Least squares Lehmann-Scheffé estimation of variances and covariances with mixed linear models.

Abstract We present a unified approach to the use of linear models and matrix least squares with the intention of providing a better understanding of the techniques themselves and of the statistics that arise from these techniques as they are used in clinical chemistry. Emphasis is placed on the importance of appropriate experimental designs and adequately precise measurement processes for efficiently obtaining the desired information.

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Fitting generalized linear models and their nonlinear extensions with least squares calculations

Computational Statistics & Data Analysis ◽

10.1016/0167-9473(88)90059-x ◽

1988 ◽

Vol 6 (1) ◽

pp. 7-19 ◽

Cited By ~ 2

Author(s):

W.Douglas Stirling

Keyword(s):

Least Squares ◽

Generalized Linear Models ◽

Linear Models ◽

Nonlinear Extensions

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A Method for Assessing Extent and Sources of Heterogeneity of Residual Variances in Mixed Linear Models

Journal of Dairy Science ◽

10.3168/jds.s0022-0302(90)78832-7 ◽

1990 ◽

Vol 73 (6) ◽

pp. 1612-1624 ◽

Cited By ~ 33

Author(s):

J.L. Foulley ◽

D. Gianola ◽

M. San Cristobal ◽

S. Im

Keyword(s):

Linear Models ◽

Mixed Linear Models ◽

Residual Variances

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Fuzzy C-Regression Models

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.278-280.1323 ◽

2013 ◽

Vol 278-280 ◽

pp. 1323-1326

Author(s):

Yan Hua Yu ◽

Li Xia Song ◽

Kun Lun Zhang

Keyword(s):

Linear Regression ◽

Least Squares ◽

Linear Models ◽

Least Squares Method ◽

Least Square Method ◽

Least Square ◽

Estimation Methods ◽

Statistical Regression ◽

Fuzzy Linear Regression ◽

Fuzzy Degree

Fuzzy linear regression has been extensively studied since its inception symbolized by the work of Tanaka et al. in 1982. As one of the main estimation methods, fuzzy least squares approach is appealing because it corresponds, to some extent, to the well known statistical regression analysis. In this article, a restricted least squares method is proposed to fit fuzzy linear models with crisp inputs and symmetric fuzzy output. The paper puts forward a kind of fuzzy linear regression model based on structured element, This model has precise input data and fuzzy output data, Gives the regression coefficient and the fuzzy degree function determination method by using the least square method, studies the imitation degree question between the observed value and the forecast value.

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