CAJ | 학술논문

部分线性模型也就是响应变量关于一个或者多个协变量是线性的,但对于其他的协变量是非线性的关系.对于部分线性模型中的参数和非参数部分的估计方法,惩罚最小二乘估计是重要的估计方法之一.对于这种估计方法,广义交叉验证法提供了一种确定光滑参数的方法.但是,在部分线性模型中,用广义交叉验证法确定光滑参数的最优性还没有被证明.本文证明了利用惩罚最小二乘估计对于部分线性模型估计时,用广义交叉验证法选择光滑参数的最优性.通过模拟验证了本文中所提出的用广义交叉验证法选择光滑参数具有很好的效果,同时,本文在模拟部分比较了广义交叉验证和最小二乘交叉验证的优劣.
부분선성모형야취시향응변량관우일개혹자다개협변량시선성적,단대우기타적협변량시비선성적관계.대우부분선성모형중적삼수화비삼수부분적고계방법,징벌최소이승고계시중요적고계방법지일.대우저충고계방법,엄의교차험증법제공료일충학정광활삼수적방법.단시,재부분선성모형중,용엄의교차험증법학정광활삼수적최우성환몰유피증명.본문증명료이용징벌최소이승고계대우부분선성모형고계시,용엄의교차험증법선택광활삼수적최우성.통과모의험증료본문중소제출적용엄의교차험증법선택광활삼수구유흔호적효과,동시,본문재모의부분비교료엄의교차험증화최소이승교차험증적우렬.
Partially linear models are assumed to be linearly related to one or more variable, but the relation to an additional variable or variables is not assumed to be easily parameterized. One primary approach to estimate the parameter and nonparametric part is the method of penalized least squares method, generalized cross-validation (GCV) approach is a popular method for selecting the smoothing parameters. However, the optimality of GCV in the partial linear model with penalized least squares has not been proved. In this article, we provide the support for using GCV through its optimality of the smoothing parameter. Simulation studies are employed to investigate the empirical performance of generalized cross-validation and that of cross-validation for comparison in the context.