scholarly journals Least squares and shrinkage estimation under bimonotonicity constraints

2009 ◽  
Vol 20 (2) ◽  
pp. 177-189 ◽  
Author(s):  
Rudolf Beran ◽  
Lutz Dümbgen
Keyword(s):  
Least Squares ◽  
Shrinkage Estimation

Bayes and Empirical Bayes Shrinkage Estimation of Regression Coefficients: A Cross-Validation Study

1988 ◽  
Vol 13 (3) ◽  
pp. 199-213 ◽  
Author(s):  
Fassii Nebebe ◽  
T. W. F. Stroud
Keyword(s):  
Least Squares ◽  
Empirical Bayes ◽  
Cross Validation ◽  
Regression Coefficients ◽  
Data Sets ◽  
Shrinkage Estimation ◽  
Bayes Methods ◽  
Least Absolute Deviations ◽  
Empirical Bayes Methods ◽  
Empirical Bayes Approach

A Bayesian and an empirical Bayes approach to shrinkage estimation of regression coefficients and the uses of these in prediction are investigated. The methods, along with least squares and least absolute deviations, are applied to data sets of different sizes and cross-validated with observations not in the data sets. The fully Bayes and empirical Bayes methods are seen to perform consistently better in predicting the response variable than either of least squares or least absolute deviations.

Heteroscedastic Methods for Performing All Pairwise Comparisons of Regression Lines Associated With J Independent Groups

Methodology ◽  
2015 ◽  
Vol 11 (3) ◽  
pp. 110-115 ◽  
Author(s):  
Rand R. Wilcox ◽  
Jinxia Ma
Keyword(s):  
Least Squares ◽  
Pairwise Comparisons ◽  
Simple Extension ◽  
Type I ◽  
Type I Errors ◽  
Well Elderly ◽  
Using Data

Abstract. The paper compares methods that allow both within group and between group heteroscedasticity when performing all pairwise comparisons of the least squares lines associated with J independent groups. The methods are based on simple extension of results derived by Johansen (1980) and Welch (1938) in conjunction with the HC3 and HC4 estimators. The probability of one or more Type I errors is controlled using the improvement on the Bonferroni method derived by Hochberg (1988) . Results are illustrated using data from the Well Elderly 2 study, which motivated this paper.

An fMRI study examining spatial navigation through a virtual environment: Partial least squares analysis

2005 ◽  
Author(s):  
Richard Mraz ◽  
Nancy J. Lobaugh ◽  
Genevieve Quintin ◽  
Konstantine K. Kakzanis ◽  
Simon J. Graham
Keyword(s):  
Least Squares ◽  
Virtual Environment ◽  
Partial Least Squares ◽  
Spatial Navigation ◽  
Partial Least Squares Analysis ◽  
Fmri Study

‘Least squares’ method—theorem or law?

1980 ◽  
Vol 59 (9) ◽  
pp. 8
Author(s):  
D.E. Turnbull
Keyword(s):  
Least Squares ◽  
Least Squares Method

The Estimation of Blood Platelet Survival

1972 ◽  
Vol 28 (03) ◽  
pp. 447-456 ◽  
Author(s):  
E. A Murphy ◽  
M. E Francis ◽  
J. F Mustard
Keyword(s):  
Standard Deviation ◽  
Least Squares ◽  
Experimental Error ◽  
Blood Platelet ◽  
Least Squares Estimation ◽  
Systematic Relationship ◽  
Platelet Survival ◽  
The Mean ◽  
Normally Distributed

SummaryThe characteristics of experimental error in measurement of platelet radioactivity have been explored by blind replicate determinations on specimens taken on several days on each of three Walker hounds.Analysis suggests that it is not unreasonable to suppose that error for each sample is normally distributed ; and while there is evidence that the variance is heterogeneous, no systematic relationship has been discovered between the mean and the standard deviation of the determinations on individual samples. Thus, since it would be impracticable for investigators to do replicate determinations as a routine, no improvement over simple unweighted least squares estimation on untransformed data suggests itself.

Sign in / Sign up

Export Citation Format

Share Document