A Least Squares Estimate, Nonquadratic Losses, and Gaussian Distributions

1992 ◽  
Vol 36 (1) ◽  
pp. 115-123 ◽  
Author(s):  
A. A. Zinger ◽  
A. M. Kagan
Keyword(s):  
Least Squares ◽  
Gaussian Distributions ◽  
Least Squares Estimate

A Least Squares Estimate of Satellite Attitude (Grace Wahba)

SIAM Review ◽  
1966 ◽  
Vol 8 (3) ◽  
pp. 384-386 ◽  
Author(s):  
J. L. Farrell ◽  
J. C. Stuelpnagel ◽  
R. H. Wessner ◽  
J. R. Velman ◽  
J. E. Brook
Keyword(s):  
Least Squares ◽  
Least Squares Estimate ◽  
Satellite Attitude

scholarly journals Tracking—A

2021 ◽  
pp. 163-192
Author(s):  
Jean Walrand
Keyword(s):  
Kalman Filter ◽  
Linear Regression ◽  
Least Squares ◽  
Recursive Algorithm ◽  
Nonlinear Function ◽  
Random Variables ◽  
Random Variable ◽  
Linear Least Squares ◽  
Least Squares Estimate ◽  
Related Notion

AbstractThis chapter explains how to estimate an unobserved random variable or vector from available observations. This problem arises in many examples, as illustrated in Sect. 9.1. The basic problem is defined in Sect. 9.2. One commonly used approach is the linear least squares estimate explained in Sect. 9.3. A related notion is the linear regression covered in Sect. 9.4. Section 9.5 comments on the problem of overfitting. Sections 9.6 and 9.7 explain the minimum means squares estimate that may be a nonlinear function of the observations and the remarkable fact that it is linear for jointly Gaussian random variables. Section 9.8 is devoted to the Kalman filter, which is a recursive algorithm for calculating the linear least squares estimate of the state of a system given previous observations.

Least-squares estimation of diet composition from n-alkanes in herbage and faeces using matrix mathematics

1995 ◽  
Vol 46 (4) ◽  
pp. 793 ◽  
Author(s):  
JA Newman ◽  
WA Thompson ◽  
PD Penning ◽  
RW Mayes
Keyword(s):  
Least Squares ◽  
Diet Composition ◽  
Least Squares Estimation ◽  
Simultaneous Equations ◽  
Desirable Property ◽  
Least Squares Estimate ◽  
Ruminant Animals

It is possible to estimate diet composition from an analysis of n-alkanes in the faeces of ruminant animals. For instance, to estimate the proportion of two species in a diet, two equations are constructed using the known concentrations of two different n-alkanes in the herbage and in the animal's faeces. These two equations are solved for the two unknown quantities of the diet components. Two problems exist with this method. First, it is often the case that we have estimated concentrations of more than two different n-alkanes. This can lead to a problem in deciding which two n-alkanes to use to construct the simultaneous equations. The choice of this pair of n-alkanes is arbitrary in its selection and wasteful of other useful information. The second problem is that sometimes the solution to the simultaneous equations yields nonsensical answers, such as a negative proportion of one species in the diet. In addition to making it difficult to estimate dietary proportions, estimating digestibility becomes impossible. In this paper, we present a technique which provides an estimate of the dietary proportions. This estimate uses information on all the n-alkanes available, and it has a very desirable property of being a least squares estimate. We also present a method for determining the least squares estimate subject to the constraint that all proportions must be non-negative. We provide examples for estimating the proportions of grass and clover in the diet of sheep and the digestibility of those diets.

scholarly journals The Implications of Intergenic Polymorphism for Major Histocompatibility Complex Evolution

Genetics ◽  
2000 ◽  
Vol 156 (2) ◽  
pp. 867-877 ◽  
Author(s):  
Colm O'hUigin ◽  
Yoko Satta ◽  
Anja Hausmann ◽  
Roger L Dawkins ◽  
Jan Klein
Keyword(s):  
Major Histocompatibility Complex ◽  
Least Squares ◽  
Balancing Selection ◽  
Low Frequency ◽  
Least Squares Estimate ◽  
B Locus ◽  
Histocompatibility Complex ◽  
Intergenic Regions ◽  
Major Histocompatibility Complex Evolution ◽  
High Degree

Abstract A systematic survey of six intergenic regions flanking the human HLA-B locus in eight haplotypes reveals the regions to be up to 20 times more polymorphic than the reported average degree of human neutral polymorphism. Furthermore, the extent of polymorphism is directly related to the proximity to the HLA-B locus. Apparently linkage to HLA-B locus alleles, which are under balancing selection, maintains the neutral polymorphism of adjacent regions. For these linked polymorphisms to persist, recombination in the 200-kb interval from HLA-B to TNF must occur at a low frequency. The high degree of polymorphism found distal to HLA-B suggests that recombination is uncommon on both sides of the HLA-B locus. The least-squares estimate is 0.15% per megabase with an estimated range from 0.02 to 0.54%. These findings place strong restrictions on possible recombinational mechanisms for the generation of diversity at the HLA-B.

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