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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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]0urnal of National Cheng-Kung University, Vol. 25, Sci. & Med. Section pp. 233-248(1990)