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

高孝先

指導教授 ： 黃禮珊

國立清華大學/理學院/統計學研究所/碩士(2012年)

https://doi.org/10.6843/NTHU.2012.00443

摘要

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.

關鍵字

樣本數計算 ； 無母數迴歸 ； 部分線性模型

參考文獻

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

[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.