Related papers: Asymptotics for M-type smoothing splines with non-…

In this paper we provide a priori error estimates with explicit constants for both the $L^2$-projection and the Ritz projection onto spline spaces of arbitrary smoothness defined on arbitrary grids. This extends the results recently…

Method of moment estimators exhibit appealing statistical properties, such as asymptotic unbiasedness, for nonconvex problems. However, they typically require a large number of samples and are extremely sensitive to model misspecification.…

This paper develops and analyzes three families of estimators that continuously interpolate between classical quantiles and the sample mean. The construction begins with a smoothed version of the $L_{1}$ loss, indexed by a location…

We prove lower bounds for the approximation error of the variation-diminishing Schoenberg operator on the interval $[0,1]$ in terms of classical moduli of smoothness depending on the degree of the spline basis using a functional analysis…

Theoretical estimates of the convergence rate of many well-known gradient-type optimization methods are based on quadratic interpolation, provided that the Lipschitz condition for the gradient is satisfied. In this article we obtain a…

The paper considers a universal approach that allows one to quite simply obtain nonlinear asymptotic estimates of various summation functions. It is shown the application of this approach to the asymptotic estimation of divergent Dirichlet…

We establish asymptotic properties of $M$-estimators, defined in terms of a contrast function and observations from a continuous-time locally stationary process. Using the stationary approximation of the sequence, $\theta$-weak dependence,…

In this paper, we discuss the problem of minimizing the sum of two convex functions: a smooth function plus a non-smooth function. Further, the smooth part can be expressed by the average of a large number of smooth component functions, and…

A general method is presented for deriving the limiting behavior of estimators that are defined as the values of parameters optimizing an empirical criterion function. The asymptotic behavior of such estimators is typically deduced from…

Nonparametric methods are widely applicable to statistical inference problems, since they rely on a few modeling assumptions. In this context, the fresh look advocated here permeates benefits from variable selection and compressive…

We consider data-adaptive wavelet estimation of a trend function in a time series model with strongly dependent Gaussian residuals. Asymptotic expressions for the optimal mean integrated squared error and corresponding optimal smoothing and…

This paper investigates the nonparametric estimation of a circular regression function in an errors-in-variables framework. Two settings are studied, depending on whether the covariates are circular or linear. Adaptive estimators are…

Consider the problem of joint parameter estimation and prediction in a Markov random field: i.e., the model parameters are estimated on the basis of an initial set of data, and then the fitted model is used to perform prediction (e.g.,…

Image smoothing is a fundamental procedure in applications of both computer vision and graphics. The required smoothing properties can be different or even contradictive among different tasks. Nevertheless, the inherent smoothing nature of…

In this paper a new family of minimum divergence estimators based on the Bregman divergence is proposed, where the defining convex function has an exponential nature. These estimators avoid the necessity of using an intermediate kernel…

Indirect inference estimators (i.e., simulation-based minimum distance estimators) in a parametric model that are based on auxiliary non-parametric maximum likelihood density estimators are shown to be asymptotically normal. If the…

We propose a unified framework for establishing existence of nonparametric M-estimators, computing the corresponding estimates, and proving their strong consistency when the class of functions is exceptionally rich. In particular, the…

We derive asymptotic normality of kernel type deconvolution estimators of the density, the distribution function at a fixed point, and of the probability of an interval. We consider the so called super smooth case where the characteristic…

We consider estimation of a multivariate normal mean vector under sum of squared error loss. We propose a new class of smooth estimators parameterized by \alpha dominating the James-Stein estimator. The estimator for \alpha=1 corresponds to…

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…