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We discuss some extensions of results from the recent paper by Chernoyarov et al. (Ann. Inst. Stat. Math., October 2016) concerning limit distributions of Bayesian and maximum likelihood estimators in the model "signal plus white noise"…

Statistics Theory · Mathematics 2017-05-23 Nino Kordzakhia , Yury Kutoyants , Alex Novikov , Lin-Yee Hin

In recent years, there has been a substantive interest in rough volatility models. In this class of models, the local behavior of stochastic volatility is much more irregular than semimartingales and resembles that of a fractional Brownian…

Statistics Theory · Mathematics 2024-06-17 Carsten Chong , Marc Hoffmann , Yanghui Liu , Mathieu Rosenbaum , Grégoire Szymanski

We prove the asymptotic mixed normality of the least absolute deviation (LAD) estimator for a locally $\alpha$-stable stochastic differential equation (SDE) observed at high frequency, where $\alpha\in(0,2)$. We investigate both ergodic and…

Statistics Theory · Mathematics 2026-03-31 Oleksii M. Kulyk , Hiroki Masuda

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

In this paper, we study non-asymptotic deviation bounds of the least squares estimator in Gaussian AR($n$) processes. By relying on martingale concentration inequalities and a tail-bound for $\chi^2$ distributed variables, we provide a…

Machine Learning · Statistics 2020-05-26 Rodrigo A. González , Cristian R. Rojas

Let alpha,T>0. We study the asymptotic properties of a least squares estimator for the parameter alpha of a fractional bridge defined as dX_t=-alpha*X_t/(T-t)dt+dB_t, with t in [0,T) and where B is a fractional Brownian motion of Hurst…

Probability · Mathematics 2013-08-06 Khalifa Es-Sebaiy , Ivan Nourdin

This paper discusses asymptotic distributions of various estimators of the underlying parameters in some regression models with long memory (LM) Gaussian design and nonparametric heteroscedastic LM moving average errors. In the simple…

Statistics Theory · Mathematics 2008-12-18 Hongwen Guo , Hira L. Koul

We define two minimum distance estimators for dependent data by minimizing some approximated Maximum Mean Discrepancy distances between the true empirical distribution of observations and their assumed (parametric) model distribution. When…

Methodology · Statistics 2026-01-19 Pierre Alquier , Jean-David Fermanian , Benjamin Poignard

In this article, we derive the weak limiting distribution of the least squares estimator (LSE) of a convex probability mass function (pmf) with a finite support. We show that it can be defined via a certain convex projection of a Gaussian…

Statistics Theory · Mathematics 2014-04-14 Fadoua Balabdaoui , Cécile Durot , François Koladjo

We study the problem of predicting as well as the best linear predictor in a bounded Euclidean ball with respect to the squared loss. When only boundedness of the data generating distribution is assumed, we establish that the least squares…

Statistics Theory · Mathematics 2021-03-09 Tomas Vaškevičius , Nikita Zhivotovskiy

Combining information both within and between sample realizations, we propose a simple estimator for the local regularity of surfaces in the functional data framework. The independently generated surfaces are measured with errors at…

Statistics Theory · Mathematics 2023-10-03 Omar Kassi , Nicolas Klutchnikoff , Valentin Patilea

We consider two nonparametric procedures for estimating a concave distribution function based on data corrupted with additive noise generated by a bounded decreasing density on $(0,\infty)$. For the maximum likelihood (ML) estimator and…

Statistics Theory · Mathematics 2009-04-02 Geurt Jongbloed , Frank H. van der Meulen

The problem of estimating a linear functional based on observational data is canonical in both the causal inference and bandit literatures. We analyze a broad class of two-stage procedures that first estimate the treatment effect function,…

Statistics Theory · Mathematics 2022-09-28 Wenlong Mou , Martin J. Wainwright , Peter L. Bartlett

This paper deals with the consistency of the least squares estimator of a convex regression function when the predictor is multidimensional. We characterize and discuss the computation of such an estimator via the solution of certain…

Statistics Theory · Mathematics 2015-03-13 Emilio Seijo , Bodhisattva Sen

We study asymptotic properties of some (essentially conditional least squares) parameter estimators for the subcritical Heston model based on discrete time observations derived from conditional least squares estimators of some modified…

Statistics Theory · Mathematics 2016-07-25 Matyas Barczy , Gyula Pap , Tamas T. Szabo

Causal inference with observational studies often relies on the assumptions of unconfoundedness and overlap of covariate distributions in different treatment groups. The overlap assumption is violated when some units have propensity scores…

Methodology · Statistics 2022-07-19 Shu Yang , Peng Ding

We herein establish an asymptotic representation theorem for locally asymptotically normal quantum statistical models. This theorem enables us to study the asymptotic efficiency of quantum estimators such as quantum regular estimators and…

Quantum Physics · Physics 2024-11-14 Akio Fujiwara , Koichi Yamagata

We consider a one dimensional ballistic random walk evolving in a parametric independent and identically distributed random environment. We study the asymptotic properties of the maximum likelihood estimator of the parameter based on a…

Statistics Theory · Mathematics 2014-04-29 Mikael Falconnet , Dasha Loukianova , Catherine Matias

We give sufficient conditions for the asymptotic normality of linear combinations of order statistics (L-statistics) in the case of simple random samples without replacement. In the first case, restrictions are imposed on the weights of…

Statistics Theory · Mathematics 2012-04-11 Andrius Čiginas

This work studies an experimental design problem where {the values of a predictor variable, denoted by $x$}, are to be determined with the goal of estimating a function $m(x)$, which is observed with noise. A linear model is fitted to…

Statistics Theory · Mathematics 2023-05-03 David Azriel