On local linear regression for strongly mixing random fields

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Abstract

We investigate the local linear kernel estimator of the regression function g of a stationary and strongly mixing real random field observed over a general subset of the lattice Zd. Assuming that g is differentiable with derivative g, we provide a new criterion on the mixing coefficients for the consistency and the asymptotic normality of the estimators of g and g under mild conditions on the bandwidth parameter. Our results improve the work of Hallin et al. (2004) in several directions.

AMS 2000 subject classifications

62G05
60J25
62G07

Keywords

Local linear regression estimation
Strong mixing
Random fields
Asymptotic normality

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