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math.ST2006★ 1 cited
Nonlinear renewal theorems for random walks with perturbations of intermediate order
Keiji Nagai, Cun-Hui Zhang
We develop nonlinear renewal theorems for a perturbed random walk without assuming stochastic boundedness of centered perturbation terms. A second order expansion of the expected s…
math.ST2006★ 43 cited
Estimation of sums of random variables: Examples and information bounds
Cun-Hui Zhang
This paper concerns the estimation of sums of functions of observable and unobservable variables. Lower bounds for the asymptotic variance and a convolution theorem are derived in…