In this paper, the performance of existing biased estimators (Ridge Estimator (RE), Almost Unbiased Ridge Estimator (AURE), Liu Estimator (LE), Almost Unbiased Liu Estimator (AULE), Principal Component Regression Esti...In this paper, the performance of existing biased estimators (Ridge Estimator (RE), Almost Unbiased Ridge Estimator (AURE), Liu Estimator (LE), Almost Unbiased Liu Estimator (AULE), Principal Component Regression Estimator (PCRE), r-k class estimator and r-d class estimator) and the respective predictors were considered in a misspecified linear regression model when there exists multicollinearity among explanatory variables. A generalized form was used to compare these estimators and predictors in the mean square error sense. Further, theoretical findings were established using mean square error matrix and scalar mean square error. Finally, a numerical example and a Monte Carlo simulation study were done to illustrate the theoretical findings. The simulation study revealed that LE and RE outperform the other estimators when weak multicollinearity exists, and RE, r-k class and r-d class estimators outperform the other estimators when moderated and high multicollinearity exist for certain values of shrinkage parameters, respectively. The predictors based on the LE and RE are always superior to the other predictors for certain values of shrinkage parameters.展开更多
In regression, despite being both aimed at estimating the Mean Squared Prediction Error (MSPE), Akaike’s Final Prediction Error (FPE) and the Generalized Cross Validation (GCV) selection criteria are usually derived ...In regression, despite being both aimed at estimating the Mean Squared Prediction Error (MSPE), Akaike’s Final Prediction Error (FPE) and the Generalized Cross Validation (GCV) selection criteria are usually derived from two quite different perspectives. Here, settling on the most commonly accepted definition of the MSPE as the expectation of the squared prediction error loss, we provide theoretical expressions for it, valid for any linear model (LM) fitter, be it under random or non random designs. Specializing these MSPE expressions for each of them, we are able to derive closed formulas of the MSPE for some of the most popular LM fitters: Ordinary Least Squares (OLS), with or without a full column rank design matrix;Ordinary and Generalized Ridge regression, the latter embedding smoothing splines fitting. For each of these LM fitters, we then deduce a computable estimate of the MSPE which turns out to coincide with Akaike’s FPE. Using a slight variation, we similarly get a class of MSPE estimates coinciding with the classical GCV formula for those same LM fitters.展开更多
We considered the following semiparametric regres-sion model yi = X iT β+ s ( t i ) + ei (i =1,2,,n). First,the general-ized ridge estimators of both parameters and non-parameters are given without a restrained desig...We considered the following semiparametric regres-sion model yi = X iT β+ s ( t i ) + ei (i =1,2,,n). First,the general-ized ridge estimators of both parameters and non-parameters are given without a restrained design matrix. Second,the generalized ridge estimator will be compared with the penalized least squares estimator under a mean squares error,and some conditions in which the former excels the latter are given. Finally,the validity and feasibility of the method is illustrated by a simulation example.展开更多
In this paper, we introduce a generalized Liu estimator and jackknifed Liu estimator in a linear regression model with correlated or heteroscedastic errors. Therefore, we extend the Liu estimator. Under the mean squar...In this paper, we introduce a generalized Liu estimator and jackknifed Liu estimator in a linear regression model with correlated or heteroscedastic errors. Therefore, we extend the Liu estimator. Under the mean square error（MSE）, the jackknifed estimator is superior to the Liu estimator and the jackknifed ridge estimator. We also give a method to select the biasing parameter for d. Furthermore, a numerical example is given to illustvate these theoretical results.展开更多
In this paper,we propose a new biased estimator of the regression parameters,the generalized ridge and principal correlation estimator.We present its some properties and prove that it is superior to LSE(least squares ...In this paper,we propose a new biased estimator of the regression parameters,the generalized ridge and principal correlation estimator.We present its some properties and prove that it is superior to LSE(least squares estimator),principal correlation estimator,ridge and principal correlation estimator under MSE(mean squares error) and PMC(Pitman closeness) criterion,respectively.展开更多
气候系统是典型的非平稳性系统,然而对于气候观测数据的处理通常是在时间序列平稳的假定下完成的,比如气温和降水的多步预报,这通常会导致预报准确度较低。为改进该缺陷,首先将非平稳数据序列分解成平稳的、多尺度特征的本征模态函数分...气候系统是典型的非平稳性系统,然而对于气候观测数据的处理通常是在时间序列平稳的假定下完成的,比如气温和降水的多步预报,这通常会导致预报准确度较低。为改进该缺陷,首先将非平稳数据序列分解成平稳的、多尺度特征的本征模态函数分量(IMF),再使用数值集合预报与逐步回归分析相结合的方式对每一个IMF分量构建不同的预报模型,最后线性拟合成预报结果。通过Visual Studio 2008开发平台使用上述方法建立了一个短期气候预报系统,采用广西区88个气象站1957—2005年的2月距平气温数据进行实际验证。结果表明,相对于普通预测和单一预测方法,加入了EMD和集合预报技术的方法在仅用历史资料进行多步预测的情况下,对于气候的变化趋势以及突发性气候具有更好的预报能力。展开更多
文摘In this paper, the performance of existing biased estimators (Ridge Estimator (RE), Almost Unbiased Ridge Estimator (AURE), Liu Estimator (LE), Almost Unbiased Liu Estimator (AULE), Principal Component Regression Estimator (PCRE), r-k class estimator and r-d class estimator) and the respective predictors were considered in a misspecified linear regression model when there exists multicollinearity among explanatory variables. A generalized form was used to compare these estimators and predictors in the mean square error sense. Further, theoretical findings were established using mean square error matrix and scalar mean square error. Finally, a numerical example and a Monte Carlo simulation study were done to illustrate the theoretical findings. The simulation study revealed that LE and RE outperform the other estimators when weak multicollinearity exists, and RE, r-k class and r-d class estimators outperform the other estimators when moderated and high multicollinearity exist for certain values of shrinkage parameters, respectively. The predictors based on the LE and RE are always superior to the other predictors for certain values of shrinkage parameters.
文摘In regression, despite being both aimed at estimating the Mean Squared Prediction Error (MSPE), Akaike’s Final Prediction Error (FPE) and the Generalized Cross Validation (GCV) selection criteria are usually derived from two quite different perspectives. Here, settling on the most commonly accepted definition of the MSPE as the expectation of the squared prediction error loss, we provide theoretical expressions for it, valid for any linear model (LM) fitter, be it under random or non random designs. Specializing these MSPE expressions for each of them, we are able to derive closed formulas of the MSPE for some of the most popular LM fitters: Ordinary Least Squares (OLS), with or without a full column rank design matrix;Ordinary and Generalized Ridge regression, the latter embedding smoothing splines fitting. For each of these LM fitters, we then deduce a computable estimate of the MSPE which turns out to coincide with Akaike’s FPE. Using a slight variation, we similarly get a class of MSPE estimates coinciding with the classical GCV formula for those same LM fitters.
基金Supported by the Key Project of Chinese Ministry of Educa-tion (209078)the Scientific Research Item of Hubei Provincial Department of Education (D20092207)
文摘We considered the following semiparametric regres-sion model yi = X iT β+ s ( t i ) + ei (i =1,2,,n). First,the general-ized ridge estimators of both parameters and non-parameters are given without a restrained design matrix. Second,the generalized ridge estimator will be compared with the penalized least squares estimator under a mean squares error,and some conditions in which the former excels the latter are given. Finally,the validity and feasibility of the method is illustrated by a simulation example.
基金Supported by the National Natural Science Foundation of China(11071022)Science and Technology Project of Hubei Provincial Department of Education(Q20122202)
文摘In this paper, we introduce a generalized Liu estimator and jackknifed Liu estimator in a linear regression model with correlated or heteroscedastic errors. Therefore, we extend the Liu estimator. Under the mean square error（MSE）, the jackknifed estimator is superior to the Liu estimator and the jackknifed ridge estimator. We also give a method to select the biasing parameter for d. Furthermore, a numerical example is given to illustvate these theoretical results.
基金Foundation item： the National Natural Science Foundation of China （Nos. 60736047 10671007+2 种基金 60772036） the Foundation of Beijing Jiaotong University （Nos. 2006XM037 2007XM046）.
文摘In this paper,we propose a new biased estimator of the regression parameters,the generalized ridge and principal correlation estimator.We present its some properties and prove that it is superior to LSE(least squares estimator),principal correlation estimator,ridge and principal correlation estimator under MSE(mean squares error) and PMC(Pitman closeness) criterion,respectively.
文摘气候系统是典型的非平稳性系统,然而对于气候观测数据的处理通常是在时间序列平稳的假定下完成的,比如气温和降水的多步预报,这通常会导致预报准确度较低。为改进该缺陷,首先将非平稳数据序列分解成平稳的、多尺度特征的本征模态函数分量(IMF),再使用数值集合预报与逐步回归分析相结合的方式对每一个IMF分量构建不同的预报模型,最后线性拟合成预报结果。通过Visual Studio 2008开发平台使用上述方法建立了一个短期气候预报系统,采用广西区88个气象站1957—2005年的2月距平气温数据进行实际验证。结果表明,相对于普通预测和单一预测方法,加入了EMD和集合预报技术的方法在仅用历史资料进行多步预测的情况下,对于气候的变化趋势以及突发性气候具有更好的预报能力。
