Efficient Digital Pre-filtering for Least-Squares Linear Approximation

2006 ◽  
pp. 161-169 ◽  
Author(s):  
Marco Dalai ◽  
Riccardo Leonardi ◽  
Pierangelo Migliorati
Keyword(s):  
Least Squares ◽  
Linear Approximation

Continuous and Discontinuous Linear Approximation of the Window Spectrum by Least Squares Method

2011 ◽  
Vol 18 (3) ◽  
pp. 379-390 ◽  
Author(s):  
Józef Borkowski
Keyword(s):  
Least Squares ◽  
Linear Approximation ◽  
Least Squares Method ◽  
Analytical Form ◽  
Linear Functions ◽  
Approximation Solution ◽  
Approximation Accuracy ◽  
Approximation Characteristic ◽  
Zero Padding ◽  
Approximation Parameter

Continuous and Discontinuous Linear Approximation of the Window Spectrum by Least Squares Method This paper presents the general solution of the least-squares approximation of the frequency characteristic of the data window by linear functions combined with zero padding technique. The approximation characteristic can be discontinuous or continuous, what depends on the value of one approximation parameter. The approximation solution has an analytical form and therefore the results have universal character. The paper presents derived formulas, analysis of approximation accuracy, the exemplary characteristics and conclusions, which confirm high accuracy of the approximation. The presented solution is applicable to estimating methods, like the LIDFT method, visualizations, etc.

XVI.—Studies in Practical Mathematics. IV. On Linear Approximation by Least Squares

1946 ◽  
Vol 62 (2) ◽  
pp. 138-146 ◽  
Author(s):  
A. C. Aitken
Keyword(s):  
Least Squares ◽  
Linear Approximation ◽  
Linear Representation ◽  
Moment Matrix ◽  
Linear Transformations ◽  
Matrix Methods ◽  
Variance Matrix ◽  
Practical Mathematics ◽  
Algebra Of Matrices ◽  
The Way

R. Frisch, in a paper (Frisch, 1928) on correlation and scatter in statistical variables, made an extensive use of matrices, and in particular of the moment matrix, as he called it, of a set of variables. The matrices were square arrays, with an equal number of rows and columns. This paper of Frisch pointed the way to an even more extensive use of the algebra of matrices in problems of statistics.What Frisch called the moment matrix may perhaps be more suitably called, nowadays, the variance matrix of a set or vector of variates, since the moments in question are all variances or covariances. In the present paper, which is illustrative of matrix methods, we explore the familiar ground of linear approximation by Least Squares, making full use of the properties of the variance matrix. We also study the linear transformations that convert crude data into smoothed or graduated values, or into residuals, or into coefficients in a linear representation by chosen functions.

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.

Sign in / Sign up

Export Citation Format

Share Document