Estimation of the distribution function for stationary random fields of associated processes
Commun. Korean Math. Soc. 2004 Vol. 19, No. 1, 169-177
Printed March 1, 2004
Tae-Sung Kim, Mi-Hwa Ko, Yeon-Sun Yoo
WonKwang University, Seoul National University, WonKwang University
Abstract : For a stationary field $\{X_{\underline{j}} , \underline{j} \in \mathbb{Z}_+^d \}$ of associated random variables with distribution function $ {F}(x) =P(X_{\underline{1}} \le x)$ we study strong consistency and asymptotic normality of the empirical distribution function, which is proposed as an estimator for ${F} (x)$. We also consider strong consistency and asymptotic normality of the empirical survival function by applying these results.
Keywords : empirical distribution function, associated, random field, asymptotic normality, estimator, survival function
MSC numbers : 60F05
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