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转移原理：完整案例分析的工具AI 解读

This paper gives a general method for deriving limiting distributions of complete case statistics for missing data models from corresponding results for the model where all data are observed. This provides a convenient tool for obtaining the asymptotic behavior of complete case versions of established full data methods without lengthy proofs. The methodology is illustrated by analyzing three inference procedures for partially linear regression models with responses missing…

弱依赖可逆线性过程的一致根号样本量收敛密度估计AI 解读

Convergence rates of kernel density estimators for stationary time series are well studied. For invertible linear processes, we construct a new density estimator that converges, in the supremum norm, at the better, parametric, rate n−1/2. Our estimator is a convolution of two different residual-based kernel estimators. We obtain in particular convergence rates for such residual-based kernel estimators; these results are of independent interest.

线性与非线性自回归模型的有效预测AI 解读

Conditional expectations given past observations in stationary time series are usually estimated directly by kernel estimators, or by plugging in kernel estimators for transition densities. We show that, for linear and nonlinear autoregressive models driven by independent innovations, appropriate smoothed and weighted von Mises statistics of residuals estimate conditional expectations at better parametric rates and are asymptotically efficient. The proof is based on a…

用U统计量估计线性过程的平稳分布泛函AI 解读

Suppose we observe an invertible linear process with independent mean-zero innovations and with coefficients depending on a finite-dimensional parameter, and we want to estimate the expectation of some function under the stationary distribution of the process. The usual estimator would be the empirical estimator. It can be improved using the fact that the innovations are centered. We construct an even better estimator using the representation of the observations as…

随机系数自回归模型中的自适应估计AI 解读

This paper proves the local asymptotic normality of a stationary and ergodic first order random coefficient autoregressive model in a semiparametric setting. This result is used to show that Stein's necessary condition for adaptive estimation of the mean of the random coefficient is satisfied if the distributions of the innovations and the errors in the random coefficients are symmetric around zero. Under these symmetry assumptions, a locally asymptotically minimax adaptive…

参数与半参数模型中的渐近一致最强检验AI 解读

Tests of hypotheses about finite-dimensional parameters in a semiparametric model are studied from Pitman's moving alternative (or local) approach using Le Cam's local asymptotic normality concept. For the case of a real parameter being tested, asymptotically uniformly most powerful (AUMP) tests are characterized for one-sided hypotheses, and AUMP unbiased tests for two-sided ones. An asymptotic invariance principle is introduced for multidimensional hypotheses, and AUMP…

摘要暂缺

半参数模型的有效与自适应估计AI 解读

Introduction.- Asymptotic Inference for (Finite-Dimensional) Parametric Models.- Information Bounds for Euclidean Parameters in Infinite-Dimensional Models.- Euclidean Parameters: Further Examples.- Information Bounds for Infinite-Dimensional Parameters.- Infinite-Dimensional Parameters: Further Examples: Construction of Examples.

回归模型中的有效估计AI 解读

In this paper we consider the regression model with smooth regression function and smooth error and covariate distributions. We study how well one can estimate functionals of the regression function which may also depend on the distribution of the covariate. This is done by deriving the efficient influence functions of least dispersed regular estimators of such functionals under various assumptions on the parameters of our model. Then we demonstrate how efficient estimates…

半参数模型中的渐近有效估计AI 解读

A general method for the construction of asymptotically efficient estimates in semiparametric models is presented. It improves and modifies Bickel's (1982) construction of adaptive estimates and obtains asymptotically efficient estimates under conditions weaker than those in Bickel.