本論文主要是探討在封閉區間中具有有界及恆正的權重函數的d次單變數多項式迴歸模型的最少點D最適設計。當d趨近於無窮大時，我們證明最少點D最適設計會弱收歛至反正弦分布。另外，我們利用D效率值將此最適設計和兩種跟反正弦分布有關的設計來做比較。最後我們也證明當設計區間為[-1,1]，權重函數1/√(α-x^2), α>1時，最少點D最適設計會收斂到D最適反正弦點設計。

Consider the minimally-supported D-optimal designs for dth degree polynomial regression with bounded and positive weight function on a compact interval. We show that the optimal design converges weakly to the arcsin distribution as d goes to infinity. Comparisons of the optimal design with the arcsin distribution and D-optimal arcsin support design by D-efficiencies are also given. We also show that if the design interval is [−1, 1], then the minimally-supported D-optimal design converges to the D-optimal arcsin support design with the specific weight function 1/√(α-x^2), α>1, as α→1+.

Abstract ii
1 Introduction 1
2 Arcsin limit theorem of d 2
3 Examples 5
4 Conclusions 11
References 12

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