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Asymptotic normality of a smooth estimate of a random field distribution function under association

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  • Roussas, George G.

Abstract

Let Zd be the lattice of points in d with integer coordinates, and let {Xn}, n [epsilon] Zd, be a random field of real-valued translation invariant random variables with unknown distribution function F. For u and v in Zd with u [infinity] as N --> [infinity], I = 1, ..., d. On the basis of the random variables Xn, n [epsilon] B0k(N), let be a smooth kernel-type estimate of F. Under suitable regularity conditions, including that of association, it is shown that , properly normalized and centered, is asymptotically normal with specified parameters.

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  • Roussas, George G., 1995. "Asymptotic normality of a smooth estimate of a random field distribution function under association," Statistics & Probability Letters, Elsevier, vol. 24(1), pages 77-90, July.
    • Handle: RePEc:eee:stapro:v:24:y:1995:i:1:p:77-90
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    1. Ioannides, D. A. & Roussas, G. G., 1999. "Exponential inequality for associated random variables," Statistics & Probability Letters, Elsevier, vol. 42(4), pages 423-431, May.
    2. Henriques, Carla & Eduardo Oliveira, Paulo, 2008. "Large deviations for the empirical mean of associated random variables," Statistics & Probability Letters, Elsevier, vol. 78(6), pages 594-598, April.
    3. Li, Yongming & Yang, Shanchao & Zhou, Yong, 2008. "Consistency and uniformly asymptotic normality of wavelet estimator in regression model with associated samples," Statistics & Probability Letters, Elsevier, vol. 78(17), pages 2947-2956, December.
    4. Roussas, George G., 2001. "An Esséen-type inequality for probability density functions, with an application," Statistics & Probability Letters, Elsevier, vol. 51(4), pages 397-408, February.
    5. Li, Yongming & Yang, Shanchao & Wei, Chengdong, 2011. "Some inequalities for strong mixing random variables with applications to density estimation," Statistics & Probability Letters, Elsevier, vol. 81(2), pages 250-258, February.
    6. Masry, Elias, 2002. "Multivariate probability density estimation for associated processes: strong consistency and rates," Statistics & Probability Letters, Elsevier, vol. 58(2), pages 205-219, June.
    7. Masry, Elias, 2003. "Local polynomial fitting under association," Journal of Multivariate Analysis, Elsevier, vol. 86(2), pages 330-359, August.
    8. Guodong Xing & Shanchao Yang, 2010. "Some Exponential Inequalities for Positively Associated Random Variables and Rates of Convergence of the Strong Law of Large Numbers," Journal of Theoretical Probability, Springer, vol. 23(1), pages 169-192, March.

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