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乘性误差平滑回归模型中的变量变换AI 解读

Summary We consider whether one should transform to estimate nonparametrically a regression curve sampled from data with a constant coefficient of variation, i.e. with multiplicative errors. Kernel-based smoothing methods are used to provide curve estimates from the data both in the original units and after transformation. Comparisons are based on the mean-squared error (MSE) or mean integrated squared error (MISE), calculated in the original units. Even when the data are…

非参数回归中方差估计量的比较AI 解读

SUMMARY We compare two estimators of error variance, both based on quadratic forms in the residuals about smoothing spline fits to data. The estimators are compared over the whole range of values of the smoothing parameter as well as for data-based choices of the smoothing parameter. We show that the commonly used estimator of variance has the serious drawback of underestimating the error variance for small choices of the smoothing parameter. This drawback is not shared by a…

Reinsch 样条与 Speckman 样条的比较AI 解读

In the context of nonparametric regression, spline smoothers can be used both for the estimation of the curve itself and for the estimation of the error variance. We compare two approaches that have been suggested: the Reinsch spline, i.e. roughness penalty, and the Speckman spline, minimax. The comparison is made on the basis of the summed mean squared error for curve estimation and on the basis of a closely related criterion for variance estimation. We show in both…

Reinsch 与 Speckman 样条的比较AI 解读

In the context of nonparametric regression, spline smoothers can be used both for the estimation of the curve itself and for the estimation of the error variance. We compare two approaches that have been suggested: the Reinsch spline, i.e. roughness penalty, and the Speckman spline, minimax. The comparison is made on the basis of the summed mean squared error for curve estimation and on the basis of a closely related criterion for variance estimation. We show in both…

非参数回归中残差方差估计的图方法AI 解读

If one wishes to make inferences about a regression, then an accurate estimator of the residual variance is required. However, except in the simplest cases, all estimators of variance are biased by an amount which depends on the unknown regression. Here, a graphical procedure is proposed which indicates whether the bias in a particular estimate is small. This procedure is studied in some detail for estimators which are weighted sums of squares of divided differences of the…

非参数回归残差方差估计的图形方法AI 解读

If one wishes to make inferences about a regression, then an accurate estimator of the residual variance is required. However, except in the simplest cases, all estimators of variance are biased by an amount which depends on the unknown regression. Here, a graphical procedure is proposed which indicates whether the bias in a particular estimate is small. This procedure is studied in some detail for estimators which are weighted sums of squares of divided differences of the…

非参数回归中的残差方差估计AI 解读

A wide class of estimators of the residual variance in nonparametric regression is considered, namely those that are quadratic in the data, unbiased for linear regression, and always nonnegative. The minimax mean squared error estimator over a natural class of regression functions is derived. This optimal estimator has an interesting structure and is closely related to a minimax estimator of the regression curve itself.

非参数回归中残差方差的估计AI 解读

A wide class of estimators of the residual variance in nonparametric regression is considered, namely those that are quadratic in the data, unbiased for linear regression, and always nonnegative. The minimax mean squared error estimator over a natural class of regression functions is derived. This optimal estimator has an interesting structure and is closely related to a minimax estimator of the regression curve itself.

大规模秩相关系数集合的评估AI 解读

A recent Poisson limit theorem for dissociated random variables is shown to apply to rank correlation coefficients which have been calculated from independently distributed vectors. This allows the asymptotic distribution of the largest of the rank correlations to be derived. Simulations show that the asymptotic approximations are close in the tails of the distributions. An example indicates how these approximations can be used to assess the significance of the large…

大量秩相关系数的显著性评估AI 解读

A recent Poisson limit theorem for dissociated random variables is shown to apply to rank correlation coefficients which have been calculated from independently distributed vectors. This allows the asymptotic distribution of the largest of the rank correlations to be derived. Simulations show that the asymptotic approximations are close in the tails of the distributions. An example indicates how these approximations can be used to assess the significance of the large…

三变量分布中线性回归的一则札记AI 解读

Sufficient conditions that one marginal variable should be linearly regressed on the others are obtained for those trivariate distributions, generated by having additive random elements in common.