The Experts below are selected from a list of 309 Experts worldwide ranked by ideXlab platform
John H Kalivas - One of the best experts on this subject based on the ideXlab platform.
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graphical diagnostics for regression Model determinations with consideration of the bias variance trade off
Chemometrics and Intelligent Laboratory Systems, 2002Co-Authors: Robert L Green, John H KalivasAbstract:Abstract Estimates of Model parameters (regression coefficients forming the regression vector) for a Multivariate Linear Model have been the subject of considerable discussion. Regression diagnostics utilized in chemometrics for a Multivariate Linear Model are often based on a single number such as the coefficient of determination, root mean square error of cross-validation, selectivity, etc. Additionally, regression diagnostics commonly applied focus on Model bias and do not include variance or Model complexity. This paper demonstrates that substantial information is available through a graphical study of trends in Model parameters as determined by plots of regression diagnostics using bias, variance, and/or Model complexity measures. Also illustrated is that by using harmonious graphics which simultaneously use bias and variance information, determination of proper Model parameters without cross-validation is possible. This paper concludes with comments on the next level of regression diagnostics, including use of color, sound, and virtual reality.
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Graphical diagnostics for regression Model determinations with consideration of the bias/variance trade-off
Chemometrics and Intelligent Laboratory Systems, 2002Co-Authors: Robert L Green, John H KalivasAbstract:Abstract Estimates of Model parameters (regression coefficients forming the regression vector) for a Multivariate Linear Model have been the subject of considerable discussion. Regression diagnostics utilized in chemometrics for a Multivariate Linear Model are often based on a single number such as the coefficient of determination, root mean square error of cross-validation, selectivity, etc. Additionally, regression diagnostics commonly applied focus on Model bias and do not include variance or Model complexity. This paper demonstrates that substantial information is available through a graphical study of trends in Model parameters as determined by plots of regression diagnostics using bias, variance, and/or Model complexity measures. Also illustrated is that by using harmonious graphics which simultaneously use bias and variance information, determination of proper Model parameters without cross-validation is possible. This paper concludes with comments on the next level of regression diagnostics, including use of color, sound, and virtual reality.
Sik-yum Lee - One of the best experts on this subject based on the ideXlab platform.
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Bayesian Estimation and Model Selection of Multivariate Linear Model with Polytomous Variables
Multivariate behavioral research, 2002Co-Authors: Xin-yuan Song, Sik-yum LeeAbstract:This article provides a Bayesian analysis of the Multivariate Linear Model with polytomous variables. The computational burden due to the intractable multiple integrals induced by the polytomous variables and the Model is solved by augmenting the underlying latent continuous measurements of the observed polytomous data. A Gibbs sampler algorithm is implemented to produce the Bayesian estimate. A Bayes factor approach is proposed for Model selection, and it is approximated by the Bayesian information criterion (BIC) via the bridge sampling. The proposed methodology is illustrated by examples using Multivariate Linear regression and Multivariate two-way analysis of variance with real data.
Fan Shun - One of the best experts on this subject based on the ideXlab platform.
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Optimal Experimental Designs for the Generalized Multivariate Linear Model
Journal of Tianjin Normal University, 2000Co-Authors: Fan ShunAbstract:The equivalence theorem of optimal experimental designs for the Multivariate Linear Model in the thesis [1] has been further studied and the conclusions have been applied to the generalized Multivariate Linear Model. As deductions, two important results in matrix theory have been obtained.
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Equivalence Theorem of Optimal Experimental Designs for the Multivariate Linear Model
Journal of Tianjin Normal University, 2000Co-Authors: Fan ShunAbstract:The optimal experimental designs for the Multivariate Linear Model are discussed under \%Φ\% optimal criteria. A general popularization of the original equivalence theorem is obtained. As an example, Multivariate \%D\% optimal design and \%A\% optimal design are discussed.
Yu Sheng - One of the best experts on this subject based on the ideXlab platform.
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Conditional Optimal Prediction in Multivariate Linear Model
Journal of Hunan University, 2003Co-Authors: Yu ShengAbstract:The conditional optimal prediction of the conditional predictable variable in the Multivariate Linear Model with arbitrary rank and Linear equality constrains was investigated. Specifically , a class of special prediction function:φLinear prediction function was considered, and the definitions of the conditional φLinear predictable variable and the conditional optimal φLinear unbiased predictor were given.The conditional optimum φLinear unbiased predictors of the conditional φLinear predictable variable, which is unique with probability one, were obtained.
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The simple projection predictor in Multivariate Linear Model with arbitrary rank
2002Co-Authors: Yu ShengAbstract:Considering the Multivariate Linear Model with arbitrary rank Y=XB+e ,where E( Vec (e))=0 and V( Vec (e))=σ 2ΔΣ, the unknown observation matrix Y 0=X 0B+e 0 is predicted using the known observation matrix Y .Srndal and Wright emphasized the need for predictors with simple and intuitive forms.The most intuitive and simple predictor certainly is the simple projection predictor (SPP). H.Bolfarine, et al obtained several necessary and sufficient conditions for optimum of the simple projection predictor under a superpopulation Model. The above Multivariate Linear Model is studied. For arbitrary Linear predictable variable θ=KY 0L ,its SPP is then defined by SPP = KX 0(X ′T -X) -X ′T -YL, where T=Σ+XX ′ .A number of necessary and sufficient conditions where SPP is also the best Linear unbiased predictor are obtained,and the robustness of the SPP on the covariance matrix is investigated, and thus the relevant results drawn by H. Bolfarine, et al are widely used.
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The simple projection predictor in Multivariate Linear Model with arbitrary rank
2002Co-Authors: Yu ShengAbstract:Considering the Multivariate Linear Model with arbitrary rank Y=XB+e ,where E( Vec (e))=0 and V( Vec (e))=σ 2ΔΣ, the unknown observation matrix Y 0=X 0B+e 0 is predicted using the known observation matrix Y .Srndal and Wright emphasized the need for predictors with simple and intuitive forms.The most intuitive and simple predictor certainly is the simple projection predictor (SPP). H.Bolfarine, et al obtained several necessary and sufficient conditions for optimum of the simple projection predictor under a superpopulation Model. The above Multivariate Linear Model is studied. For arbitrary Linear predictable variable θ=KY 0L ,its SPP is then defined by SPP = KX 0(X ′T -X) -X ′T -YL, where T=Σ+XX ′ .A number of necessary and sufficient conditions where SPP is also the best Linear unbiased predictor are obtained,and the robustness of the SPP on the covariance matrix is investigated, and thus the relevant results drawn by H. Bolfarine, et al are widely used.
Robert L Green - One of the best experts on this subject based on the ideXlab platform.
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graphical diagnostics for regression Model determinations with consideration of the bias variance trade off
Chemometrics and Intelligent Laboratory Systems, 2002Co-Authors: Robert L Green, John H KalivasAbstract:Abstract Estimates of Model parameters (regression coefficients forming the regression vector) for a Multivariate Linear Model have been the subject of considerable discussion. Regression diagnostics utilized in chemometrics for a Multivariate Linear Model are often based on a single number such as the coefficient of determination, root mean square error of cross-validation, selectivity, etc. Additionally, regression diagnostics commonly applied focus on Model bias and do not include variance or Model complexity. This paper demonstrates that substantial information is available through a graphical study of trends in Model parameters as determined by plots of regression diagnostics using bias, variance, and/or Model complexity measures. Also illustrated is that by using harmonious graphics which simultaneously use bias and variance information, determination of proper Model parameters without cross-validation is possible. This paper concludes with comments on the next level of regression diagnostics, including use of color, sound, and virtual reality.
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Graphical diagnostics for regression Model determinations with consideration of the bias/variance trade-off
Chemometrics and Intelligent Laboratory Systems, 2002Co-Authors: Robert L Green, John H KalivasAbstract:Abstract Estimates of Model parameters (regression coefficients forming the regression vector) for a Multivariate Linear Model have been the subject of considerable discussion. Regression diagnostics utilized in chemometrics for a Multivariate Linear Model are often based on a single number such as the coefficient of determination, root mean square error of cross-validation, selectivity, etc. Additionally, regression diagnostics commonly applied focus on Model bias and do not include variance or Model complexity. This paper demonstrates that substantial information is available through a graphical study of trends in Model parameters as determined by plots of regression diagnostics using bias, variance, and/or Model complexity measures. Also illustrated is that by using harmonious graphics which simultaneously use bias and variance information, determination of proper Model parameters without cross-validation is possible. This paper concludes with comments on the next level of regression diagnostics, including use of color, sound, and virtual reality.
