Some problems in nonparametric inference for the stress release process related to the local time

Takayuki Fujii; Yoichi Nishiyama

doi:10.1007/s10463-011-0344-7

Some problems in nonparametric inference for the stress release process related to the local time

Takayuki Fujii^*, Yoichi Nishiyama

^*Corresponding author for this work

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

1 Citation (Scopus)

Abstract

This paper is concerned with nonparametric statistics for the stress release process. We propose the local time estimator (LTE) for the stationary density and show that it is unbiased and uniformly consistent. The LTE is used in constructing an estimator for the intensity function. A goodness of fit test for the intensity function is also presented. In these studies, the local time of the stress release process plays an important role.

Original language	English
Pages (from-to)	991-1007
Number of pages	17
Journal	Annals of the Institute of Statistical Mathematics
Volume	64
Issue number	5
DOIs	https://doi.org/10.1007/s10463-011-0344-7
Publication status	Published - 2012 Oct
Externally published	Yes

Keywords

Goodness of fit test
Local time
Stationary density
Stress release process
Uniform consistency

ASJC Scopus subject areas

Statistics and Probability

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10.1007/s10463-011-0344-7

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title = "Some problems in nonparametric inference for the stress release process related to the local time",

abstract = "This paper is concerned with nonparametric statistics for the stress release process. We propose the local time estimator (LTE) for the stationary density and show that it is unbiased and uniformly consistent. The LTE is used in constructing an estimator for the intensity function. A goodness of fit test for the intensity function is also presented. In these studies, the local time of the stress release process plays an important role.",

keywords = "Goodness of fit test, Local time, Stationary density, Stress release process, Uniform consistency",

author = "Takayuki Fujii and Yoichi Nishiyama",

note = "Funding Information: Acknowledgments The authors would like to thank the Associate Editor and two anonymous referees for their valuable comments. This research was supported by Grant-in-Aid for Young Scientists (B), No. 21700320 [T.F.] and Grant-in-Aid for Scientific Research (C), No. 21540157 [Y.N.] from Japan Society for the Promotion of Science (JSPS).",

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AU - Fujii, Takayuki

AU - Nishiyama, Yoichi

N1 - Funding Information: Acknowledgments The authors would like to thank the Associate Editor and two anonymous referees for their valuable comments. This research was supported by Grant-in-Aid for Young Scientists (B), No. 21700320 [T.F.] and Grant-in-Aid for Scientific Research (C), No. 21540157 [Y.N.] from Japan Society for the Promotion of Science (JSPS).

PY - 2012/10

Y1 - 2012/10

N2 - This paper is concerned with nonparametric statistics for the stress release process. We propose the local time estimator (LTE) for the stationary density and show that it is unbiased and uniformly consistent. The LTE is used in constructing an estimator for the intensity function. A goodness of fit test for the intensity function is also presented. In these studies, the local time of the stress release process plays an important role.

AB - This paper is concerned with nonparametric statistics for the stress release process. We propose the local time estimator (LTE) for the stationary density and show that it is unbiased and uniformly consistent. The LTE is used in constructing an estimator for the intensity function. A goodness of fit test for the intensity function is also presented. In these studies, the local time of the stress release process plays an important role.

KW - Goodness of fit test

KW - Local time

KW - Stationary density

KW - Stress release process

KW - Uniform consistency

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JF - Annals of the Institute of Statistical Mathematics

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ER -

Some problems in nonparametric inference for the stress release process related to the local time

Abstract

Keywords

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