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利用 lasso 收缩与选择回归系数及自回归阶数AI 解读

Summary The least absolute shrinkage and selection operator (‘lasso’) has been widely used in regression shrinkage and selection. We extend its application to the regression model with autoregressive errors. Two types of lasso estimators are carefully studied. The first is similar to the traditional lasso estimator with only two tuning parameters (one for regression coefficients and the other for autoregression coefficients). These tuning parameters can be easily calculated…

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收缩切片逆回归札记AI 解读

We employ Lasso shrinkage within the context of sufficient dimension reduction to obtain a shrinkage sliced inverse regression estimator, which provides easier interpretations and better prediction accuracy without assuming a parametric model. The shrinkage sliced inverse regression approach can be employed for both single-index and multiple-index models. Simulation studies suggest that the new estimator performs well when its tuning parameter is selected by either the…

用于纳入先验信息的约束逆回归AI 解读

Inverse regression methods facilitate dimension-reduction analyses of high-dimensional data by extracting a small number of factors that are linear combinations of the original predictor variables. But the estimated factors may not lend themselves readily to interpretation consistent with prior information. Our approach to solving this problem is to first incorporate prior information via theory- or data-driven constraints on model parameters, and then apply the proposed…

经典测量误差线性模型中若干得分检验的不变性AI 解读

The linear model with classical measurement error is an alternative to the standard regression model, in which it is assumed that the independent variables are subject to error. This assumption can cause statistical inferences and parameter estimators to differ dramatically from those obtained by the standard regression model. However, in some cases, inferences remain unchanged even though the independent variables are assumed to be subject to error. This article…

回归模型选择：残差似然方法AI 解读

Summary We obtain the residual information criterion RIC, a selection criterion based on the residual log-likelihood, for regression models including classical regression models, Box–Cox transformation models, weighted regression models and regression models with autoregressive moving average errors. We show that RIC is a consistent criterion, and that simulation studies for each of the four models indicate that RIC provides better model order choices than the Akaike…

单指标模型的偏最小二乘估计AI 解读

Summary The partial least squares (PLS) approach first constructs new explanatory variables, known as factors (or components), which are linear combinations of available predictor variables. A small subset of these factors is then chosen and retained for prediction. We study the performance of PLS in estimating single-index models, especially when the predictor variables exhibit high collinearity. We show that PLS estimates are consistent up to a constant of proportionality.…

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利用改进的 Akaike 信息准则选择非参数回归的平滑参数AI 解读

Summary Many different methods have been proposed to construct nonparametric estimates of a smooth regression function, including local polynomial, (convolution) kernel and smoothing spline estimators. Each of these estimators uses a smoothing parameter to control the amount of smoothing performed on a given data set. In this paper an improved version of a criterion based on the Akaike information criterion (AIC), termed AICC, is derived and examined as a way to choose the…

线性回归中有效模型选择准则的相对收敛速度AI 解读

Two approaches to estimating a smooth regression function not specified by a finite number of parameters are (i) to fit a parametric model to the data, with the number of parameters selected by the Akaike information criterion, AIC, and (ii) to use nonparametric smoothing techniques, with the smoothing parameter selected by cross-validation or some other automatic method. We consider the relative rate of convergence of the mean integrated squared error of the selected…

关于Jorgensen迭代定义统计量的札记AI 解读

The Newton-Raphson and Fisher scoring iteratively reweighted least squares methods are two fundamental tools for computing parameter estimators and deletion diagnostics. Jorgensen (1993) proposed a modified method to compute deletion diagnostics. In this paper, we study the relationship between Jorgensen's, Newton-Raphson and Fisher scoring one-step deletion estimators by using the observed and expected Fisher information matrices. In addition, we extend Jorgensen's true…

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欠拟合回归与时间序列模型中修正 AIC 的偏差AI 解读

The Akaike Information Criterion, AIC (Akaike, 1973), and a bias-corrected version, AICC(Sugiura, 1978; Hurvich & Tsai, 1989) are two methods for selection of regression and autoregressive models. Both criteria may be viewed as estimators of the expected Kullback-Leibler information. The bias of AIC and AICC is studied in the underfitting case, where none of the candidate models includes the true model (Shibata, 1980, 1981; Parzen, 1978). Both normal linear regression and…

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指数族非线性模型中正态近似准确性的诊断AI 解读

Diagnostics are investigated for assessing the agreement between likelihood and standard large-sample confidence regions for parameters from an exponential family nonlinear model (Cordeiro and Paula 1989). The development connects the contour methods proposed by Hodges (1985, 1987) with the curvature measures for normal, nonlinear regression proposed by Bates and Watts (1980) and Jennings's (1982, 1986) diagnostics for logistic regression. The proposed methodology is…

指数族非线性模型中正态近似准确性的诊断AI 解读

Diagnostics are investigated for assessing the agreement between likelihood and standard large-sample confidence regions for parameters from an exponential family nonlinear model (Cordeiro and Paula 1989). The development connects the contour methods proposed by Hodges (1985, 1987) with the curvature measures for normal, nonlinear regression proposed by Bates and Watts (1980) and Jennings's (1982, 1986) diagnostics for logistic regression. The proposed methodology is…

小样本自回归模型选择中 Kullback–Leibler 信息的改进估计AI 解读

A new estimator, AICl, of the Kuliback-Leibler information is proposed for Gaussian autoregressive time series model selection. The expected information is decomposed into two terms, the first being estimated without bias. The second term is a penalty function which depends only weakly on the model parameters, and hence can be tabulated by simulation from a white noise process. The estimated information, AICl, is very nearly unbiased when the model is either correct or…

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小样本中的回归与时间序列模型选择AI 解读

A bias correction to the Akaike information criterion, AIC, is derived for regression and autoregressive time series models. The correction is of particular use when the sample size is small, or when the number of fitted parameters is a moderate to large fraction of the sample size. The corrected method, called AICC, is asymptotically efficient if the true model is infinite dimensional. Furthermore, when the true model is of finite dimension, AICC is found to provide better…

异方差一阶自回归模型的得分检验AI 解读

A score test is proposed for simultaneous testing of independence and homoscedasticity in the first-order autoregressive model with nonconstant variance. The relationships between the score test statistic and the local influence of minor perturbations on a statistical model are examined.

异方差一阶自回归模型的得分检验AI 解读

A score test is proposed for simultaneous testing of independence and homoscedasticity in the first-order autoregressive model with nonconstant variance. The relationships between the score test statistic and the local influence of minor perturbations on a statistical model are examined.

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非线性回归中的残差AI 解读

We employ a quadratic expansion to investigate the behaviour of the ordinary residuals in nonlinear regression. These residuals can produce misleading results when used in diagnostic methods analogous to those for linear regression. We suggest a new type of residual that overcomes many of the potential shortcomings of the ordinary residuals.