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双重抽样设计下回归分析的统一方法AI 解读

Summary We propose a unified approach to the estimation of regression parameters under double-sampling designs, in which a primary sample consisting of data on the rough or proxy measures for the response and/or explanatory variables as well as a validation subsample consisting of data on the exact measurements are available. We assume that the validation sample is a simple random subsample from the primary sample. Our proposal utilizes a specific parametric model to extract…

半参数广义线性模型中的渐近有效估计AI 解读

We use the method of maximum likelihood and regression splines to derive estimates of the parametric and nonparametric components of semiparametric generalized linear models. The resulting estimators of both components are shown to be consistent. Also, the asymptotic theory for the estimator of the parametric component is derived, indicating that the parametric component can be estimated efficiently without under-smoothing the nonparametric component.

部分线性模型的数据驱动有效估计量AI 解读

Chen and Shiau showed that a two-stage spline smoothing method and the partial regression method lead to efficient estimators for the parametric component of a partially linear model when the smoothing parameter is a deterministic sequence tending to zero at an appropriate rate. This paper is concerned with the large-sample behavior of these estimators when the smoothing parameter is chosen by the generalized cross validation (GCV) method or Mallows' $C_L$. Under mild…

投影寻踪型回归模型的估计AI 解读

Since the pioneering work of Friedman and Stuetzle in 1981, projection-pursuit algorithms have attracted increasing attention. This is mainly due to their potential for overcoming or reducing difficulties arising in nonparametric regression models associated with the so-called curse of dimensionality, that is, the amount of data required to avoid an unacceptably large variance increasing rapidly with dimensionality. Subsequent work has, however, uncovered a dependence on…

部分线性模型中参数分量的收敛速度AI 解读

Consider the regression model $Y_i = X'_i\beta + g(t_i) + e_i$ for $i = 1, \cdots, n$. Here $g$ is an unknown Holder continuous function of known order $p$ in $R, \beta$ is a $k \times 1$ parameter vector to be estimated and $e_i$ is an unobserved disturbance. Such a model is often encountered in situations in which there is little real knowledge about the nature of $g$. A piecewise polynomial $g_n$ is proposed to approximate $g$. The least-squares estimator $\hat\beta$ is…