Lp convergence of reciprocals of sample means with applications to sequential estimation in linear regression

Let {Z(n); n greater than or equal to 1} be a stationary sequence of non-negative random variables with finite first moment. It is known that the sample average (Z) over bar(n) converges to a random variable Z with probability one. In this paper we have two objectives: First, we obtain a necessary and sufficient condition for the L-p(p > 0) convergence of (Z) over bar(n)(-1) to Z(-1). Second, we use this result in the sequential point estimation of the slope parameter in a linear regression model under relative squared error loss. We establish first and second order properties of the stopping times and the sequential procedures involved here. (C) 1997 Elsevier Science B.V.