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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

We consider the semi-parametric estimation of a scale parameter of a one-dimensional Gaussian process with known smoothness. We suggest an estimator based on quadratic variations and on the moment method. We provide asymptotic…

Statistics Theory · Mathematics 2020-01-22 Jean-Marc Azaïs , François Bachoc , Agnès Lagnoux , Thi Mong Ngoc Nguyen

We construct an objective function that consists of a quadratic approximation term and a penalty term. Thanks to the quadratic approximation, we can deal with various kinds of loss functions into a unified way, and by taking advantage of…

Statistics Theory · Mathematics 2018-11-26 Takumi Suzuki , Nakahiro Yoshida

We consider model selection and estimation for partial spline models and propose a new regularization method in the context of smoothing splines. The regularization method has a simple yet elegant form, consisting of roughness penalty on…

Methodology · Statistics 2013-11-25 Guang Cheng , Hao Helen Zhang , Zuofeng Shang

In this Letter, we propose a low-complexity estimator for the correlation coefficient based on the signed $\operatorname{AR}(1)$ process. The introduced approximation is suitable for implementation in low-power hardware architectures. Monte…

Signal Processing · Electrical Eng. & Systems 2020-08-25 A. Borges , R. J. Cintra , D. F. G. Coelho , V. S. Dimitrov

We discuss parametric quasi-maximum likelihood estimation for quadratic ARCH process with long memory introduced in Doukhan et al. (2015) and Grublyt\.e and \v{S}karnulis (2015) with conditional variance given by a strictly positive…

Statistics Theory · Mathematics 2015-09-23 Ieva Grublytė , Donatas Surgailis , Andrius Škarnulis

The paper introduces a new estimation method for the standard linear regression model. The procedure is not driven by the optimisation of any objective function rather, it is a simple weighted average of slopes from observation pairs. The…

Econometrics · Economics 2024-02-27 Felix Chan , Laszlo Matyas

We study the problem of parameter estimation for reflected stochastic processes driven by a standard Brownian motion. The estimator is obtained using nonlinear least squares method based on discretely observed processes. Under some certain…

Statistics Theory · Mathematics 2022-05-03 Han Yuecai , Zhang Dingwen

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

It is now widely accepted that volatility models have to incorporate the so-called leverage effect in order to to model the dynamics of daily financial returns.We suggest a new class of multivariate power transformed asymmetric models. It…

Statistics Theory · Mathematics 2019-10-17 Yacouba Boubacar Maïnassara , Othman Kadmiri , Bruno Saussereau

We propose and investigate a new estimation method for the parameters of models consisting of smooth density functions on the positive half axis. The procedure is based on a recently introduced characterization result for the respective…

Statistics Theory · Mathematics 2021-06-16 Steffen Betsch , Bruno Ebner , Bernhard Klar

This paper develops the limit theory of the GARCH(1,1) process that moderately deviates from IGARCH process towards both stationary and explosive regimes. The GARCH(1,1) process is defined by equations $u_t = \sigma_t \varepsilon_t$,…

Statistics Theory · Mathematics 2021-07-22 Yubo Tao

We construct and analyze an estimator of association between random variables based on their similarity in both direction and magnitude. Under special conditions, the proposed measure becomes a robust and consistent estimator of the linear…

Econometrics · Economics 2026-01-21 Ilya Archakov

We present a new finite-time analysis of the estimation error of the Ordinary Least Squares (OLS) estimator for stable linear time-invariant systems. We characterize the number of observed samples (the length of the observed trajectory)…

Statistics Theory · Mathematics 2020-03-27 Yassir Jedra , Alexandre Proutiere

The $GARCH$ algorithm is the most renowned generalisation of Engle's original proposal for modelising {\it returns}, the $ARCH$ process. Both cases are characterised by presenting a time dependent and correlated variance or {\it…

Statistical Mechanics · Physics 2009-11-11 Silvio M. Duarte Queiros , Constantino Tsallis

We study the asymptotic behavior of the least squares estimators of the unknown parameters of bifurcating autoregressive processes. Under very weak assumptions on the driven noise of the process, namely conditional pair-wise independence…

Probability · Mathematics 2009-06-29 Bernard Bercu , Benoite de Saporta , Anne Gegout-Petit

This paper proposes a new algorithm for Gaussian process classification based on posterior linearisation (PL). In PL, a Gaussian approximation to the posterior density is obtained iteratively using the best possible linearisation of the…

Machine Learning · Computer Science 2019-04-19 Ángel F. García-Fernández , Filip Tronarp , Simo Särkkä

The quasi-maximum likelihood estimation is a commonly-used method for estimating GARCH parameters. However, such estimators are sensitive to outliers and their asymptotic normality is proved under the finite fourth moment assumption on the…

Statistics Theory · Mathematics 2020-09-03 Hang Liu , Kanchan Mukherjee

Consider a process satisfying a stochastic differential equation with unknown drift parameter, and suppose that discrete observations are given. It is known that a simple least squares estimator (LSE) can be consistent, but numerically…

Statistics Theory · Mathematics 2017-03-17 Yasutaka Shimizu

Strong consistency and asymptotic normality of the Gaussian pseudo-maximum likelihood estimate of the parameters in a wide class of ARCH$(\infty)$ processes are established. The conditions are shown to hold in case of exponential and…

Statistics Theory · Mathematics 2007-06-13 Peter M. Robinson , Paolo Zaffaroni