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半参数模型的有效与自适应估计
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.
针对半参数备择检验参数模型
This paper describes a method for testing a parametric model of the mean of a random variable Y conditional on a vector of explanatory variables X against a semiparametric alternative. The test is motivated by a conditional moment test against a parametric alternative and amounts to replacing the parametric alternative model with a semiparametric model. The resulting semiparametric test is consistent against a larger set of alternatives than are parametric conditional…
半参数估计量的渐近方差
This paper derives a general formula for the asymptotic variance of semiparametric estimators that accounts for the presence of nonparametric estimators of functions. The general formula is specialized to show invariance of the asymptotic variance to the type of nonparametric estimator and to obtain correction terms for estimation of densities and mean-square projections (including conditional expectations). Regularity conditions for the validity of the formula are also…
混合比例风险模型的效率界
The semiparametric efficiency bound of the mixed proportional hazard model is derived. The density of the model factors in such a way that there exists a complete sufficient statistic for the individual heterogeneity. The efficient score is shown to be the difference between the score in the parametric direction and its conditional expectation given the sufficient statistic. Applying this result to the single-spell Weibull mixed proportional hazard model, it is shown that…
随机前沿模型中的有效半参数估计
Abstract This article considers the semiparametric stochastic frontier model with panel data that arises in the problem of measuring technical inefficiency in production processes. We assume a parametric form for the frontier function, which is linear in production inputs. The density of the individual firm-specific effects is considered to be unknown. We construct an efficient estimator of the slope parameters in the frontier function. We also give an estimator of the level…
用二元数据测量潜在子群变化：无条件、条件与半参数极大似然估计
Changes in dichotomous data caused by treatments can be analyzed by means of the so-called linear logistic model with relaxed assumptions (LLRA). In contrast to models of the Rasch type, the LLRA allows incidental multidimensional parameters describing the response behavior of the subjects so that each observable criterion used for assessing the changes is governed by its own subject parameter. Because generalizability of the treatment effects over subjects and criteria is…
在干扰参数置信集合上最大化的 p 值
For testing problems of the form H 0: v = v 0 with unknown nuisance parameter θ, various methods are used to deal with θ. The simplest approach is exemplified by the t test where the unknown variance is replaced by the sample variance and the t distribution accounts for estimation of the variance. In other problems, such as the 2 × 2 contingency table, one conditions on a sufficient statistic for 0 and proceeds as in Fisher's exact test. Because neither of these standard…
部分回归变量并非始终可观测时的回归系数估计
In applied problems it is common to specify a model for the conditional mean of a response given a set of regressors. A subset of the regressors may be missing for some study subjects either by design or happenstance. In this article we propose a new class of semiparametric estimators, based on inverse probability weighted estimating equations, that are consistent for parameter vector α0 of the conditional mean model when the data are missing at random in the sense of Rubin…
利用二元数据测量潜在亚组的变化：三类极大似然估计
Changes in dichotomous data caused by treatments can be analyzed by means of the so-called linear logistic model with relaxed assumptions (LLRA). In contrast to models of the Rasch type, the LLRA allows incidental multidimensional parameters describing the response behavior of the subjects so that each observable criterion used for assessing the changes is governed by its own subject parameter. Because generalizability of the treatment effects over subjects and criteria is…
半参数模型中的拟似然估计
Suppose the expected value of a response variable Y may be written h(Xβ +γ(T)) where X and T are covariates, each of which may be vector-valued, β is an unknown parameter vector, γ is an unknown smooth function, and h is a known function. In this article, we outline a method for estimating the parameter β, γ of this type of semiparametric model using a quasi-likelihood function. Algorithms for computing the estimates are given and the asymptotic distribution theory for the…
基于枢轴估计函数的重抽样方法
Suppose that, under a semiparametric model setting, one is interested in drawing inferences about a finite-dimensional parameter vector β based on an estimating function. Generally a consistent point estimator β^ for βo, the true value for β, can be easily obtained by finding a root of the corresponding estimating equation. To estimate the variance of β^, however, may involve complicated and subjective nonparametric functional estimates. In this paper, a general and simple…
广义半参数回归估计量分析中的 U 过程
We prove -consistency and asymptotic normality of a generalized semiparametric regression estimator that includes as special cases Ichimura's semiparametric least-squares estimator for single index models, and the estimator of Klein and Spady for the binary choice regression model. Two function expansions reveal a type of U-process structure in the criterion function; then new U-process maximal inequalities are applied to establish the requisite stochastic equicontinuity…
非嵌套计量模型的半参数设定检验
We propose a specification test of a parametrically specified nonlinear model against a weakly specified non-nested alternative. We estimate the alternative model by using nonparametric regression (nearest neighbours). The test is based on the t-statistic of an artificial regression. Monte-Carlo simulations suggest that the test has good power and size characteristics.
调制更新过程的半参数推断
Modulated renewal processes, suggested by D. R. Cox, give a flexible way to introduce dependencies into point processes. We discuss the asymptotics of partial likelihood inference for modulated renewal processes when the random covariate for the process involves its history. We show, in some generality, that the estimators of the regression parameter and the cumulative hazard have the same asymptotic distributions that they would have under the usual proportional hazards…
加性风险模型的半参数分析
In contrast to the proportional hazards model, the additive risk model specifies that the hazard function associated with a set of possibly time-varying covariates is the sum of, rather than the product of, the baseline hazard function and the regression function of covariates. This formulation describes a different aspect of the association between covariates and the failure time than the proportional hazards model, and is more plausible than the latter for many…
长记忆时间序列的半参数分析
We study problems of semiparametric statistical inference connected with long-memory covariance stationary time series, having spectrum which varies regularly at the origin: There is an unknown self-similarity parameter, but elsewhere the spectrum satisfies no parametric or smoothness conditions, it need not be in $L_p$, for any $p > 1$, and in some circumstances the slowly varying factor can be of unknown form. The basic statistic of interest is the discretely averaged…
退化U过程的最大不等式及其在优化估计中的应用
Maximal inequalities for degenerate $U$-processes of order $k, k \geq 1$, are established. The results rest on a moment inequality (due to Bonami) for $k$th-order forms and on extensions of chaining and symmetrization inequalities from the theory of empirical processes. Rates of uniform convergence are obtained. The maximal inequalities can be used to determine the limiting distribution of estimators that optimize criterion functions having $U$-process structure. As an…
回归泛函的级数估计
Two-step estimators, where the first step is the predicted value from a nonparametric regression, are useful in many contexts. Examples include a non-parametric residual variance, probit with nonparametric generated regressors, efficient GMM estimation with randomly missing data, heteroskedasticity corrected least squares, semiparametric regression, and efficient nonlinear instrumental variables estimators. The purpose of this paper is the development of consistency and…