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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 propose a new method for estimating the minimizer $\boldsymbol{x}^*$ and the minimum value $f^*$ of a smooth and strongly convex regression function $f$ from the observations contaminated by random noise. Our estimator $\boldsymbol{z}_n$…

Statistics Theory · Mathematics 2023-10-10 Arya Akhavan , Davit Gogolashvili , Alexandre B. Tsybakov

We consider a recursive algorithm to construct an aggregated estimator from a finite number of base decision rules in the classification problem. The estimator approximately minimizes a convex risk functional under the l1-constraint. It is…

Statistics Theory · Mathematics 2007-06-13 Anatoli Juditsky , Alexander Nazin , Alexandre Tsybakov , Nicolas Vayatis

We construct an efficient estimator for the error distribution function of the nonparametric regression model Y = r(Z) + e. Our estimator is a kernel smoothed empirical distribution function based on residuals from an under-smoothed local…

Statistics Theory · Mathematics 2018-10-26 Ursula U. Müller , Anton Schick , Wolfgang Wefelmeyer

In this paper we study the problem of recovering a structured but unknown parameter ${\bf{\theta}}^*$ from $n$ nonlinear observations of the form $y_i=f(\langle {\bf{x}}_i,{\bf{\theta}}^*\rangle)$ for $i=1,2,\ldots,n$. We develop a…

Machine Learning · Statistics 2016-10-25 Samet Oymak , Mahdi Soltanolkotabi

We consider the problem of estimating the structural function in nonparametric instrumental regression, where in the presence of an instrument W a response Y is modeled in dependence of an endogenous explanatory variable Z. The proposed…

Statistics Theory · Mathematics 2015-03-13 Jan Johannes , Maik Schwarz

Spatial unilateral autoregressive model $X_{k,\ell}=\alpha X_{k-1,\ell}+\beta X_{k,\ell-1}+\gamma X_{k-1,\ell-1}+\epsilon_{k,\ell}$ is investigated in the unit root case, that is when the parameters are on the boundary of the domain of…

Statistics Theory · Mathematics 2014-04-09 Sándor Baran , Gyula Pap

This paper presents a model selection technique of estimation in semiparametric regression models of the type Y_i=\beta^{\prime}\underbarX_i+f(T_i)+W_i, i=1,...,n. The parametric and nonparametric components are estimated simultaneously by…

Statistics Theory · Mathematics 2007-06-13 Florentina Bunea

Bifurcating autoregressive processes, which can be seen as an adaptation of au-toregressive processes for a binary tree structure, have been extensively studied during the last decade in a parametric context. In this work we do not specify…

Statistics Theory · Mathematics 2016-02-12 Siméon Valère Bitseki Penda , Adélaïde Olivier

Contamination of covariates by measurement error is a classical problem in multivariate regression, where it is well known that failing to account for this contamination can result in substantial bias in the parameter estimators. The nature…

Methodology · Statistics 2017-12-13 Anirvan Chakraborty , Victor M. Panaretos

Regression evaluation has been performed for decades. Some metrics have been identified to be robust against shifting and scaling of the data but considering the different distributions of data is much more difficult to address (imbalance…

Machine Learning · Computer Science 2020-09-14 Mario Michael Krell , Bilal Wehbe

We consider the problem of estimating the slope parameter in circular functional linear regression, where scalar responses Y1,...,Yn are modeled in dependence of 1-periodic, second order stationary random functions X1,...,Xn. We consider an…

Statistics Theory · Mathematics 2010-10-01 Fabienne Comte , Jan Johannes

In this paper, we study finite-sample properties of the least squares estimator in first order autoregressive processes. By leveraging a result from decoupling theory, we derive upper bounds on the probability that the estimate deviates by…

Statistics Theory · Mathematics 2020-05-26 Rodrigo A. González , Cristian R. Rojas

Parameter estimation and the variable selection are two pioneer issues in regression analysis. While traditional variable selection methods require prior estimation of the model parameters, the penalized methods simultaneously carry on…

Methodology · Statistics 2021-09-01 Yetkin Tuaç , Olcay Arslan

Given a large number of covariates $Z$, we consider the estimation of a high-dimensional parameter $\theta$ in an individualized linear threshold $\theta^T Z$ for a continuous variable $X$, which minimizes the disagreement between…

Statistics Theory · Mathematics 2019-05-28 Huijie Feng , Yang Ning , Jiwei Zhao

We study estimation of a multivariate function $f:{\bf R}^d \to {\bf R}$ when the observations are available from function $Af$, where $A$ is a known linear operator. Both the Gaussian white noise model and density estimation are studied.…

Statistics Theory · Mathematics 2009-04-21 Jussi Klemelä , Enno Mammen

We consider maximum likelihood estimation for both causal and noncausal autoregressive time series processes with non-Gaussian $\alpha$-stable noise. A nondegenerate limiting distribution is given for maximum likelihood estimators of the…

Statistics Theory · Mathematics 2009-08-14 Beth Andrews , Matthew Calder , Richard A. Davis

Regression models that ignore measurement error in predictors may produce highly biased estimates leading to erroneous inferences. It is well known that it is extremely difficult to take measurement error into account in Gaussian…

Methodology · Statistics 2023-02-03 Mohammad W. Hattab , David Ruppert

In the present paper, we consider the linear autoregressive model in $\rr$, $$ X_{k,n}=\theta_n X_{k,n-1}+\xi_k, k=0,1,...,n, n\ge 1$$ where $\theta_n\in [0,1)$ is unknown, $(\xi_k)_{k\in\zz}$ is a sequence of centered i.i.d. r.v. valued in…

Probability · Mathematics 2012-07-18 Yu Miao , Yanling Wang , Guangyu Yang

The purpose of the article is twofold. Firstly, we review some recent results on the maximum likelihood estimation in the regression model of the form $X_t = \theta G(t) + B_t$, where $B$ is a Gaussian process, $G(t)$ is a known function,…

Probability · Mathematics 2018-12-27 Yuliya Mishura , Kostiantyn Ralchenko , Sergiy Shklyar