Asymptotic normality of least squares estimates of the regression coefficients of homogeneous and isotropic random fields

Cybernetics ◽  
1977 ◽  
Vol 13 (2) ◽  
pp. 260-265
Author(s):  
N. N. Leonenko ◽  
M. I. Yadrenko
Keyword(s):  
Asymptotic Normality ◽  
Least Squares ◽  
Random Fields ◽  
Regression Coefficients ◽  
Least Squares Estimates ◽  
Isotropic Random

scholarly journals A Note on the Asymptotic Normality Theory of the Least Squares Estimates in Multivariate HAR-RV Models

Mathematics ◽  
2020 ◽  
Vol 8 (11) ◽  
pp. 2083
Author(s):  
Won-Tak Hong ◽  
Jiwon Lee ◽  
Eunju Hwang
Keyword(s):  
Asymptotic Normality ◽  
Least Squares ◽  
Average Length ◽  
Real Data ◽  
Spot Price ◽  
Correlated Errors ◽  
Sample Mean ◽  
Q Model ◽  
Multiple Assets ◽  
Least Squares Estimates

In this work, multivariate heterogeneous autoregressive-realized volatility (HAR-RV) models are discussed with their least squares estimations. We consider multivariate HAR models of order p with q multiple assets to explore the relationships between two or more assets’ volatility. The strictly stationary solution of the HAR(p,q) model is investigated as well as the asymptotic normality theories of the least squares estimates are established in the cases of i.i.d. and correlated errors. In addition, an exponentially weighted multivariate HAR model with a common decay rate on the coefficients is discussed together with the common rate estimation. A Monte Carlo simulation is conducted to validate the estimations: sample mean and standard error of the estimates as well as empirical coverage and average length of confidence intervals are calculated. Lastly, real data of volatility of Gold spot price and S&P index are applied to the model and it is shown that the bivariate HAR model fitted by selected optimal lags and estimated coefficients is well matched with the volatility of the financial data.

Asymptotic Normality of the Least-Squares Estimates for Higher Order Autoregressive Integrated Processes with Some Applications

1993 ◽  
Vol 9 (2) ◽  
pp. 263-282 ◽  
Author(s):  
In Choi
Keyword(s):  
Asymptotic Normality ◽  
Least Squares ◽  
Confidence Intervals ◽  
Unit Roots ◽  
Small Sample ◽  
Asymptotic Distributions ◽  
Standard Normal Distribution ◽  
Finite Sample ◽  
Standard Normal ◽  
Least Squares Estimates

Using the asymptotic normality of the least-squares estimates for the autoregressive (AR) process with real, positive unit roots and at least one stable root, we consider the asymptotic distributions of the Wald and t ratio tests on AR coefficients. In addition, we propose a method of constructing confidence intervals for the sum of AR coefficients possibly in the presence of a unit root. Using simulation methods, we compare the finite-sample cumulative distributions of the t ratios for individual autoregressive coefficients with those of standard normal distributions, and investigate the finite-sample performance of our confidence intervals and t ratios. Our simulation results show that the t ratios for nonstationary processes converge to a standard normal distribution more slowly than those for stationary processes. Further, the confidence intervals are shown to work reasonably well in moderately large samples, but they display unsatisfactory performance at small sample sizes.

scholarly journals Generalized least squares estimates for mixture of nonlinear regressions

2018 ◽  
pp. 25-29 ◽  
Author(s):  
V. Miroshnychenko
Keyword(s):  
Least Squares ◽  
Generalized Estimating Equations ◽  
Regression Models ◽  
Generalized Least Squares ◽  
Regression Coefficients ◽  
Nonlinear Regression Model ◽  
Logistic Regression Models ◽  
Continuous Response ◽  
True Number ◽  
Least Squares Estimates

We consider data in which each observed subject belongs to one of different subpopulations (components). The true number of component which a subject belongs to is unknown, but the researcher knows the probabilities that a subject belongs to a given component (concentration of the component in the mixture). The concentrations are different for different observations. So the distribution of the observed data is a mixture of components’ distributions with varying concentrations. A set of variables is observed for each subject. Dependence between these variables is described by a nonlinear regression model. The coefficients of this model are different for different components. An estimator is proposed for these regression coefficients estimation based on the least squares and generalized estimating equations. Consistency of this estimator is demonstrated under general assumptions. A mixture of logistic regression models with continuous response is considered as an example. It is shown that the general consistency conditions are satisfied for this model under very mild assumptions. Performance of the estimator is assessed by simulations.

scholarly journals Representation and prediction for locally harmonizable isotropic random fields

1995 ◽  
Vol 8 (2) ◽  
pp. 101-114 ◽  
Author(s):  
Randall J. Swift
Keyword(s):  
Least Squares ◽  
Random Fields ◽  
Natural Extension ◽  
Linear Least Squares ◽  
Spectral Representations ◽  
Isotropic Random

The class of harmonizable fields is a natural extension of the class of stationary fields. This paper considers fields whose increments are harmonizable and isotropic. Spectral representations are obtained for locally harmonizable isotropic fields. A linear least squares prediction for locally harmonizable isotropic fields is considered.

scholarly journals Needlet approximation for isotropic random fields on the sphere

2017 ◽  
Vol 216 ◽  
pp. 86-116 ◽  
Author(s):  
Quoc T. Le Gia ◽  
Ian H. Sloan ◽  
Yu Guang Wang ◽  
Robert S. Womersley
Keyword(s):  
Random Fields ◽  
Isotropic Random
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