Abstract
ABSTRACTIn this paper, we mainly study the Berry-Esseen type bounds of estimators in a semiparametric model , where β is an unknown parameter, are nonrandom design points, are the response variables, is an unknown function designed on the closed interval , and the errors are formed by with and are α-mixing random variables. Under appropriate conditions, the Berry-Esseen type bounds for estimators of β and can attain nearly and , respectively, and under further restriction for the weights, the Berry-Esseen type bound for estimator of can also achieve nearly . A numerical simulation is also carried out to verify the validity of the theoretical results.
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