Large deviations of regression parameter estimator in continuous-time models with sub-Gaussian noise

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].

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“…The next example demonstrates the fulfillment of the condition C 2 (compare with Ivanov and Orlovskyi [39]).…”

Section: Appendix a Lse Consistencymentioning

confidence: 74%

“…(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: 99%

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

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Large deviation inequalities of Bayesian estimator in nonlinear regression models

Miao

Tang²

2022

Stat Inference Stoch Process

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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

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Large deviations of regression parameter estimator in continuous-time models with sub-Gaussian noise

Abstract: A continuous-time regression model with a jointly strictly sub-Gaussian random noise is considered in the paper. Upper exponential bounds for probabilities of large deviations of the least squares estimator for the regression parameter are obtained.

Cited by 3 publications

References 12 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

Large deviation inequalities of Bayesian estimator in nonlinear regression models

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

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