On the Whittle Estimator of the Parameter of Spectral Density of Random Noise in the Nonlinear Regression Model

Ivanov, A. V.; Prykhodko, Vladyslav

doi:10.1007/s11253-016-1145-1

Cited by 5 publications

(4 citation statements)

References 18 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…(41) Note that the functions (41) are continuous on R × Θ c as well as functions (39) and (40). Therefore the condition N 4 (iii) is fulfilled.…”

Section: Example the Motion Of A Pendulum In A Turbulent Fluidmentioning

confidence: 98%

“…In the paper by Ivanov and Prihod'ko [40] sufficient conditions on consistency and asymptotic normality of the Whittle estimator of the spectral density parameter of the Gaussian stationary random noise in continuous-time nonlinear regression model were obtained using residual periodogram. The current paper continues this research extending it to the case of the LГқvy-driven linear random noise and more general classes of regression functions including trigonometric ones.…”

mentioning

confidence: 99%

“…The current paper continues this research extending it to the case of the LГқvy-driven linear random noise and more general classes of regression functions including trigonometric ones. We use the scheme of the proof in the case of Gaussian noise [40] and some results of the papers [4,6]. For linear random noise the proofs utilize essentially another types of limits theorems.…”

mentioning

confidence: 99%

See 2 more Smart Citations

On the Whittle estimator for linear random noise spectral density parameter in continuous-time nonlinear regression models

Ivanov

Leonenko

Orlovskyi

2019

Stat Inference Stoch Process

View full text Add to dashboard Cite

A continuous-time nonlinear regression model with LГқvy-driven linear noise process is considered. Sufficient conditions of consistency and asymptotic normality of the Whittle estimator for the parameter of the noise spectral density are obtained in the paper. IntroductionThe paper is focused on such an important aspect of the study of regression models with correlated observations as an estimation of random noise functional characteristics. When considering this problem the regression function unknown parameter becomes nuisance and complicates the analysis of noise. To neutralise its presence, we must estimate the parameter and then build estimators, say, of spectral density parameter of a stationary random noise using residuals, that is the difference between the values of the observed process and fitted regression function.So, in the first step we employ the least squares estimator (LSE) for unknown parameter of nonlinear regression, because of its relative simplicity. Asymptotic properties of the LSE in nonlinear regression model were studied by many authors. Numerous results on the subject can be found in monograph by Ivanov and Leonenko [34], Ivanov [32].

show abstract

“…(41) Note that the functions (41) are continuous on R × Θ c as well as functions (39) and (40). Therefore the condition N 4 (iii) is fulfilled.…”

Section: Example the Motion Of A Pendulum In A Turbulent Fluidmentioning

confidence: 98%

mentioning

confidence: 99%

mentioning

confidence: 99%

See 1 more Smart Citation

On the Whittle estimator for linear random noise spectral density parameter in continuous-time nonlinear regression models

Ivanov

Leonenko

Orlovskyi

2019

Stat Inference Stoch Process

View full text Add to dashboard Cite

show abstract

“…For the stationary noise it can be estimation of the noise spectral density or covariance function. Asymptotic properties of the Whittle and Ibragimov estimators of spectral density parameters in the continuous time nonlinear regression model were considered in Ivanov and Prykhod'ko [16,15], Ivanov et al [17]. Exponential bounds for the probabilities of large deviations of the stationary Gaussian noise covariance function in the similar regression model are obtained in Ivanov et al [11].…”

Section: Introductionmentioning

confidence: 99%

Asymptotic normality of the residual correlogram in the continuous-time nonlinear regression model

Ivanov¹,

Moskvychova²

2020

Modern Stochastics: Theory and Applications

View full text Add to dashboard Cite

Large deviations of the correlogram estimator of the random noise covariance function in the nonlinear regression model

Ivanov

Kozachenko

Moskvychova

2020

Communications in Statistics - Theory and Methods

View full text Add to dashboard Cite

On the Whittle Estimator of the Parameter of Spectral Density of Random Noise in the Nonlinear Regression Model

Abstract: We consider a nonlinear regression model with continuous time and establish the consistency and asymptotic normality of the Whittle minimum contrast estimator for the parameter of spectral density of stationary Gaussian noise.

Cited by 5 publications

References 18 publications

On the Whittle estimator for linear random noise spectral density parameter in continuous-time nonlinear regression models

On the Whittle estimator for linear random noise spectral density parameter in continuous-time nonlinear regression models

Asymptotic normality of the residual correlogram in the continuous-time nonlinear regression model

Large deviations of the correlogram estimator of the random noise covariance function in the nonlinear regression model

Contact Info

Product

Resources

About