We consider the class of simple random walks or birth and death chains on the nonnegative integers. The set of return probabilities Pn00, n [greater-or-equal, slanted] 0, uniquely determines the spectral measure of the process. We characterize the class of simple random walks with the same...

In a recent paper González Manteiga and Vilar Fernández (1995) considered the problem of testing linearity of a regression under MA(infinity) structure of the errors using a weighted L2-distance between a parametric and a nonparametric fit. They established asymptotic normality of the...