ESTIMATION OF THE DISTRIBUTION FUNCTION FOR STATIONARY RANDOM FIELDS OF ASSOCIATED PROCESSES

• Published : 2004.01.01
• 41 13

Abstract

For a stationary field $\{X_{\b{j}},\b{j}{\;}\in{\;}{\mathbb{Z}}^d_{+}\}$ of associated random variables with distribution function $F(x)\;=\;P(X_{\b{1}}\;{\leq}\;x)$ 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

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