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316594

Properties of Legendre Series Estimation of Probability Density

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Last updated: 28 Dec 2024

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Abstract

An unknown density function f(x) and its derivatives have been estimated by means of Legendre functions pⱼ... The estimates use the partial sums of series of Legendre functions with coefficients âⱼₙ = n⁻¹ Σₖ₌₁ⁿ pⱼ(Xₖ) where X₁,...,Xₙ represent a sequence of independent identically distributed random variables (i.i.d.) with the unknown density function f. The integrated mean square rate of convergence of the sth derivative of the estimate is obtained. Similar results are obtained for the case of strictly mixing stationary processes.

DOI

10.21608/esju.1985.316594

Keywords

Convergence Rate, Estimation Properties, Legendre Series, Probability Density, Stationary Processes

Authors

First Name

El Fahham

Last Name

Mostafa

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Volume

29

Article Issue

1

Related Issue

43406

Issue Date

1985-06-01

Receive Date

2023-09-07

Publish Date

1985-06-01

Page Start

79

Page End

86

Print ISSN

0542-1748

Online ISSN

2786-0086

Link

https://esju.journals.ekb.eg/article_316594.html

Detail API

https://esju.journals.ekb.eg/service?article_code=316594

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4

Type

Original Article

Type Code

1,914

Publication Type

Journal

Publication Title

The Egyptian Statistical Journal

Publication Link

https://esju.journals.ekb.eg/

MainTitle

Properties of Legendre Series Estimation of Probability Density

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Article

Created At

28 Dec 2024