Yule–Walker type estimators in periodic bilinear models: strong consistency and asymptotic normality

2008 ◽  
Vol 19 (1) ◽  
pp. 1-30 ◽  
Author(s):  
Abdelouahab Bibi ◽  
Abdelhakim Aknouche
Keyword(s):  
Asymptotic Normality ◽  
Strong Consistency ◽  
Bilinear Models ◽  
Consistency And Asymptotic Normality

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 Nonparametric estimation of boundary measures and related functionals: asymptotic results

2009 ◽  
Vol 41 (2) ◽  
pp. 311-322 ◽  
Author(s):  
Inés Armendáriz ◽  
Antonio Cuevas ◽  
Ricardo Fraiman
Keyword(s):  
Asymptotic Normality ◽  
Surface Area ◽  
Nonparametric Estimation ◽  
Strong Consistency ◽  
Nonparametric Method ◽  
Asymptotic Results ◽  
Minkowski Content ◽  
Compact Body ◽  
Consistency And Asymptotic Normality ◽  
The One

We study a nonparametric method for estimating the boundary measure of a compact body G ⊂ ℝd (the boundary length when d = 2 and the surface area for d = 3) in the case when this measure agrees with the corresponding Minkowski content. The estimator we consider is closely related to the one proposed in Cuevas, Fraiman and Rodríguez-Casal (2007). Our method relies on two sets of random points, drawn inside and outside the set G, with different sampling intensities. Strong consistency and asymptotic normality are obtained under some shape hypotheses on the set G. Some applications and practical aspects are briefly discussed.

THE GLOBAL WEIGHTED LAD ESTIMATORS FOR FINITE/INFINITE VARIANCE ARMA(p,q) MODELS

2012 ◽  
Vol 28 (5) ◽  
pp. 1065-1086 ◽  
Author(s):  
Ke Zhu ◽  
Shiqing Ling
Keyword(s):  
Time Series ◽  
Asymptotic Normality ◽  
Simulation Study ◽  
Strong Consistency ◽  
Asymptotic Theory ◽  
Infinite Variance ◽  
Time Series Models ◽  
Absolute Deviation ◽  
Consistency And Asymptotic Normality ◽  
First Time

This paper investigates the global self-weighted least absolute deviation (SLAD) estimator for finite and infinite variance ARMA(p, q) models. The strong consistency and asymptotic normality of the global SLAD estimator are obtained. A simulation study is carried out to assess the performance of the global SLAD estimators. In this paper the asymptotic theory of the global LAD estimator for finite and infinite variance ARMA(p, q) models is established in the literature for the first time. The technique developed in this paper is not standard and can be used for other time series models.

scholarly journals Nonparametric estimation of boundary measures and related functionals: asymptotic results

2009 ◽  
Vol 41 (02) ◽  
pp. 311-322 ◽  
Author(s):  
Inés Armendáriz ◽  
Antonio Cuevas ◽  
Ricardo Fraiman
Keyword(s):  
Asymptotic Normality ◽  
Surface Area ◽  
Nonparametric Estimation ◽  
Strong Consistency ◽  
Nonparametric Method ◽  
Asymptotic Results ◽  
Minkowski Content ◽  
Compact Body ◽  
Consistency And Asymptotic Normality ◽  
The One

We study a nonparametric method for estimating the boundary measure of a compact body G ⊂ ℝ d (the boundary length when d = 2 and the surface area for d = 3) in the case when this measure agrees with the corresponding Minkowski content. The estimator we consider is closely related to the one proposed in Cuevas, Fraiman and Rodríguez-Casal (2007). Our method relies on two sets of random points, drawn inside and outside the set G, with different sampling intensities. Strong consistency and asymptotic normality are obtained under some shape hypotheses on the set G. Some applications and practical aspects are briefly discussed.

scholarly journals PARAMETER ESTIMATION IN NONLINEAR AR–GARCH MODELS

2011 ◽  
Vol 27 (6) ◽  
pp. 1236-1278 ◽  
Author(s):  
Mika Meitz ◽  
Pentti Saikkonen
Keyword(s):  
Asymptotic Normality ◽  
Autoregressive Models ◽  
Garch Models ◽  
Martingale Difference ◽  
First Order ◽  
First Results ◽  
Consistency And Asymptotic Normality ◽  
Quasi Maximum Likelihood ◽  
Nonlinear Autoregressive ◽  
Nonlinear Autoregressive Models

This paper develops an asymptotic estimation theory for nonlinear autoregressive models with conditionally heteroskedastic errors. We consider a general nonlinear autoregression of order p (AR(p)) with the conditional variance specified as a general nonlinear first-order generalized autoregressive conditional heteroskedasticity (GARCH(1,1)) model. We do not require the rescaled errors to be independent, but instead only to form a stationary and ergodic martingale difference sequence. Strong consistency and asymptotic normality of the global Gaussian quasi-maximum likelihood (QML) estimator are established under conditions comparable to those recently used in the corresponding linear case. To the best of our knowledge, this paper provides the first results on consistency and asymptotic normality of the QML estimator in nonlinear autoregressive models with GARCH errors.

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