The asymptotic normality for the least squares estimator of parameters in a two dimensional sinusoidal model of observations

2020 ◽  
Vol 100 ◽  
pp. 107-131
Author(s):  
O. V. Ivanov ◽  
O. V. Lymar
Keyword(s):  
Asymptotic Normality ◽  
Least Squares ◽  
Least Squares Estimator ◽  
Two Dimensional ◽  
Sinusoidal Model

On the least squares estimator asymptotic normality of the multivariate symmetric textured surface parameters

2021 ◽  
Vol 105 (0) ◽  
pp. 151-169
Author(s):  
A. Ivanov ◽  
I. Savych
Keyword(s):  
Asymptotic Normality ◽  
Least Squares ◽  
Random Noise ◽  
Least Squares Estimator ◽  
Textured Surface ◽  
Textured Surfaces ◽  
Bivariate Model ◽  
Content Type ◽  
Trigonometric Regression ◽  
Trigonometric Model

A multivariate trigonometric regression model is considered. Various discrete modifications of the similar bivariate model received serious attention in the literature on signal and image processing due to multiple applications in the analysis of symmetric textured surfaces. In the paper asymptotic normality of the least squares estimator for amplitudes and angular frequencies is obtained in multivariate trigonometric model assuming that the random noise is a homogeneous or homogeneous and isotropic Gaussian, in particular, strongly dependent random field on  R M , M > 2. \mathbb {R}^M,\,\, M>2.

Bridging the Gap between Quantitative and Qualitative Historical Research: an application of multiple regression analysis and homogeneity analysis with alternating least squares

1996 ◽  
Vol 8 (3) ◽  
pp. 133-144 ◽  
Author(s):  
María del Mar del Pozo Andrés ◽  
Jacques F A Braster
Keyword(s):  
Least Squares ◽  
Multiple Regression ◽  
Historical Research ◽  
Alternating Least Squares ◽  
Categorical Variables ◽  
Two Dimensional ◽  
Homogeneity Analysis ◽  
Regression Approach ◽  
Dimensional Picture ◽  
Selection Of

In this article we propose two research techniques that can bridge the gap between quantitative and qualitative historical research. These are: (1) a multiple regression approach that gives information about general patterns between numerical variables and the selection of outliers for qualitative analysis; (2) a homogeneity analysis with alternating least squares that results in a two-dimensional picture in which the relationships between categorical variables are graphically presented.

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