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Logistic 测量误差模型的半参数估计AI 解读

SUMMARY We describe semiparametric estimation and inference in a logistic regression model with measurement error in the predictors. The particular measurement error model consists of a primary data set in which only the response Y and a fallible surrogate W of the true predictor X are observed, plus a smaller validation data set for which (Y, X, W) are observed. Except for the underlying assumption of a logistic model in the true predictor, no parametric distributional…

质量工程中最优性能准则的非参数估计AI 解读

Box and Leon, Shoemaker and Kackar have discussed the problem of closeness to target in quality engineering. If the mean response $f(x, z)$ depends on $(x, z)$, the variance function is a PERMIA if it is $g(z)$, i.e., depends only on $z$. The goal is to find $(x_0, z_0)$ which minimizes variance while achieving a target mean value. We pose and answer the question: For given smoothness assumptions about $f$ and $g$, how accurately can we estimate $x_0$ and $z_0$? As part of…

回归中的方差函数估计：估计均值的影响AI 解读

SUMMARY We consider estimation of a variance function g in regression problems. Such estimation requires simultaneous estimation of the mean function f. We obtain clear results on the extent to which the smoothness of f influences best rates of convergence for estimating g. For example, in nonparametric regression with two derivatives on g, ‘classical' rates of convergence are possible if and only if the unknown f satisfies a Lipschitz condition of order 13 or more. If a…

扩展拟似然方法的一则注记AI 解读

SUMMARY We study the method of extended quasi-likelihood estimation and inference of a variance function recently proposed by Nelder and Pregibon. The estimates are inconsistent in general, and the test levels can be biased, but in many cases such as the exponential family the inconsistency and bias will not be a major concern. Extended quasi-likelihood is compared with Carroll and Ruppert's pseudo-likelihood method, which gives consistent estimates and, when slightly…

测定分析中的方差函数与最低可检测浓度AI 解读

Assay data are often fitted by a nonlinear heteroscedastic regression model with the standard deviation of the response typically taken to be proportional to a power θ of the mean. For many assays, how one estimates θ does not greatly affect estimates of the mean regression function. Assay analysis also involves estimation of auxiliary calibration constructs such as minimum detectable concentration. An asymptotic theory is developed to show that standard methods for…

检测分析中的方差函数与最低可检测浓度AI 解读

Assay data are often fitted by a nonlinear heteroscedastic regression model with the standard deviation of the response typically taken to be proportional to a power θ of the mean. For many assays, how one estimates θ does not greatly affect estimates of the mean regression function. Assay analysis also involves estimation of auxiliary calibration constructs such as minimum detectable concentration. An asymptotic theory is developed to show that standard methods for…

方差函数估计AI 解读

Heteroscedastic regression models are used in fields including economics, engineering, and the biological and physical sciences. Often, the heteroscedasticity is modeled as a function of the covariates or the regression and other structural parameters. Standard asymptotic theory implies that how one estimates the variance function, in particular the structural parameters, has no effect on the first-order properties of the regression parameter estimates; there is evidence,…

异方差线性模型中最大似然与广义最小二乘的比较AI 解读

We consider a linear model with normally distributed but heteroscedastic errors. When the error variances are functionally related to the regression parameter, one can use either maximum likelihood or generalized least squares to estimate the regression parameter. We show that likelihood is more sensitive to small misspecifications in the functional relationship between the error variances and the regression parameter.