相关论文: Consistency of a nonparametric least squares estim…

The estimation of parameters in a linear model is considered under the hypothesis that the noise, with finite second order statistics, can be represented in a given deterministic basis by random coefficients. An extended underdetermined…

We consider the estimation of quadratic functionals in a Gaussian sequence model where the eigenvalues are supposed to be unknown and accessible through noisy observations only. Imposing smoothness assumptions both on the signal and the…

A recursive least squares algorithm with variable rate forgetting (VRF) is derived by minimizing a quadratic cost function.Under persistent excitation and boundedness of the forgetting factor, the minimizer given by VRF is shown to converge…

In this paper, we consider a functional linear regression model, where both the covariate and the response variable are functional random variables. We address the problem of optimal nonparametric estimation of the conditional expectation…

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)…

This paper presents a first-order {distributed continuous-time algorithm} for computing the least-squares solution to a linear equation over networks. Given the uniqueness of the solution, with nonintegrable and diminishing step size,…

The Rasch model is widely used for item response analysis in applications ranging from recommender systems to psychology, education, and finance. While a number of estimators have been proposed for the Rasch model over the last decades, the…

In this paper, we consider a statistical problem of learning a linear model from noisy samples. Existing work has focused on approximating the least squares solution by using leverage-based scores as an importance sampling distribution.…

In this paper, we consider the nonparametric least square regression in a Reproducing Kernel Hilbert Space (RKHS). We propose a new randomized algorithm that has optimal generalization error bounds with respect to the square loss, closing a…

This article investigates nonparametric estimation of variance functions for functional data when the mean function is unknown. We obtain asymptotic results for the kernel estimator based on squared residuals. Similar to the finite…

Let $(X_i)_{i=1,...,n}$ be a possibly nonstationary sequence such that $\mathscr{L}(X_i)=P_n$ if $i\leq n\theta$ and $\mathscr{L}(X_i)=Q_n$ if $i>n\theta$, where $0<\theta <1$ is the location of the change-point to be estimated. We…

We consider a multivariate functional measurement error model $AX\approx B$. The errors in $[A,B]$ are uncorrelated, row-wise independent, and have equal (unknown) variances. We study the total least squares estimator of $X$, which, in the…

Non-parametric inference for functional data over two-dimensional domains entails additional computational and statistical challenges, compared to the one-dimensional case. Separability of the covariance is commonly assumed to address these…

In this paper we propose a recursive online algorithm for estimating the parameters of a time-varying ARCH process. The estimation is done by updating the estimator at time point $t-1$ with observations about the time point $t$ to yield an…

We study the asymptotics for jump-penalized least squares regression aiming at approximating a regression function by piecewise constant functions. Besides conventional consistency and convergence rates of the estimates in $L^2([0,1))$ our…

Convergence properties of empirical risk minimizers can be conveniently expressed in terms of the associated population risk. To derive bounds for the performance of the estimator under covariate shift, however, pointwise convergence rates…

In this paper, we construct an estimator of an errors-in-variables linear regression model. The regression model leads to a constrained total least squares problems with row and column constraints. Although this problem can be numerically…

We study the maximum likehood estimator and least squares estimator for drift parameters of nonlinear reflected stochastic differential equations based on continuous observations. Under some regular conditions, we obtain the consistency and…

It is a standard criterium in statistics to define an optimal estimator the one with the minimum variance. Thus, the optimality is proved with inequality among variances of competing estimators. The inequalities, demonstrated here, disfavor…

In this paper, we study nonparametric models allowing for locally stationary regressors and a regression function that changes smoothly over time. These models are a natural extension of time series models with time-varying coefficients. We…