簡易檢索 / 詳目顯示

回結果列表
研究生： 高孝先
論文名稱： 無母數迴歸與部分線性模型的樣本數計算
On Sample Size for Nonparametric Regression and Partial Linear Models
指導教授： 黃禮珊
口試委員: 黃禮珊
鄭又仁
謝叔蓉
學位類別： 碩士
Master
系所名稱： 理學院 - 統計學研究所
Institute of Statistics
論文出版年： 2012
畢業學年度： 100
語文別： 英文
論文頁數： 53
中文關鍵詞： 樣本數計算 、無母數迴歸 、部分線性模型
相關次數： 點閱：3  下載：0 
分享至:
查詢本校圖書館目錄 查詢臺灣博碩士論文知識加值系統 勘誤回報

    • Non- and semi-parametric regression models have received considerable
    attention in statistics with a wide range of applications. However, to our
    knowledge, sample size calculations for non- and sem-iparametric models have
    not been discussed in the literature. This paper examines the sample size
    required for a curve estimated by local polynomial regression to achieve
    significance based on the F-tests investigated in Huang and Chen (2008) for
    univariate nonparametric regression and in Huang and Davidson (2010) for
    partial linear models. We describe explicit procedures for power/sample size
    calculation based on these two tests. Two real-data examples are provided to
    demonstrate the use of the procedures. Simulation results indicate that the
    proposed methods are conservative and the empirical power is often larger
    than the desired power.

    1 Introduction 1 2 Review of sample size calculations in linear models 4 3 Assessing E ect Size of Linear Models 9 3.1 Estimating e ect size in practice . . . . . . . . . . . . . . . . . 9 3.2 Approximately linear sample sizes . . . . . . . . . . . . . . . . 10 3.3 Sample size Tables . . . . . . . . . . . . . . . . . . . . . . . . 14 4 Nonparametric ANOVA F-tests 31 4.1 Analysis of variance and F-test for local linear regression . . . 31 4.2 Analysis of variance and F-test for partial linear models . . . 34 5 Nonparametric sample size determination: methods and nu- merical results 37 5.1 Methodology for nonparametric regression . . . . . . . . . . . 37 5.2 Examples for local linear regression . . . . . . . . . . . . . . . 39 5.3 Methodology for partial linear models . . . . . . . . . . . . . . 42 5.4 Examples for partial linear models . . . . . . . . . . . . . . . . 43 6 Discussion 51

    [1] Bowman, A.W. and Azzalini, A. (1997), Applied Smoothing Techniques for Data Analysis, Oxford, London.

    [2] Cohen, J. (1988), Statistical Power Analysis for the Behavioral Sciences, Academic Press.

    [3] Fan, J., and Gijbels, I. (1996), Local Polynomial Modelling and Its Applications, London: Chapman and Hall.

    [4] Green, P. J., and Silverman, B.W. (1994), Nonparametric Regression and Generalized Linear Models: A Roughness Penalty Approach, London: Chapman & Hall.

    [5] Huang, L.-S., and Chen, J. (2008), ``Analysis of Variance, Coefficient of Determination, and F-test for Local Polynomial Regression,'' Annals of Statistics, 36, 2085-2109.

    [6] Huang, L.-S. and Davidson, P.W. (2010), ``Analysis of Variance and F-Tests for Partial Linear Models with Applications to Environmental Health Data,'' Journal of the American Statistical Association, 105:491, 991-1004.

    [7] Horton, R. L. (1978), The General Linear Model: Data Analysis in the Social and Behavioral Sciences, London ; New York : McGraw-Hill.

    [8] H\"{a}rdle,W., Liang, H., and Gao, J. (2000), Partially Linear Models, Heidelberg: Physica-Verlag.

    [9] Opsomer, J. D., and Ruppert, D. (1999),
    ``A Root-n Consistent Backfitting Estimator for Semiparametric Additive Modeling,'' Journal of Computational and Graphical Statistics, 8, 715-732.

    [10] Speckman, P. (1988), ``Kernel Smoothing in Partial Linear Models,'' Journal of the Royal Statistical Society, Ser.B, 50, 413-436.

    無法下載圖示 全文公開日期 本全文未授權公開 (校內網路)
    全文公開日期 本全文未授權公開 (校外網路)

    QR CODE