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Moment bounds for mixing random variables useful in nonparametric function estimation

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  • Cox, Dennis D.
  • Kim, Tae Yoon

Abstract

Bounds for even moments of sums of strong mixing random variables are given which extend existing bounds. The method of proof uses simple facts about strong mixing random variables and combinatorial methods. The bound is particularly useful for triangular arrays with entries decreasing in size. To illustrate this, applications are being discussed to nonparametric kernel estimation with dependent observations.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:spapps:v:56:y:1995:i:1:p:151-158
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    References listed on IDEAS

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    1. Roussas, George G., 1990. "Nonparametric regression estimation under mixing conditions," Stochastic Processes and their Applications, Elsevier, vol. 36(1), pages 107-116, October.
    2. Kim, Tae Yoon, 1993. "A note on moment bounds for strong mixing sequences," Statistics & Probability Letters, Elsevier, vol. 16(2), pages 163-168, January.
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    Cited by:

    1. Gao, Jiti & Tong, Howell & Wolff, Rodney, 2002. "Model Specification Tests in Nonparametric Stochastic Regression Models," Journal of Multivariate Analysis, Elsevier, vol. 83(2), pages 324-359, November.
    2. Fernández-Val, Iván & Weidner, Martin, 2016. "Individual and time effects in nonlinear panel models with large N, T," Journal of Econometrics, Elsevier, vol. 192(1), pages 291-312.
    3. David Veredas & Juan Rodriguez-Poo & Antoni Espasa, 2001. "On the (Intradaily) Seasonality and Dynamics of a Financial Point Process : A Semiparametric Approach," Working Papers 2001-19, Center for Research in Economics and Statistics.
    4. Hyungsik Roger Roger Moon & Martin Weidner, 2013. "Linear regression for panel with unknown number of factors as interactive fixed effects," CeMMAP working papers 49/13, Institute for Fiscal Studies.
    5. Hyungsik Roger Roger Moon & Martin Weidner, 2014. "Linear regression for panel with unknown number of factors as interactive fixed effects," CeMMAP working papers 35/14, Institute for Fiscal Studies.
    6. Kim, Tae Yoon & Cox, Dennis D., 1996. "Uniform strong consistency of kernel density estimators under dependence," Statistics & Probability Letters, Elsevier, vol. 26(2), pages 179-185, February.
    7. Gao, Jiti & Lu, Zudi & Tjøstheim, Dag, 2008. "Moment inequalities for spatial processes," Statistics & Probability Letters, Elsevier, vol. 78(6), pages 687-697, April.
    8. Chu, Ba & Jacho-Chávez, David T., 2012. "k-NEAREST NEIGHBOR ESTIMATION OF INVERSE-DENSITY-WEIGHTED EXPECTATIONS WITH DEPENDENT DATA," Econometric Theory, Cambridge University Press, vol. 28(4), pages 769-803, August.
    9. Ivan Fernandez-Val & Martin Weidner, 2014. "Individual and time effects in nonlinear panel models with large N , T," CeMMAP working papers 32/14, Institute for Fiscal Studies.
    10. Blacher, René, 2007. "Central Limit Theorem by moments," Statistics & Probability Letters, Elsevier, vol. 77(17), pages 1647-1651, November.
    11. Hyungsik Roger Moon & Martin Weidner, 2015. "Linear Regression for Panel With Unknown Number of Factors as Interactive Fixed Effects," Econometrica, Econometric Society, vol. 83(4), pages 1543-1579, July.
    12. Estévez-Pérez, Graciela, 2002. "On convergence rates for quadratic errors in kernel hazard estimation," Statistics & Probability Letters, Elsevier, vol. 57(3), pages 231-241, April.
    13. Ivan Fernandez-Val & Martin Weidner, 2013. "Individual and time effects in nonlinear panel models with large N, T," CeMMAP working papers 60/13, Institute for Fiscal Studies.
    14. Gao, Jiti & Anh, Vo, 2000. "A central limit theorem for a random quadratic form of strictly stationary processes," Statistics & Probability Letters, Elsevier, vol. 49(1), pages 69-79, August.

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