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A central limit theorem for a random quadratic form of strictly stationary processes

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  • Gao, Jiti
  • Anh, Vo
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Abstract

In this paper, we consider a random quadratic form of strictly stationary processes. A central limit theorem for the quadratic form is established and an application to nonparametric series regression is given.

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Bibliographic Info

Article provided by Elsevier in its journal Statistics & Probability Letters.

Volume (Year): 49 (2000)
Issue (Month): 1 (August)
Pages: 69-79

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Handle: RePEc:eee:stapro:v:49:y:2000:i:1:p:69-79

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Keywords: Central limit theorem Quadratic form Stationary process;

References

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  1. Hong, Yongmiao & White, Halbert, 1995. "Consistent Specification Testing via Nonparametric Series Regression," Econometrica, Econometric Society, vol. 63(5), pages 1133-59, September.
  2. Cox, Dennis D. & Kim, Tae Yoon, 1995. "Moment bounds for mixing random variables useful in nonparametric function estimation," Stochastic Processes and their Applications, Elsevier, vol. 56(1), pages 151-158, March.
  3. Hall, Peter, 1984. "Central limit theorem for integrated square error of multivariate nonparametric density estimators," Journal of Multivariate Analysis, Elsevier, vol. 14(1), pages 1-16, February.
  4. Gallant, A. Ronald & Souza, Geraldo, 1991. "On the asymptotic normality of Fourier flexible form estimates," Journal of Econometrics, Elsevier, vol. 50(3), pages 329-353, December.
  5. Vidar Hjellvik & Qiwei Yao & Dag Tjostheim, 1998. "Linearity testing using local polynominal approximation," LSE Research Online Documents on Economics 6638, London School of Economics and Political Science, LSE Library.
  6. Fan, Yanqin & Li, Qi, 1996. "Consistent Model Specification Tests: Omitted Variables and Semiparametric Functional Forms," Econometrica, Econometric Society, vol. 64(4), pages 865-90, July.
  7. Boente, Graciela & Fraiman, Ricardo, 1988. "Consistency of a nonparametric estimate of a density function for dependent variables," Journal of Multivariate Analysis, Elsevier, vol. 25(1), pages 90-99, April.
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Cited by:
  1. Gao, Jiti & Tong, Howell, 2002. "Nonparametric and semiparametric regression model selection," MPRA Paper 11987, University Library of Munich, Germany, revised Feb 2004.
  2. Gao, Jiti, 2007. "Nonlinear time series: semiparametric and nonparametric methods," MPRA Paper 39563, University Library of Munich, Germany, revised 01 Sep 2007.
  3. Gao, Jiti & Hong, Yongmiao, 2007. "Central limit theorems for weighted quadratic forms of dependent processes with applications in specification testing," MPRA Paper 11977, University Library of Munich, Germany, revised Dec 2007.

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