A Characterization of Best Linear Unbiased Estimators in the General Linear Model

1980 ◽  
pp. 365-373 ◽  
Author(s):  
Roman Zmyślony
Keyword(s):  
Linear Model ◽  
General Linear Model ◽  
General Linear ◽  
Unbiased Estimators ◽  
Best Linear Unbiased ◽  
Best Linear Unbiased Estimators

scholarly journals On decompositions of estimators under a general linear model with partial parameter restrictions

2017 ◽  
Vol 15 (1) ◽  
pp. 1300-1322 ◽  
Author(s):  
Bo Jiang ◽  
Yongge Tian ◽  
Xuan Zhang
Keyword(s):  
Linear Model ◽  
General Linear Model ◽  
Matrix Analysis ◽  
General Linear ◽  
Full Model ◽  
Linear Regression Models ◽  
Statistical Inferences ◽  
Best Linear Unbiased ◽  
Best Linear Unbiased Estimators ◽  
The Given

Abstract A general linear model can be given in certain multiple partitioned forms, and there exist submodels associated with the given full model. In this situation, we can make statistical inferences from the full model and submodels, respectively. It has been realized that there do exist links between inference results obtained from the full model and its submodels, and thus it would be of interest to establish certain links among estimators of parameter spaces under these models. In this approach the methodology of additive matrix decompositions plays an important role to obtain satisfactory conclusions. In this paper, we consider the problem of establishing additive decompositions of estimators in the context of a general linear model with partial parameter restrictions. We will demonstrate how to decompose best linear unbiased estimators (BLUEs) under the constrained general linear model (CGLM) as the sums of estimators under submodels with parameter restrictions by using a variety of effective tools in matrix analysis. The derivation of our main results is based on heavy algebraic operations of the given matrices and their generalized inverses in the CGLM, while the whole contributions illustrate various skillful uses of state-of-the-art matrix analysis techniques in the statistical inference of linear regression models.

scholarly journals Motility characterization of albumin sexed spermatozoa in two different diluents and additional antioxidant

2020 ◽  
Vol 45 (4) ◽  
pp. 277-286
Author(s):  
D. Ratnawati ◽  
M. Luthfi ◽  
D. Pamungkas ◽  
L. Affandhy
Keyword(s):  
Linear Model ◽  
Cold Storage ◽  
General Linear Model ◽  
General Linear ◽  
Spermatozoa Motility ◽  
Progressive Motility ◽  
Sexed Semen ◽  
Fresh Semen

The purpose of this study was to characterize spermatozoa motility of sexed semen (X and Y) using albumin by diluents and antioxidant treatments. The material used in this study was fresh semen of Ongole Crossbreed (OC) bull with progressive motility >70%. The sperm sexing methodology used albumin gradient of 5%, 10%, and 15%. The diluents used were CEP-2 and andromed with or without the addition of 1mM Glutathione as an antioxidant. The sexed semen was made into liquid semen and stored at 3-5°C. The motility was observed at day 0 (H0) and day 5 (H5). Motility was analyzed using SCA v.2.1. The parameters measured were total motility, progressive motility, VCL, VSL, VAP, LIN, STR, WOB, ALH, BCF and sperm hyperactive. The experimental applied was the factorial pattern 2 x 2. The first factor was the type of diluents (CEP-2 and Andromed), and the second factor was additional glutathione (with or without). Data was analyzed by general linear model of SPSS-IBM 24 program. Sexed semen with CEP-2 diluents showed better motility of spermatozoa than andromed in the upper layers (spermatozoa X) and lower layers (spermatozoa Y). The CEP-2 diluent had a big role to maintain motility, progressive motility and velocity spermatozoa during cold storage. The addition of Glutathione 1mM could support the motility of sexed spermatozoa at cold storage, especially for LIN, STR, and WOB values. 

Decomposition of approaches of a general linear model with fixed parameters

2017 ◽  
Vol 32 ◽  
pp. 232-253 ◽  
Author(s):  
Bo Jiang ◽  
Yongge Tian
Keyword(s):  
Linear Model ◽  
Sufficient Conditions ◽  
Algebraic Approach ◽  
General Linear Model ◽  
Ordinary Least Squares ◽  
Generalized Inverses ◽  
Matrix Analysis ◽  
General Linear ◽  
Linear Regression Models ◽  
Best Linear Unbiased Estimators

The well-known ordinary least-squares estimators (OLSEs) and the best linear unbiased estimators (BLUEs) under linear regression models can be represented by certain closed-form formulas composed by the given matrices and their generalized inverses in the models. This paper provides a general algebraic approach to relationships between OLSEs and BLUEs of the whole and partial mean parameter vectors in a constrained general linear model (CGLM) with fixed parameters by using a variety of matrix analysis tools on generalized inverses of matrices and matrix rank formulas. In particular, it establishes a variety of necessary and sufficient conditions for OLSEs to be BLUEs under a CGLM, which include many reasonable statistical interpretations on the equalities of OLSEs and BLUEs of parameter space in the CGLM. The whole work shows how to effectively establish matrix equalities composed by matrices and their generalized inverses and how to use them when characterizing performances of estimators of parameter spaces in linear models under most general assumptions.

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