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估计函数的正交性与干扰参数AI 解读

Cox & Reid (1987) proposed the technique of orthogonalizing parameters, to deal with the general problem of nuisance parameters, within fully parametric models. They obtained a large-sample approximation to the conditional likelihood. Along the same lines Davison (1988) studied generalized linear models. In the present paper we deal with the problem of nuisance parameters, within a semiparametric setup which includes the class of distributions associated with generalized…

面向 Lp 损失函数的非线性随机逼近程序AI 解读

The classical stochastic approximation problem can be regarded as choosing design points so that the responses are close to some target level in the expected squared distance. Motivated by different loss criteria, a family of stochastic approximation algorithms is proposed. This family has the same simplicity as the classical Robbins-Monro procedure does and contains the latter as a special case. Using appropriate representations and martingale limit theorems, we establish…

工资收入与生育时点及间隔：瑞典纵向数据证据AI 解读

This paper considers the formulation, estimation, and evaluation of semiparametric multistates duration models with time-varying regressors and unobservables correlated over spells. The authors' models are applied to test a dynamic version of the neoclassical theory of fertility. Using Swedish data, they find that rising female wages over the lifecycle delay times to all conceptions, but barely affect childlessness. The authors estimate a model that predicts fertility…

基于贝塔过程的生命历程数据非参数贝叶斯估计AI 解读

Several authors have constructed nonparametric Bayes estimators for a cumulative distribution function based on (possibly right-censored) data. The prior distributions have, for example, been Dirichlet processes or, more generally, processes neutral to the right. The present article studies the related problem of finding Bayes estimators for cumulative hazard rates and related quantities, w.r.t. prior distributions that correspond to cumulative hazard rate processes with…

带置信集合的密度估计：星系超星系团与空洞示例AI 解读

A method is presented for forming both a point estimate and a confidence set of semiparametric densities. The final product is a three-dimensional figure that displays a selection of density estimates for a plausible range of smoothing parameters. The boundaries of the smoothing parameter are determined by a nonparametric goodness-of-fit test that is based on the sample spacings. For each value of the smoothing parameter our estimator is selected by choosing the normal…

簇相关数据半参数广义线性模型的回归参数检验AI 解读

Generalized and ‘working’ Wald and score tests for regression coefficients in the class of semiparametric marginal generalized linear models for cluster correlated data (Liang & Zeger, 1986) are proposed, and their asymptotic distribution examined. In addition, the asymptotic distribution of the naive likelihood ratio test, or deviance difference, is presented. Following Rao & Scott (1984), we propose simple adjustments to such ‘working’ tests. The asymptotic distributions…

非参数与半参数模型中信息界的可达性AI 解读

We consider in this paper two widely studied examples of nonparametric and semiparametric models in which the standard information bounds are totally misleading. In fact, no estimators converge at the $n^{-\alpha}$ rate for any $\alpha > 0$, although the information is strictly positive "promising" that $n^{-1/2}$ is achievable. The examples are the estimation of $\int p^2$ and the slope in the model of Engle et al. A class of models in which the parameter of interest can be…

删失线性回归半参数估计中的带宽选择AI 解读

Quantile and semiparametric M estimation are methods for estimating a censored linear regression model without assuming that the distribution of the random component of the model belongs to a known parametric family. Both methods require estimating derivatives of the unknown cumulative distribution function of the random component. The derivatives can be estimated consistently using kernel estimators in the case of quantile estimation and finite difference quotients in the…

半参数效率界AI 解读

Abstract Semiparametric models are those where the functional form of some components is unknown. Efficiency bounds are of fundamental importance for such models. They provide a guide to estimation methods and give an asymptotic efficiency standard. The purpose of this paper is to provide an introduction to research methods and problems for semiparametric efficiency bounds. The nature of the bounds is discussed, as well as ways of calculating them. Their uses in solving…

失效类型缺失时竞争风险的修正对数秩检验AI 解读

We propose a modified log rank test for the analysis of competing risks survival data, when failure type is missing for some individuals. The proposed test reduces to a standard log rank test when all failure types are known. The test arises from a partial likelihood, constructed under semiparametric assumptions on the relationship between cause-specific hazards.

多项式—三角回归的曲线拟合AI 解读

We consider a method of estimating an unknown regression curve by regression on a combination of low-order polynomial terms and trigonometric terms. Estimation based on trigonometric functions alone is known to suffer from bias problems at the boundaries due to the periodic nature of the fitted functions. We show that these boundary problems are alleviated by adding low-order polynomial terms. The utility of the method is illustrated with examples, and asymptotic results…

删失数据线性回归模型中的估计AI 解读

We consider the semiparametric linear regression model with censored data and with unknown error distribution. We describe estimation equations of the Buckley-James type that admit $\sqrt n$-consistent and asymptotically normal solutions. The derived estimator is efficient at a particular error distribution. We show the equivalence between this type of estimator and an estimator based on a linear rank test suggested by Tsiatis. This equivalence is an extension of a basic…

回归曲线的半参数比较AI 解读

The comparison of nonparametric regression curves is considered. It is assumed that there are parametric (possibly nonlinear) transformations of the axes which map one curve into the other. Estimation and testing of the parameters in the transformations are studied. The rate of convergence is $n^{-1/2}$ although the nonparametric components of the model typically have a rate slower than that. A statistic is provided for testing the validity of a given completely parametric…

失效类型缺失时竞争风险数据的修正对数秩检验AI 解读

We propose a modified log rank test for the analysis of competing risks survival data, when failure type is missing for some individuals. The proposed test reduces to a standard log rank test when all failure types are known. The test arises from a partial likelihood, constructed under semiparametric assumptions on the relationship between cause-specific hazards.

具有单位根和无限方差误差的时间序列回归AI 解读

In [4] Chan and Tran give the limit theory for the least-squares coefficient in a random walk with i.i.d. (identically and independently distributed) errors that are in the domain of attraction of a stable law. This paper discusses their results and provides generalizations to the case of I (1) processes with weakly dependent errors whose distributions are in the domain of attraction of a stable law. General unit root tests are also studied. It is shown that the…

This paper studies the asymptotic properties of instrumental variable (IV) estimates of multivariate cointegrating regressions and allows for deterministic and stochastic regressors as well as quite general deterministic processes in the data-generating mechanism. It is found that IV regressions are consistent even when the instruments are stochastically independent of the regressors. This phenomenon, which contrasts with traditional theory for stationary time series, is a…

组内相关数据半参数广义线性模型的回归参数检验AI 解读

Generalized and ‘working’ Wald and score tests for regression coefficients in the class of semiparametric marginal generalized linear models for cluster correlated data (Liang & Zeger, 1986) are proposed, and their asymptotic distribution examined. In addition, the asymptotic distribution of the naive likelihood ratio test, or deviance difference, is presented. Following Rao & Scott (1984), we propose simple adjustments to such ‘working’ tests. The asymptotic distributions…

关于剩余寿命的一则札记AI 解读

Two further characterizations are given of a family of survival distributions introduced by Hall & Wellner (1984). The second result involves a new family of semiparametric models requiring proportional mean residual life.

关于自然死亡率半参数估计量的一则说明AI 解读

A semiparametric estimator of natural mortality, introduced by Hearn, Sandland & Hampton (1987), was studied by Leigh (1988), who noted that its asymptotic variance may sometimes be infinite. We discuss the nonnorrnal asymptotic behaviour that can occur in this case, and remark on difficulties that it causes in practice.

删失回归模型的设定检验：参数与半参数方法AI 解读

We define a hierarchy of parametric and semiparametric specifications for censored regression models that is ordered according to the strength of the assumptions that are made. We review the estimation techniques and specification tests that are available at each level of the hierarchy. The estimation and testing procedures are illustrated by applying them to a model of strike duration. Several tests (some graphical) are able to detect errors in standard parametric…

指标模型系数的半参数估计AI 解读

This paper gives a solution to the problem of estimating coefficients of index models, through the estimation of the density-weighted average derivative of a general regression function. A normalized version of the density-weighted average derivative can be estimated by certain linear instrumental variables coefficients. The estimators, based on sample analogies of the product moment representation of the average derivative, are constructed using nonparametric kernel…

计量时间序列半参数与非参数模型的假设检验AI 解读

A restriction on a semiparametric or nonparametric econometric time series model determines the value of a finite-dimensional functional τ of an infinite-dimensional nuisance function. The estimate of τ and its estimated covariance matrix use nonparametric probability and spectral density estimation. A consequent test of the restriction is given approximate large sample justification under absolute regularity on the time series and other conditions. The methodology relates…

半参数 Tobit 估计量的蒙特卡洛比较AI 解读

Abstract This paper focuses on a performance comparison of semiparametric Tobit estimators. Firstly, a conditional expectation version of Horowitz's distribution‐free least‐squares estimator is proposed, together with a short description of the other estimators considered in the later Monte Carlo experiment. Then, a performance comparison of the following selected estimators is made through a Monte Carlo experiment: the standard Tobit maximum‐likelihood estimator, the…

随机截断数据的半参数模型AI 解读

For randomly censored data, it is known that the maximum likelihood estimate (MLE) of the survival curve is not affected by parametric assumption on the censoring variable. The Kaplan-Meier (1958) estimate is the MLE for both nonparametric and semiparametric models. For randomly truncated data, the truncation product-limit estimate is the MLE for nonparametric models. This is not the case if the truncation mechanism is parameterized, however. Specifically, let X be a generic…