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误设模型惩罚似然估计中正则化参数选择的效率AI 解读

It has been shown that Akaike information criterion (AIC)-type criteria are asymptotically efficient selectors of the tuning parameter in nonconcave penalized regression methods under the assumption that the population variance is known or that a consistent estimator is available. We relax this assumption to prove that AIC itself is asymptotically efficient and we study its performance in finite samples. In classical regression, it is known that AIC tends to select overly…

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…

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多维有序稀疏列联表的几何组合估计AI 解读

A geometric combination estimator is proposed for $d$-dimensional ordinal contingency tables. The proposed estimator is nonnegative. It is shown that, assuming sufficient smoothness and boundary conditions for the underlying probabilities, the rate of convergence of mean summed squared error (MSSE) of this estimator is $O(K^{-1}N^{-8/(d+8)})$ for $d$-dimensional tables $(d \leq 4)$ with $K$ cells and sample size $N$. This rate is optimal under the smoothness assumptions, and…

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线性模型中多个离群点的识别程序AI 解读

We consider the problem of identifying and testing multiple outliers in linear models. The available outlier identification methods often do not succeed in detecting multiple outliers because they are affected by the observations they are supposed to identify. We introduce two test procedures for the detection of multiple outliers that appear to be less sensitive to this problem. Both procedures attempt to separate the data into a set of “clean” data points and a set of…

响应变量受删失时回归估计量的比较AI 解读

Several methods of estimating parameters in a linear regression when the response variable is censored are compared. The estimator of Buckley & James (1979) is preferred. Further, it is shown that the strength of the regression, the support and distribution of the censoring variable, and the magnitude of the slope all have an effect on the relative performance of the estimators.

响应变量被删失时回归估计器的比较AI 解读

Several methods of estimating parameters in a linear regression when the response variable is censored are compared. The estimator of Buckley & James (1979) is preferred. Further, it is shown that the strength of the regression, the support and distribution of the censoring variable, and the magnitude of the slope all have an effect on the relative performance of the estimators.

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最小二乘回归中缺失数据的诊断图AI 解读

The usual approach to handling missing data in a regression is to assume that the points are missing at random (MAR) and use either a fill-in method to replace the missing points or a method using maximally available pairs in the sample covariance matrix. We derive limits for the values of the least squares estimates of the coefficients (and their associated t statistics) when there are missing observations in one carrier. These limits are derived subject to a constraint on…

最小二乘回归缺失数据的诊断图AI 解读

The usual approach to handling missing data in a regression is to assume that the points are missing at random (MAR) and use either a fill-in method to replace the missing points or a method using maximally available pairs in the sample covariance matrix. We derive limits for the values of the least squares estimates of the coefficients (and their associated t statistics) when there are missing observations in one carrier. These limits are derived subject to a constraint on…

稀疏多项分布的改进拟合优度统计量AI 解读

A new goodness-of-fit statistic for sparse multinomials is proposed. It is assumed that the null distribution exhibits smoothness. The test statistic is based on the maximum posterior estimator probability estimates of Simonoff (1983). Computer simulations are used to estimate the null distribution, significance levels, and the power function of the test. It is shown that power of the test is a great improvement over that of the standard tests if the alternative distribution…

大型稀疏列联表平滑的惩罚函数方法AI 解读

Probabilities in a large sparse contingency table are estimated by maximizing the likelihood modified by a roughness penalty. It is shown that if certain smoothness criteria on the underlying probability vector are met, the estimator proposed is consistent in a one-dimensional table under a sparse asymptotic framework. Suggestions are made for techniques to apply the estimator in practice, and generalization to higher dimensional tables is considered.