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测量误差回归模型中最小二乘估计的极限分布AI 解读

It is well-known that the ordinary least squares (OLS) estimator $\hat{\beta}$ of the slope and intercept parameters $\beta$ in a linear regression model with errors of measurement for some of the independent variables (predictors) is inconsistent. However, Gallo (1982) has shown that certain linear combinations of $\beta$. In this paper, it is shown that under reasonable regularity conditions such linear combinations of $\hat{\beta}$ are (jointly) asymptotically normally…

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…

最小二乘与误差变量回归的比较：聚焦随机化协方差分析AI 解读

In an errors-in-variables regression model, the least squares estimate is generally inconsistent for the complete regression parameter but can be consistent for certain linear combinations of this parameter. We explore the conjecture that, when the least squares estimate is consistent for a linear combination of the regression parameter, it will be preferred to an errors-in-variables estimate, at least asymptotically. The conjecture is false, in general, but it is true for…

关于二项分布中试验次数 N 估计量的说明AI 解读

Consider k success counts from a binomial distribution with unknown N and success probability p. We examine the problem of estimating N. By integrating the likelihood for N and p over a beta density for p, we obtain the beta-binomial distribution resulting in stable and reasonably efficient estimators of N, which compare favorably with and are often better than the estimates introduced by Olkin et al. (1981).

摘要暂缺

理论模型拟合中的幂变换AI 解读

We investigate power transformations in nonlinear regression problems when there is a physical model for the response but little understanding of the underlying error structure. In such circumstances, and unlike the ordinary power transformation model, both the response and the model must be transformed simultaneously and in the same way. We show by an asymptotic theory and a small Monte Carlo study that for estimating the model parameters there is little cost for not…

二元回归模型中的变量测量误差AI 解读

We consider binary regression models when some of the predictors are measured with error. For normal measurement errors, structural maximum likelihood estimates are considered. We show that if the measurement error is large, the usual estimate of the probability of the event in question can be substantially in error, especially for high risk groups. In the situation of large measurement error, we investigate a conditional maximum likelihood estimator and its properties.

二元回归模型中的变量测量误差AI 解读

We consider binary regression models when some of the predictors are measured with error. For normal measurement errors, structural maximum likelihood estimates are considered. We show that if the measurement error is large, the usual estimate of the probability of the event in question can be substantially in error, especially for high risk groups. In the situation of large measurement error, we investigate a conditional maximum likelihood estimator and its properties.

线性模型中的异方差自适应估计AI 解读

In a heteroscedastic linear model, it is known that if the variances are a parametric function of the design, then one can construct an estimate of the regression parameter which is asymptotically equivalent to the weighted least squares estimate with known variances. We show that the same is true when the only thing known about the variances is that they are determined by an unknown but smooth function of the design or the mean response.

异方差线性模型中的稳健估计AI 解读

We consider a heteroscedastic linear model in which the variances are given by a parametric function of the mean responses and a parameter $\theta$. We propose robust estimates for the regression parameter $\beta$ and show that, as long as a reasonable starting estimate of $\theta$ is available, our estimates of $\beta$ are asymptotically equivalent to the natural estimate obtained with known variances. A particular method for estimating $\theta$ is proposed and shown by…

异方差的稳健检验AI 解读

We extend Bickel's tests for heteroscedasticity to include wider classes of test statistics and fitting methods. The test statistics include those based on Huber's function, while the fitting techniques include Huber's Proposal 2 for robust regression.

线性模型中的修剪最小二乘估计AI 解读

We consider two methods of defining a regression analog to a trimmed mean. The first was suggested by Koenker and Bassett and uses their concept of regression quantiles. Its asymptotic behavior is completely analogous to that of a trimmed mean. The second method uses residuals from a preliminary estimator. Its asymptotic behavior depends heavily on the preliminary estimate; it behaves, in general, quite differently than the estimator proposed by Koenker and Bassett, and it…

检验近似正态化变换的稳健方法AI 解读

Summary We propose a competitor to likelihood and significance methods for power transformations to achieve approximate normality in a linear model. The new method is shown in theory and a Monte Carlo experiment to produce more robust inferences than the likelihood method and more powerful (although possibly slightly less robust) inferences than the significance method.

误差非对称时稳健估计量的方差估计AI 解读

We investigate the effects of asymmetry on estimates of variance of robust estimates in location and regression problems, thus showing that heavy skewness of errors can bias seriously the common variance estimates for location and intercept. This is a problem that can be corrected by jackknifing for location, but is more intractable for the intercept in regression. The slope parameters in linear regression seem not to be so seriously subject to this bias if the sample size…

有限总体子总体均值的序贯置信区间AI 解读

Sequential confidence intervals for the parameters of a subpopulation of a finite population are studied. Procedures are suggested using the mean, median, and trimmed means; these procedures are shown to be more efficient than their counterparts which are based on independent, identically distributed observations from infinite populations. The major technique used is to “linearize” the estimates, yielding as a simple consequence proofs of central limit theorems. A Monte…

有限总体中子总体均值的序贯置信区间AI 解读

Sequential confidence intervals for the parameters of a subpopulation of a finite population are studied. Procedures are suggested using the mean, median, and trimmed means; these procedures are shown to be more efficient than their counterparts which are based on independent, identically distributed observations from infinite populations. The major technique used is to “linearize” the estimates, yielding as a simple consequence proofs of central limit theorems. A Monte…

M估计量的几乎必然展开AI 解读

Let $T_n$ be an $M$-estimator with defining function $\psi$ and preliminary estimate of scale $s_n$. Without loss of generality, let $s_n \rightarrow 1$ and take $E\psi(X/\xi) = 0$. Under various conditions, it is shown that any consistent version of $T_n$ is almost surely to order $O(n^{-1} \log_2 n)$ a linear combination of $n^{-1} \sum^n_1 \psi(X_i)$ and $s_n$. Only in the case $EX_1\psi'(X_1) = 0$ does the contribution of $S_n$ vanish; it is shown how this affects the…

摘要暂缺

固定宽度置信区间估计的两种方法比较AI 解读

The recent method of Serfling and Wackerly (1976) for constructing fixed-width confidence intervals for the center of location is extended to include M estimators. The resultant class of procedures is compared to the stopping times of Chow and Robbins (1965), as both the interval length d and intended noncoverage probability 2α converge to zero. Except in certain special cases, the stopping times are found to have different asymptotic distributions. The coverage probability…

序贯程序的一致性保证：分布类上的均匀性AI 解读

An extension of a central limit theorem for a mean of a random number of observations is given. A natural application occurs in the area of fixed-width confidence intervals. We provide an example which shows that the standard procedure does not preserve the intended coverage probability uniformly over nontrivial sets of distribution functions. The major weak convergence result is used to provide conditions for and a simple proof of such uniformity. The results are also shown…