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Abstract
Suppose Tukey's 3R (“running median”) smoothing algorithm is applied to a strictly stationary sequence X: = (Xk) of random variables, thereby creating a new stationary sequence Xœ If X satisfies the strong (Rosenblatt) mixing condition, then so does .Xœ If X is an i.i.d. sequence with each X(k:) uniformly distributed on the interval [0,1], then Xœ fails to be (mixing. Thus two questions of C. Mallows are answered.
†This work was partially supported by NSF grant MCS 81-01583
†This work was partially supported by NSF grant MCS 81-01583
Notes
†This work was partially supported by NSF grant MCS 81-01583