical Methodology
Volume	27
DOIs	https://doi.org/10.1016/j.stamet.2015.05.002
Publication status	Published - 1 Nov 2015
Externally published	Yes

Keywords

Besov spaces
Density estimation
Size-biased data
Wavelet

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10.1016/j.stamet.2015.05.002

Cite this

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title = "Multivariate wavelet-based density estimation with size-biased data",

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, Bpqs. 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 etal. (2012) to the multivariate case.",

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author = "Esmaeil Shirazi and Hassan Doosti",

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AU - Doosti, Hassan

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N2 - 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, Bpqs. 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 etal. (2012) to the multivariate case.

AB - 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, Bpqs. 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 etal. (2012) to the multivariate case.

KW - Besov spaces

KW - Density estimation

KW - Size-biased data

KW - Wavelet

UR - http://www.scopus.com/inward/record.url?scp=84930648266&partnerID=8YFLogxK

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DO - 10.1016/j.stamet.2015.05.002

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SP - 12

EP - 19

JO - Statistical Methodology

JF - Statistical Methodology

SN - 1572-3127

ER -

Multivariate wavelet-based density estimation with size-biased data

Abstract

Keywords

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