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改进调查加权最小二乘回归AI 解读

Summary The weighted least squares (WLS) estimator is often employed in linear regression using complex survey data to deal with the bias in ordinary least squares (OLS) arising from informative sampling. In this paper a ‘quasi-Aitken WLS’ (QWLS) estimator is proposed. QWLS modifies WLS in the same way that Cragg’s quasi-Aitken estimator modifies OLS. It weights by the usual inverse sample inclusion probability weights multiplied by a parameterized function of covariates,…

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大量观测下核平滑条件分位数的计算AI 解读

Quantiles of a variable Y conditional on another variable X, when plotted against X, can be a useful descriptive tool. These plots give a quick impression of the functional form of the relation between X and the location, spread, and shape of the conditional distribution of Y. If several Y are observed for each X, then sample quantiles could be calculated for each X. The resulting quantile plot may be quite noisy, however, and smoothing across X may be desired. This article…

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It is shown that selecting regressors based on the prediction error sum of squares is asymptotically related to hypothesis testing with White's (1980) heteroscedasticity-consistent covariance matrix. A simulation experiment suggest that this asymptotic relation may be useful. Illustrative examples are also given.

使用 PRESS 与 White t 统计量选择预测回归变量AI 解读

It is shown that selecting regressors based on the prediction error sum of squares is asymptotically related to hypothesis testing with White's (1980) heteroscedasticity-consistent covariance matrix. A simulation experiment suggest that this asymptotic relation may be useful. Illustrative examples are also given.

AR(1) 误差线性模型的 Edgeworth 检验尺寸修正AI 解读

T. J. Rothenberg's (1984) Edgeworth test size correction for the linear model with a nonscalar covariance matrix is applied to the special case of AR(1) errors. Simulations show that the correction reduces the overrejection that is commonly encountered in this model, although substantial overrejection remains when the original amount is large. When the regressors are autocorrelated and collinear (for example, two trended regressors) there is not nearly as much overrejection…

OLS 与可行 GLS 估计量的方差比较AI 解读

Second-order approximations to the variances of OLS and GLS estimators are compared when the covariance matrix is locally nonscalar. Using a result of Rothenberg, the comparison of OLS and GLS variances is shown to be asymptotically equivalent to a weighted mean square error comparison of the error covariance parameter estimators used in those two procedures. When there is only one covariance parameter, this comparison depends only on the noncentrality parameter of a…

处理因变量极端值的替代变换AI 解读

Transformations that could be used to reduce the influence of extreme observations of dependent variables, which can assume either sign, on regression coefficient estimates are studied in this article. Two that seem reasonable on a priori grounds—the extended Box—Cox (BC) and the inverse hyperbolic sine (IHS)—are evaluated in detail. One feature is that the log-likelihood function for IHS is defined for zero values of the dependent variable, which is not true of BC. The…

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LR、W 与 LM 检验统计量近似斜率的近似AI 解读

A Taylor series approach is used to derive approximations to the approximate slope of LR, W, and LM test statistics. These can be useful when the approximate slopes themselves are complicated. The results are applied to the test of linear coefficient restrictions in the linear model with a nonscalar covariance matrix. They can be used to find cases where the Wald test may badly over-reject in this model. The results shed some new light on the over-rejection that has been…

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