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Jackknifing Linear Estimating Equations: Asymptotic Theory and Applications in Stochastic Processes

Subhash Lele
Journal of the Royal Statistical Society. Series B (Methodological)
Vol. 53, No. 1 (1991), pp. 253-267
Published by: Wiley for the Royal Statistical Society
Stable URL: http://www.jstor.org/stable/2345740
Page Count: 15
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Jackknifing Linear Estimating Equations: Asymptotic Theory and Applications in Stochastic Processes
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Abstract

Let (X1, X2,..., Xn) be a vector of (possibly dependent) random variables having distribution F(X, θ). Let G(X, θ) = Σni = 1gi(X, θ) = 0 be an estimating equation for θ, e.g. the score function or the maximum pseudolikelihood estimating equation in spatial processes. Let θn be the estimator obtained from G such that θn → θ0 in probability and n1/2n - θ0) → N(0, V) in distribution. In many situations, it is difficult to derive an analytical expression for V, e.g. for maximum pseudolikelihood estimators for the spatial processes. In this paper, we give a jackknife estimator of V and show that it is weakly consistent. The method consists of deleting one estimating equation (instead of one observation) at a time and thus obtaining the pseudovalues. The method of proof and conditions are similar to those of Reeds with some modifications. The method applies equally to independent and identically distributed random variables, independent but not identically distributed random variables, time- or space-dependent stochastic processes. Our conditions are less severe than Carlstein's who deals with a similar problem of estimating V for dependent observations. We also give some simulation results.

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