Related papers: Mean and Variance Estimation by Kriging
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…
In this article we provide some nonnegative and positive estimators of the mean squared errors(MSEs) for shrinkage estimators of multivariate normal means. Proposed estimators are shown to improve on the uniformly minimum variance unbiased…
We consider regression models with data of the type $y_i=m(x_i)+\varepsilon_i$, where the $m(x)$ curve is taken locally constant, with unknown levels and jump points. We investigate the large-sample properties of the minimum least squares…
Small area estimators that ignore the sampling design lack design consistency when the sampling mechanism is complex and may be severely biased under informative designs. Existing procedures that account for the survey weights under…
A variance reduction technique in nonparametric smoothing is proposed: at each point of estimation, form a linear combination of a preliminary estimator evaluated at nearby points with the coefficients specified so that the asymptotic bias…
Unlike the classical smoothing theory, it is well known that quantum smoothers are, in general, not well--defined by the quantum conditional expectation. The purpose of this paper is to propose a new quantum smoothing theory based on the…
The main purpose of this article is to prove that, under certain assumptions in a linear prediction setting, optimal methods based upon model reduction and even an optimal predictor can be provided. The optimality is formulated in terms of…
We discuss techniques of estimation and inference for nonstationary nonlinear cohort panels with learning from experience, showing, inter alia, the consistency and asymptotic normality of the nonlinear least squares estimator used in…
Variance function estimation in nonparametric regression is considered and the minimax rate of convergence is derived. We are particularly interested in the effect of the unknown mean on the estimation of the variance function. Our results…
Given data drawn from a collection of Gaussian variables with a common mean but different and unknown variances, what is the best algorithm for estimating their common mean? We present an intuitive and efficient algorithm for this task. As…
The estimation of a sparse vector in the linear model is a fundamental problem in signal processing, statistics, and compressive sensing. This paper establishes a lower bound on the mean-squared error, which holds regardless of the…
In a classical regression model, it is usually assumed that the explanatory variables are independent of each other and error terms are normally distributed. But when these assumptions are not met, situations like the error terms are not…
This note presents a new definition of nonlinear statistics mean and variance to simplify the nonlinear statistics computations. These concepts aim to provide a theoretical explanation of a novel nonlinear weighted residual methodology…
The present paper discusses the problem of estimating the finite population mean of study variable in simple random sampling in the presence of non response and response error together. The estimators in this article use auxiliary…
Purpose: To develop neural network (NN)-based quantitative MRI parameter estimators with minimal bias and a variance close to the Cram\'er-Rao bound. Theory and Methods: We generalize the mean squared error loss to control the bias and…
State estimation is a classical problem in quantum information. In optimization of estimation scheme, to find a lower bound to the error of the estimator is a very important step. So far, all the proposed tractable lower bounds use…
We propose the first near-optimal quantum algorithm for estimating in Euclidean norm the mean of a vector-valued random variable with finite mean and covariance. Our result aims at extending the theory of multivariate sub-Gaussian…
In this paper we refine the procedure proposed by Lin et al. (2015) to estimate the density at a given quantile based on a resampling method. The approach consists on generating multiple samples of the zero-mean Gaussian variable from which…
Biased stochastic estimators, such as finite-differences for noisy gradient estimation, often contain parameters that need to be properly chosen to balance impacts from the bias and the variance. While the optimal order of these parameters…
To take sample biases and skewness in the observations into account, practitioners frequently weight their observations according to some marginal distribution. The present paper demonstrates that such weighting can indeed improve the…