For let be a strictly stationary sequence of random variables, where the X's and the Y's are -valued and -valued, respectively, for some integers p,. Let be an integrable Borel real-valued function defined on and set , . The function need not be bounded. The quantity is estimated by where is a kernel estimate for the probability density function of the X's and . If the sequence enjoys any one of the standard four kinds of mixing properties, then, under suitable additional assumptions, is strongly consistent, uniformly over compacts. Rates of convergence are also specified.
