Kernel-type Estimation of Bivariate Distribution Function for Associated Random Variables
نویسندگان
چکیده
Let Xn, n ∈ IN, be a stationary sequence of associated random variables with uniform distribution on [0, 1] and F the distribution function of (X1, Xk+1), for fixed k ∈ IN. We introduce a kernel estimator for F and study its asymptotic properties and moments, characterizing their convergence rates. From these we derive the optimal rate for the bandwidth, which is of order n. Conditions are also given to ensure that the finite dimensional distributions are asymptotically gaussian.
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تاریخ انتشار 2005