Asymptotics for L2-norm of ARCH innovation density estimator

Fuxia Cheng; Shuxia Sun; Miin Jye Wen

doi:10.1016/j.jspi.2011.06.013

Asymptotics for L2-norm of ARCH innovation density estimator

Fuxia Cheng
, Shuxia Sun
, Miin Jye Wen

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

Abstract

In this paper we consider the asymptotic properties of the ARCH innovation density estimator. We obtain the asymptotic normality of the Bickel-Rosenblatt test statistic (based on our density estimator) under the null hypothesis, which is the same as in the case of the one sample set up (given in Bickel and Rosenblatt, 1973). We also show the strong consistency of the estimator for the true density in L2-norm.

Original language	English
Pages (from-to)	3771-3779
Number of pages	9
Journal	Journal of Statistical Planning and Inference
Volume	141
Issue number	12
DOIs	https://doi.org/10.1016/j.jspi.2011.06.013
State	Published - Dec 2011
Externally published	Yes

ASJC Scopus Subject Areas

Statistics and Probability
Statistics, Probability and Uncertainty
Applied Mathematics

Keywords

ARCH-time series
Goodness-of-fit test
Kernel density estimation
L2-norm

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10.1016/j.jspi.2011.06.013

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title = "Asymptotics for L2-norm of ARCH innovation density estimator",

abstract = "In this paper we consider the asymptotic properties of the ARCH innovation density estimator. We obtain the asymptotic normality of the Bickel-Rosenblatt test statistic (based on our density estimator) under the null hypothesis, which is the same as in the case of the one sample set up (given in Bickel and Rosenblatt, 1973). We also show the strong consistency of the estimator for the true density in L2-norm.",

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author = "Fuxia Cheng and Shuxia Sun and Wen, \{Miin Jye\}",

year = "2011",

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doi = "10.1016/j.jspi.2011.06.013",

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journal = "Journal of Statistical Planning and Inference",

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T1 - Asymptotics for L2-norm of ARCH innovation density estimator

AU - Cheng, Fuxia

AU - Sun, Shuxia

AU - Wen, Miin Jye

PY - 2011/12

Y1 - 2011/12

N2 - In this paper we consider the asymptotic properties of the ARCH innovation density estimator. We obtain the asymptotic normality of the Bickel-Rosenblatt test statistic (based on our density estimator) under the null hypothesis, which is the same as in the case of the one sample set up (given in Bickel and Rosenblatt, 1973). We also show the strong consistency of the estimator for the true density in L2-norm.

AB - In this paper we consider the asymptotic properties of the ARCH innovation density estimator. We obtain the asymptotic normality of the Bickel-Rosenblatt test statistic (based on our density estimator) under the null hypothesis, which is the same as in the case of the one sample set up (given in Bickel and Rosenblatt, 1973). We also show the strong consistency of the estimator for the true density in L2-norm.

KW - ARCH-time series

KW - Goodness-of-fit test

KW - Kernel density estimation

KW - L2-norm

UR - https://www.scopus.com/pages/publications/79960847326

UR - https://www.scopus.com/pages/publications/79960847326#tab=citedBy

U2 - 10.1016/j.jspi.2011.06.013

DO - 10.1016/j.jspi.2011.06.013

M3 - Article

AN - SCOPUS:79960847326

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VL - 141

SP - 3771

EP - 3779

JO - Journal of Statistical Planning and Inference

JF - Journal of Statistical Planning and Inference

IS - 12

ER -

Asymptotics for L2-norm of ARCH innovation density estimator

Abstract

ASJC Scopus Subject Areas

Keywords

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