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題 名 | 在節點二階微分不連續之多項樣條迴歸模型估計量的標準誤及其分配=Standard Errors and Distributional Properties for Polynomial Spline Regression with Discontinuous Second Derivative at the Knot Point |
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作 者 | 詹世煌; 黃春美; | 書刊名 | 中國統計學報 |
卷 期 | 35:3 1997.09[民86.09] |
頁 次 | 頁207-225 |
分類號 | 319.5 |
關鍵詞 | 大樣本理論; 靴環法; 模擬; 無母數靴環法; Asymptotic theroy; Bootstrap method; Simulation; Nonparametric bootstrap; |
語 文 | 中文(Chinese) |
中文摘要 | 本文探討在節點一階微分連續但二階微分不連續的多項樣條迴歸分析上可能發 生的一些問題,包括自變數尺度對標準誤的影響,大樣本估計標準誤的不精確及因而導致 信賴區間的不可靠,和估計量分配的常態性等。我們利用靴環法來解決這些問題。利用靴 環法,我們發現多項樣條迴歸係數和節點的估計量在常態誤差下,即使在n不大時亦接近 常態。此點基本上支持Gallant(1974)所認為當n大時迴歸係數和節點的估計量有漸近常庇 的結果;但與Feder(1975)宣稱即使在n大時亦不近似常態的理論符。經由模擬我們亦驗證 得此等靴環法結果。在標準誤和信賴區上,其由靴環法所得者較大樣本所得者為精確,此 支持前人的發現;惟在靴環法分析時,應注意樣本是否有充分的代表性。此外,經由與模 擬所得結果的比較,我們發現無母數靴環法有低估標準誤的現象,惟是否真的如此有待進 一步的探討。 |
英文摘要 | The problems investigated in this paper include effects of covariate scale on standard errors, inaccurate asymptotic standard errors. and normality of the regression estimators when applying polynomial spline regression with continuous first, but not second derivatives at the knot point are investigated. Bootstrap methods are suggested to solve these problems. Using the bootstrap approach we find that under the normal error assumption, the distributions of regression coefficients and the knot point estimates are close to normal even when the sample size n is small. These findings basically support. Gallant's (1974) normality argument, but contradict to Feder's (1975), who proved that the asymptotic distributions of the estimated regression coefficients and knot point are not normal. In the estimation of the standard errors and confidence intervals, the boot- strap results are more reliable than those obtained by the large sample theory. These support previous findings. We urge, however, that the sample on which bootstrap methods are based should be a typical sample from the studied population, otherwise bias will be introduced. Besides, we find that the standard errors may be underestimated if the nonparametric bootstrap mehtod is used. Whether this is true needs further study, however. |
本系統中英文摘要資訊取自各篇刊載內容。