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利用测量误差选择似然进行核回归变量选择AI 解读

This paper develops a nonparametric shrinkage and selection estimator via the measurement error selection likelihood approach recently proposed by Stefanski, Wu, and White. The Measurement Error Kernel Regression Operator (MEKRO) has the same form as the Nadaraya-Watson kernel estimator, but optimizes a measurement error model selection likelihood to estimate the kernel bandwidths. Much like LASSO or COSSO solution paths, MEKRO results in solution paths depending on a tuning…

面向分位数的交互式 Q 学习AI 解读

A dynamic treatment regime is a sequence of decision rules, each of which recommends treatment based on features of patient medical history such as past treatments and outcomes. Existing methods for estimating optimal dynamic treatment regimes from data optimize the mean of a response variable. However, the mean may not always be the most appropriate summary of performance. We derive estimators of decision rules for optimizing probabilities and quantiles computed with…

加性模型的自动结构恢复AI 解读

We propose an automatic structure recovery method for additive models, based on a backfitting algorithm coupled with local polynomial smoothing, in conjunction with a new kernel-based variable selection strategy. Our method produces estimates of the set of noise predictors, the sets of predictors that contribute polynomially at different degrees up to a specified degree M, and the set of predictors that contribute beyond polynomially of degree M. We prove consistency of the…

通过两阶段广义经验似然实现高效稳健回归AI 解读

Large- and finite-sample efficiency and resistance to outliers are the key goals of robust statistics. Although often not simultaneously attainable, we develop and study a linear regression estimator that comes close. Efficiency obtains from the estimator's close connection to generalized empirical likelihood, and its favorable robustness properties are obtained by constraining the associated sum of (weighted) squared residuals. We prove maximum attainable finite-sample…

结构测量误差模型中的潜变量模型稳健性AI 解读

We present methods for diagnosing the effects of model misspecification of the true-predictor distribution in structural measurement error models. We first formulate latent-model robustness theoretically. Then we provide practical techniques for examining the adequacy of an assumed latent predictor model. The methods are illustrated via analytical examples, application to simulated data and with data from a study of coronary heart disease.

正态均值的非线性函数估计AI 解读

We derive a Monte-Carlo-amenable, minimum variance unbiased estimator of a nonlinear function of a normal mean and the variance of the estimator. Applications to problems arising in the analysis of data measured with error are described.

广义线性测量误差模型中的工具变量估计AI 解读

Instrumental variable estimation in generalized linear measurement error models are studied. For models with canonical link functions, unbiased estimating equations are derived. The maximum likelihood estimator for the normal theory, structural linear instrumental variable model is shown to be a solution to the estimating equations derived herein. Logistic regression is studied in detail. An example is given and a simulation study described for the logistic model based on…

非线性测量误差模型中 SIMEX 估计量的渐近理论AI 解读

Cook and Stefanski have described a computer-intensive method, the SIMEX method, for approximately consistent estimation in regression problems with additive measurement error. In this article we derive the asymptotic distribution of their estimators and show how to compute estimated standard errors. These standard error estimators can either be used alone or as prepivoting devices in a bootstrap analysis. We also give theoretical justification to some of the phenomena…

测量误差模型中基于反卷积的得分检验AI 解读

Consider a generalized linear model with response $Y$ and scalar predictor $X$. Instead of observing $X$, a surrogate $W = X + Z$ is observed, where $Z$ represents measurement error and is independent of $X$ and $Y$. The efficient score test for the absence of association depends on $m(w) = E(X\mid W = w)$ which is generally unknown. Assuming that the distribution of $Z$ is known, asymptotically efficient tests are constructed using nonparametric estimators of $m(w)$. Rates…

含替代预测变量模型的近似拟似然估计AI 解读

We consider quasi-likelihood estimation with estimated parameters in the variance function when some of the predictors are measured with error. We review and extend four approaches to estimation in this problem, all of them based on small measurement error approximations. A taxonomy of the data sets likely to be available in measurement error studies is developed. An asymptotic theory based on this taxonomy is obtained and includes measurement error and Berkson error models…

广义线性测量误差模型中的得分检验AI 解读

SUMMARY Hypothesis tests in generalized linear models are studied under the condition that a surrogate w is observed in place of the true predictor x. The efficient score test for the hypothesis of no association depends on the conditional expectation E(x|w) which is generally unknown. The usual test substitutes w for E(x|w) and is asymptotically valid but not efficient. We investigate two new test statistics appropriate when w = x + z where z is an independent measurement…

一般回归模型中条件无偏的有界影响估计及其广义线性模型应用AI 解读

In this article robust estimation in generalized linear models for the dependence of a response y on an explanatory variable x is studied. A subclass of the class of M estimators is defined by imposing the restriction that the score function must be conditionally unbiased, given x. Within this class of conditionally Fisher-consistent estimators, optimal bounded-influence estimators of regression parameters are identified, and their asymptotic properties are studied. The…

摘要暂缺

广义线性测量误差模型的条件得分与最优得分AI 解读

In this paper we study estimation of the parameters of generalized linear models In canonical form when the explanatory vector is measured with independent normal error.For the functional case, i.e., when the explanatory vectors are fixed constants, unbiased score functions are obtained by conditioning on certain sufficient statistics.This work generalizes results obtained by the authors (Stefanski & Carroll, 1986) for logistic regression.In the case that the explanatory…

广义线性测量误差模型的条件得分与最优得分AI 解读

This paper studies estimation in generalized linear models in canonical form when the explanatory vector is measured with independent normal error. For the functional case, i.e. when the explanatory vectors are fixed constants, unbiased score functions are obtained by conditioning on certain sufficient statistics. This work generalizes results obtained by the authors (Stefanski & Carroll, 1985) for logistic regression. In the case that the explanatory vectors are independent…

摘要暂缺

广义线性模型的最优有界得分函数及其在逻辑回归中的应用AI 解读

We study optimally bounded score functions for estimating regression parameters in a generalized linear model. Our work extends results obtained by Krasker & Welsch (1982) for the linear model and provides a simple proof of Krasker & Welsch's first-order condition for strong optimality. The application of these results to logistic regression is studied in some detail with an example given comparing the bounded-influence estimator with maximum likelihood.

Logistic 回归中的协变量测量误差AI 解读

In a logistic regression model when covariates are subject to measurement error the naive estimator, obtained by regressing on the observed covariates, is asymptotically biased. We introduce a bias-adjusted estimator and two estimators appropriate for normally distributed measurement errors -a functional maximum likelihood estimator and an estimator which exploits the consequences of sufficiency. The four proposals are studied asymptotically under conditions which are…

测量误差对参数估计的影响AI 解读

This paper presents a general formulation of the errors-in-variables problem, which encompasses both linear and nonlinear models, functional and structural cases, and dependent measurement errors. It is assumed that the parameter of interest is estimated by an M-estimator which is consistent in the absence of measurement error, and it is shown how to assess the asymptotic bias in this estimator when error is present, and how to construct an estimator with smaller bias. The…