Predicting a multivariate response vector in a linear multivariate regressionmodel requires the estimate of the matrix of regression parameters. Stein (Stein, C. (1973). Estimation of the mean of a multivariate norma...
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Predicting a multivariate response vector in a linear multivariate regressionmodel requires the estimate of the matrix of regression parameters. Stein (Stein, C. (1973). Estimation of the mean of a multivariate normal distribution. Proc. Prague Symp. Asymp. Statist. 345-381), van der Merwe and Zidek (van der Merwe, A., Zidek;J.V. (1980). Multivariate regression analysis and canonical variates. Canadian Journal of Statistics 8:27-39), Bilodeau and Kariya (Bilodeau, M., Kariya, T. (1989). Minimax estimators in the normal MANOVA model. Journal of Multivariate Analysis 28:260-270) and Konno (Konno, Y. (1990). On estimation of a matrix of mean. Unpublished manuscript;Konno, Y. (1991). On estimation of a matrix of normal means with unknown covariance matrix. J. Multi. Analysis 36:44-55) have shown that their shrinkage estimators perform better than the least squares estimator. Recently, Breiman and Friedman (Breiman, L., Friedman, J. H. (1997). Predicting multivariate responses in multiple regression. J. Roy. Statist. Soc. Ser. B 59:3-54) proposed another class of shrinkage estimators, called C&W-GCV estimators. Through extensive simulations, they have showed that their C&W-GCV estimator performs better than the FICYREG estimator of van der Merwe and Zidek (van der Merwe, A., Zidek, J. V. (1980). Multivariate regression analysis and canonical variates. Canadian Journal of Statistics 8:27-39), the reduced rank regression method of Anderson (Anderson, T. W. (1951). Estimating linear restrictions on regression coefficients for multivariate normal distribution. Ann. Math. Statist., 22:327-351 (Correction in Ann. Statist. (1980), 8, 1400). Estimating linear restrictions on regression coefficients for multivariate normal distribution. Ann. Math. Statist. 22:327-351. (Correction in Ann. Statist. (1980), 8, 1400)), the component-wise ridge regression and the partial least squares. They, however, did not include in their comparisons, the minimax estimators of Bilodeau and Kariya
We consider the estimation of coefficients in a linear regression model when some responses on the study variable are missing and some prior information in the form of lower and upper bounds for the average values of ...
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We consider the estimation of coefficients in a linear regression model when some responses on the study variable are missing and some prior information in the form of lower and upper bounds for the average values of missing responses is available. Employing the mixed regression framework, we present five estimators for the vector of regression coefficients. Their exact as well as asymptotic properties are discussed and superiority of one estimator over the other is examined. (c) 2004 Elsevier B.V. All rights reserved.
The central aortic pressure waveform (CW) is determined by cardiac and vascular parameters. In the intact circulatory system, the influence of individual parameters on CW cannot be readily assessed because of paramete...
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ISBN:
(纸本)0780377893
The central aortic pressure waveform (CW) is determined by cardiac and vascular parameters. In the intact circulatory system, the influence of individual parameters on CW cannot be readily assessed because of parameter interdependence. This study presents a linear regression model for estimating CW from a range of measurements of heart rate (HR), brachial systolic pressure (BSP) and frequency components of previous CWs for an individual subject. The model was constructed using data from 34 subjects (age 20-76 years) in whom multiple CWs were determined from the radial pulse waveform over a given range of HR (42-77 bpm) and BSP (90-172 mmHg). For each subject a model was created to estimate the particular CW for any given heart rate and BSP. All models were validated independently using a cross validation technique. The model was able to estimate CW to within a mean error of <1 mmHg. The models were used to compare the influence of BSP on the late systolic pressure augmentation (Augmentation Index (AIx)) for a fixed HR. This study suggests that a linear regression model that estimates the CW can be used to assess the effect of individual parameters on specific waveform features. This allows the characterization of the effect of individual parameters on CW features, such that the response can be quantified independently of other parameters as a family of CWs over a specified range.
The problem of estimating the coefficients in a linear regression model is considered when some of the response values are missing. The conventional Yates procedure employing least squares predictions for missing valu...
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This paper presents a way of using a linear regression model to produce a single-valued criterion that indicates the perceived importance of each block in a stream of speech blocks. This method is superior to the conv...
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This paper presents a way of using a linear regression model to produce a single-valued criterion that indicates the perceived importance of each block in a stream of speech blocks. This method is superior to the conventional approach, voice activity detection (VAD), in that it provides a dynamically changing priority value for speech segments with finer granularity. The approach can be used in conjunction with scalable speech coding techniques in the context of IP QoS services to achieve a flexible form of quality control for speech transmission. A simple linear regression model is used to estimate a mean opinion score (MOS) of the various cases of missing speech segments. The estimated MOS is a continuous value that can be mapped to priority levels with arbitrary granularity. Through subjective evaluation, we show the validity of the calculated priority values.
In this study, we investigated by linear regression model the SAR data of the 15 HIV-1 protease inhibitors possessing structurally diverse scaffolds. First, a regressionmodel was developed only using the enzyme-inhib...
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In this study, we investigated by linear regression model the SAR data of the 15 HIV-1 protease inhibitors possessing structurally diverse scaffolds. First, a regressionmodel was developed only using the enzyme-inhibitor interaction energy as a term of the model, but did not provide a good correlation with the inhibitory activity (R-2 = 0.580 and Q(2) = 0.500). Then, we focused on the conformational flexibility of the inhibitors which may represent the diversity of the inhibitors, and added two conformational parameters into the model, respectively: the number of rotatable bonds of ligands (Delta Srot) and the distortion energy of ligands (Delta Elig). The regressionmodel by adding DElig successfully improved the quality of the model (R-2 = 0.771 and Q(2) = 0.713) while the model with DSrot was unsuccessful. The prediction for a training inhibitor by the DElig model also showed good agreement with experimental activity. These results suggest that the conformational flexibility of HIV-1 protease inhibitors directly contributes to the enzyme inhibition.
The estimation of the covariance matrix or the multivariate components of variance is considered in the multivariate linear regression models with effects being fixed or random. In this paper, we propose a new method ...
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The estimation of the covariance matrix or the multivariate components of variance is considered in the multivariate linear regression models with effects being fixed or random. In this paper, we propose a new method to show that usual unbiased estimators are improved on by the truncated estimators. The method is based on the Stein-Haff identity, namely the integration by parts in the Wishart distribution, and it allows us to handle the general types of scale-equivariant estimators as well as the general fixed or mixed effects linearmodels. (C) 2005 Elsevier Inc. All rights reserved.
An algorithm to determine the abscissa of the partial pixels that corresponds to the peaks of an absorbance spectrum from a hyperspectral imaging camera will be described. The algorithm is based on local linear regres...
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ISBN:
(纸本)0819462896
An algorithm to determine the abscissa of the partial pixels that corresponds to the peaks of an absorbance spectrum from a hyperspectral imaging camera will be described. The algorithm is based on local linear regression models in variable order and variable sample size mode. The sample size is determined by using the estimated critical points and inflection points. The order is determined by statistically comparing the sum of squares error of the regressionmodels for different orders. Numerical results on spectra from a hyperspectral cube will be presented.
This paper discusses a method for applying a linearregression analysis to software reliability data. By expanding three traditional growth curve models, we propose a gamma function model. The unknown parameters inclu...
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ISBN:
(纸本)0976348616
This paper discusses a method for applying a linearregression analysis to software reliability data. By expanding three traditional growth curve models, we propose a gamma function model. The unknown parameters included in the model can be estimated by log-linearregression with the method of two-parameter numerical differentiation which is newly introduced in this study. This method can provide a control chart representing the degree of software reliability growth and testing progress in a software testing phase. We show several numerical examples of software reliability growth data analysis.
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