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There have been many papers presenting kernel density estimators for a strictly stationary continuous time process observed over the time interval [O, T]. However the estimators do not satisfy the property of mean-square continuity if the process is mean-square continuous. In this paper we present a modified kernel estimator and substantiate that the modified estimator satisfies the property of mean-square continuity. At last in a simulation study the results show the modified estimator is better than the original estimator in some cases.