Strong consistency and asymptotic normality of least squares estimators for PGARCH and models

2010 ◽  
Vol 80 (19-20) ◽  
pp. 1532-1542 ◽  
Author(s):  
Abdelouahab Bibi ◽  
Ines Lescheb
Keyword(s):  
Asymptotic Normality ◽  
Least Squares ◽  
Strong Consistency ◽  
Least Squares Estimators ◽  
Consistency And Asymptotic Normality

Functional least squares estimators in an additive effects outliers model

1990 ◽  
Vol 48 (2) ◽  
pp. 299-319 ◽  
Author(s):  
Sunil K. Dhar
Keyword(s):  
Asymptotic Behavior ◽  
Weak Convergence ◽  
Gaussian Process ◽  
Least Squares ◽  
Strong Consistency ◽  
Additive Effects ◽  
Uniform Consistency ◽  
Least Squares Estimators

AbstractConsider the additive effects outliers (A.O.) model where one observes , with The sequence of r.v.s is independent of and , are i.i.d. with d.f. , where the d.f.s Ln, n ≦ 0, are not necessarily known and εj's are i.i.d.. This paper discusses the asymptotic behavior of functional least squares estimators under the above model. Uniform consistency and uniform strong consistency of these estimators are proven. The weak convergence of these estimators to a Gaussian process and their asymptotic biases are also discussed under the above A.O. model.

On strong consistency and asymptotic normality of one-step Gauss-Newton estimators in ARMA time series models

Statistics ◽  
2020 ◽  
Vol 54 (5) ◽  
pp. 1030-1057
Author(s):  
Pierre Duchesne ◽  
Pierre Lafaye de Micheaux ◽  
Joseph François Tagne Tatsinkou
Keyword(s):  
Time Series ◽  
Asymptotic Normality ◽  
Strong Consistency ◽  
Time Series Models ◽  
One Step ◽  
Consistency And Asymptotic Normality

scholarly journals Strong Consistency of Estimators in a Partially Linear Model with Asymptotically Almost Negatively Associated Errors

2020 ◽  
Vol 2020 ◽  
pp. 1-19
Author(s):  
Yu Zhang ◽  
Xinsheng Liu ◽  
Mohamed Sief
Keyword(s):  
Least Squares ◽  
Strong Consistency ◽  
Weighted Least Squares ◽  
Partially Linear Model ◽  
Random Errors ◽  
Negatively Associated ◽  
Partially Linear ◽  
Least Squares Estimators ◽  
Special Cases ◽  
Asymptotically Almost Negatively Associated

This paper studies a heteroscedastic partially linear regression model in which the errors are asymptotically almost negatively associated (AANA, in short) random variables with not necessarily identical distribution and zero mean. Under some mild conditions, we establish the strong consistency of least squares estimators, weighted least squares estimators, and the ultimate weighted least squares estimators for the unknown parameter, respectively. In addition, the strong consistency of the estimator for nonparametric component is also investigated. The results derived in the paper include the corresponding ones of independent random errors and some dependent random errors as special cases. At last, two simulations are carried out to study the numerical performance of the strong consistency for least squares estimators and weighted least squares estimators of the unknown parametric and nonparametric components in the model.

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