Randomly Stopped Sequences Random Walks The Sequential Probability Ratio Test Nonlinear Renewal Theory Local Limit Theorems Open-Ended Tests Repeated Significance Tests Multiparameter Problems… Expand

Central limit theorems and invariance principles are obtained for additive functionals of a stationary ergodic Markov chain, say S n = g(X 1 ) + … + g(X n ), where E[g(X 1 )] = 0 and E[g(X 1 ) 2 ] <… Expand

For the problem of estimating a regression function, μ say, subject to shape constraints, like monotonicity or convexity, it is argued that the divergence of the maximum likelihood estimator provides… Expand

Approximations to sums of stationary and ergodic sequences by martingales are investigated. Necessary and sufficient conditions for such sums to be asymptotically normal conditionally given the past… Expand

Abstract : Three problem areas were identified and studied: nonparametric estimation with truncated data; asymptotic expansions for randomly stopped sums (with a view towards finding corrected… Expand

A sufficient condition is developed for partial sums of a function of a stationary, ergodic Markov chain to be asymptotically normal. For Bernoulli and Lebesgue shifts, the condition may be related… Expand