Estimation of Transition Distribution Function and its Quantiles in Markov Processes: Strong Consistency and Asymptotic Normality

1991 ◽  
pp. 443-462 ◽  
Author(s):  
George G. Roussas
Keyword(s):  
Distribution Function ◽  
Asymptotic Normality ◽  
Markov Processes ◽  
Strong Consistency ◽  
Transition Distribution ◽  
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 Asymptotic normality of conditional distribution estimation in the single index model

2017 ◽  
Vol 9 (1) ◽  
pp. 162-175
Author(s):  
Diaa Eddine Hamdaoui ◽  
Amina Angelika Bouchentouf ◽  
Abbes Rabhi ◽  
Toufik Guendouzi
Keyword(s):  
Distribution Function ◽  
Confidence Interval ◽  
Asymptotic Normality ◽  
Conditional Distribution ◽  
Conditional Distribution Function ◽  
Single Index ◽  
Index Model ◽  
Single Index Model ◽  
Distribution Estimation

AbstractThis paper deals with the estimation of conditional distribution function based on the single-index model. The asymptotic normality of the conditional distribution estimator is established. Moreover, as an application, the asymptotic (1 − γ) confidence interval of the conditional distribution function is given for 0 < γ < 1.

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