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Asymptotic Normality of the Estimated Variance for Polynomial Spline Regression with Unknown Knots and AR(1) Errors

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Journal of National Cheng-Kung University, Vol. 25, Sci. & Med. Section pp. 233-248(1990)

Asymptotic Normality of the Estimated

Variance for Polynomial Spline

Regression with Unknown

Knots and AR(l) Errors

Shih-Huang Chan

Abstract

We examined the asymptotic behavior for the maximum likelihood estimator of the variance of the ·pure error for polynomial spline regression with unknown knots and first-order autoregressive errors. We showed that the asymptotic distribution of the estimated variance is normal under some mild conditions. The asymptotic normality is not affected by whether or not the autoregressive coefficient of two consecutive errors is known.

Keywords: Splines, Pseudo-problem, ~D.-consistency, Asymptotic distribution, Equal in distribution.

Department of Statistics

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