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In this paper, we consider the normalized least squares estimator of the parameter in a mildly stationary first-order autoregressive (AR(1)) model with dependent errors which are modeled as a mildly stationary AR(1) process. By martingale…

Probability · Mathematics 2023-11-08 Hui Jiang , Guangyu Yang , Mingming Yu

This paper is concerned with the least squares estimator for a basic class of nonlinear autoregressive models, whose outputs are not necessarily to be ergodic. Several asymptotic properties of the least squares estimator have been…

Probability · Mathematics 2019-09-17 Zhaobo Liu , Chanying Li

In applications it is common that the exact form of a conditional expectation is unknown and having flexible functional forms can lead to improvements. Series method offers that by approximating the unknown function based on $k$ basis…

Methodology · Statistics 2017-10-05 Alexandre Belloni , Victor Chernozhukov , Denis Chetverikov , Kengo Kato

This paper considers the effect of least squares procedures for nearly unstable linear time series with strongly dependent innovations. Under a general framework and appropriate scaling, it is shown that ordinary least squares procedures…

Statistics Theory · Mathematics 2009-09-29 Boris Buchmann , Ngai Hang Chan

In this paper, by employing the asymptotic expansion method, we prove the existence and uniqueness of a smoothing solution for a time-dependent nonlinear singularly perturbed partial differential equation (PDE) with a small-scale parameter.…

Numerical Analysis · Mathematics 2022-10-11 Dmitrii Chaikovskii , Ye Zhang

In the one-parameter regression model with AR(1) and AR(2) errors we find explicit expressions and a continuous approximation of the optimal discrete design for the signed least square estimator. The results are used to derive the optimal…

Statistics Theory · Mathematics 2016-02-12 Holger Dette , Andrey Pepelyshev , Anatoly Zhigljavsky

The aim of this paper is to define a nonlinear least squares estimator for the spectral parameters of a spherical autoregressive process of order 1 in a parametric setting. Furthermore, we investigate on its asymptotic properties, such as…

Statistics Theory · Mathematics 2021-07-20 Alessia Caponera , Claudio Durastanti

De Haan and Pereira (2006) provided models for spatial extremes in the case of stationarity, which depend on just one parameter {\beta} > 0 measuring tail dependence, and they proposed different estimators for this parameter. This framework…

Statistics Theory · Mathematics 2012-02-24 Stefan Aulbach , Michael Falk

In this paper, an alternative approximation to the innovation method is introduced for the parameter estimation of diffusion processes from partial and noisy observations. This is based on a convergent approximation to the first two…

Optimization and Control · Mathematics 2013-12-19 J. C. Jimenez

We consider parametric estimation and tests for multi-dimensional diffusion processes with a small dispersion parameter $\varepsilon$ from discrete observations. For parametric estimation of diffusion processes, the main target is to…

Statistics Theory · Mathematics 2022-01-20 Tetsuya Kawai , Masayuki Uchida

Chirp signals are quite common in many natural and man-made systems like audio signals, sonar, radar etc. Estimation of the unknown parameters of a signal is a fundamental problem in statistical signal processing. Recently, Kundu and Nandi…

Applications · Statistics 2018-04-05 Rhythm Grover , Debasis Kundu , Amit Mitra

We prove mixing convergence of the least squares estimator of autoregressive parameters for supercritical autoregressive processes of order 2 with Gaussian innovations having real characteristic roots with different absolute values. We use…

Statistics Theory · Mathematics 2025-09-16 Matyas Barczy , Fanni Nedényi , Gyula Pap

We consider the problem of estimating the parameters of a linear univariate autoregressive model with sub-Gaussian innovations from a limited sequence of consecutive observations. Assuming that the parameters are compressible, we analyze…

Information Theory · Computer Science 2017-04-05 Abbas Kazemipour , Sina Miran , Piya Pal , Behtash Babadi , Min Wu

In this paper, we study parametric nonlinear regression under the Harris recurrent Markov chain framework. We first consider the nonlinear least squares estimators of the parameters in the homoskedastic case, and establish asymptotic theory…

Statistics Theory · Mathematics 2016-09-15 Degui Li , Dag Tjøstheim , Jiti Gao

Matrix completion algorithms recover a low rank matrix from a small fraction of the entries, each entry contaminated with additive errors. In practice, the singular vectors and singular values of the low rank matrix play a pivotal role for…

Methodology · Statistics 2016-05-03 Juhee Cho , Donggyu Kim , Karl Rohe

Robust inference based on the minimization of statistical divergences has proved to be a useful alternative to the classical techniques based on maximum likelihood and related methods. Recently Ghosh et al. (2013) proposed a general class…

Methodology · Statistics 2016-07-04 Abhik Ghosh

Least absolute deviation regression is applied using a fixed number of points for all values of the index to estimate the index and scale parameter of the stable distribution using regression methods based on the empirical characteristic…

Computation · Statistics 2018-11-06 J. Martin van Zyl

This paper deals with the problem of global parameter estimation of affine diffusions in $\mathbb{R}_+ \times \mathbb{R}^n$ denoted by $AD(1, n)$ where $n$ is a positive integer which is a subclass of affine diffusions introduced by Duffie…

Statistics Theory · Mathematics 2023-03-16 Mohamed Ben Alaya , Houssem Dahbi , Hamdi Fathallah

In this paper analyzes \textit{The Erd\H{o}s-Straus conjecture} asserts that $f$$(n)$ $>$ 0 for every $n$ $\geq$ 2, where $f(n)$ indicates the number of solutions to the Diophantine Equation…

General Mathematics · Mathematics 2016-09-02 Elias Rios

There has been a growing interest in providing models for multivariate spatial processes. A majority of these models specify a parametric matrix covariance function. Based on observations, the parameters are estimated by maximum likelihood…

Statistics Theory · Mathematics 2016-02-10 François Bachoc , Reinhard Furrer