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 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.

scholarly journals NONPARAMETRIC ESTIMATION WITH AGGREGATED DATA

2002 ◽  
Vol 18 (2) ◽  
pp. 420-468 ◽  
Author(s):  
Oliver Linton ◽  
Yoon-Jae Whang
Keyword(s):  
Monte Carlo ◽  
Characteristic Function ◽  
Asymptotic Normality ◽  
Nonparametric Estimation ◽  
Regression Function ◽  
Rates Of Convergence ◽  
Monte Carlo Experiment ◽  
Aggregated Data ◽  
Practical Performance ◽  
Consistency And Asymptotic Normality

We introduce a kernel-based estimator of the density function and regression function for data that have been grouped into family totals. We allow for a common intrafamily component but require that observations from different families be independent. We establish consistency and asymptotic normality for our procedures. As usual, the rates of convergence can be very slow depending on the behavior of the characteristic function at infinity. We investigate the practical performance of our method in a simple Monte Carlo experiment.

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

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.

Nonparametric Estimation and Identification of Nonlinear ARCH Time Series Strong Convergence and Asymptotic Normality: Strong Convergence and Asymptotic Normality

1995 ◽  
Vol 11 (2) ◽  
pp. 258-289 ◽  
Author(s):  
Elias Masry ◽  
Dag Tjøstheim
Keyword(s):  
Time Series ◽  
Asymptotic Normality ◽  
Strong Convergence ◽  
Nonparametric Estimation ◽  
Strong Consistency ◽  
Rates Of Convergence ◽  
Regularity Conditions ◽  
Nonlinear Functions ◽  
Kernel Estimates ◽  
Nonparametric Kernel

We consider the estimation and identification of the functional structures of nonlinear econometric systems of the ARCH type. We employ nonparametric kernel estimates for the nonlinear functions characterizing the systems, and we establish strong consistency along with sharp rates of convergence under mild regularity conditions. We also prove the asymptotic normality of the estimates.

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