臺灣博碩士論文加值系統

在本文中，我們考慮兩種以 Zhou and Hwang (2005) 對多維常態分布平均值所建議之新的縮減估計式為基礎的中心重置之兩類信賴集合 C(δ_ZH) 和 C(δ_ZH^+)。首先，因為此點估計式也許對每個座標軸有不同程度的縮減，所以我們的模擬結果指出，這兩種信賴集合的涵蓋機率如何隨著母體平均值之間的差異程度不同而變動。

其次，透過更進一步大量的模擬，在我們的研究中，提出一個如何從C(δ_ZH) 和 C(δ_ZH^+) 這兩種集合中選出最適的中心重置之信賴集合的方法，因此被選出來的集合就是我們對於多維常態分布平均值所建議的信賴集合。接著，對於所建議的信賴集合以及傳統的信賴集合 C(X) 和以 James-Stein 估計式為中心的集合C(δ_JS^+)，我們探討它們涵蓋機率的比較。本研究顯示，我們所建議的信賴集合全都優於C(X)，且其涵蓋機率的改善程度會是相當顯著的。雖然對於最適的信賴集合 C(δ_ZH) 和 C(δ_JS^+) 的比較沒有得到明確的結論，但是對於從 C(δ_ZH^+) 中我們所建議的信賴集合，改善雖是微幅，實質上的確優於 C(δ_JS^+)。

In this thesis, we consider two classes of recentered confidence sets C(δ_ZH) and C(δ_ZH^+), based on the new shrinkage estimators, recently proposed by Zhou and Hwang (2005), for multivariate normal means. First of all, since the point estimators may shrink each coordinate differently, our simulated results indicate how the coverage probabilities of these two classes of confidence sets vary with the degree in differences among the population means.

Secondly, through intensive simulations, our studies suggest the way to choose the best possible recentered confidence sets from the two classes C(δ_ZH) and C(δ_ZH^+), and thus selected ones are the confidence sets we propose for the multivariate normal means. We then investigate the comparisons among the coverage probabilities of our proposed sets with that of the classical confidence set C(X) and the one centered at the positive-part James-Stein estimator C(δ_JS^+). Our studies show that our proposed confidence sets all dominate C(X), and the improvement in coverage probabilities can be quite substantial. Though, the comparison between our best possible C(δ_ZH)’s and C(δ_JS^+) are inconclusive, with a slight improvement, our proposed confidence sets from C(δ_ZH^+) do dominate C(δ_JS^+).

1 Introduction
2 Main results about C(δ_ZH)
2.1 Simulation settings
2.2 Values of a and β so that C(δ_ZH) dominates C(X)
2.3 Comparison among C(δ_ZH), C(X) and C(δ_JS^+)
3 Main results about C(δ_ZH^+)
3.1 Values of a and β so that C(δ_ZH^+) dominates C(X)
3.2 Comparison among C(δ_ZH^+), C(X) and C(δ_JS^+)
4 Conclusion

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