相关论文: The minimum mean square estimator for a sublinear …
Evaluating treatments received by one population for application to a different target population of scientific interest is a central problem in causal inference from observational studies. We study the minimax linear estimator of the…
We study risk of the minimum norm linear least squares estimator in when the number of parameters $d$ depends on $n$, and $\frac{d}{n} \rightarrow \infty$. We assume that data has an underlying low rank structure by restricting ourselves to…
This paper proposes a new estimator for selecting weights to average over least squares estimates obtained from a set of models. Our proposed estimator builds on the Mallows model average (MMA) estimator of Hansen (2007), but, unlike MMA,…
Theoretically, the conditional expectation of a square-integrable random variable $Y$ given a $d$-dimensional random vector $X$ can be obtained by minimizing the mean squared distance between $Y$ and $f(X)$ over all Borel measurable…
In this note a new high performance least squares parameter estimator is proposed. The main features of the estimator are: (i) global exponential convergence is guaranteed for all identifiable linear regression equations; (ii) it…
General ridge estimators are typical linear estimators in a general linear model. The class of them includes some shrinkage estimators in addition to classical linear unbiased estimators such as the ordinary least squares estimator and the…
The partial least squares procedure was originally developed to estimate the slope parameter in multivariate parametric models. More recently it has gained popularity in the functional data literature. There, the partial least squares…
Consider the problem of estimating the mean of a Gaussian random vector when the mean vector is assumed to be in a given convex set. The most natural solution is to take the Euclidean projection of the data vector on to this convex set; in…
Conditions guaranteeing convergence of linear stochastic Volterra operators are studied. Necessary and sufficient conditions for mean square convergence are established, while almost sure convergence of the linear operator is shown to imply…
This article addresses the problem of estimating the population mean in the presence of auxiliary information when study variable itself is qualitative in nature. Bias and mean squared error (MSE) expressions of the class of estimators are…
The goal of this note is to present a modification of the popular median of means estimator that achieves sub-Gaussian deviation bounds with nearly optimal constants under minimal assumptions on the underlying distribution. We build on a…
This paper focuses on the minimum mean squared error (MMSE) channel estimator for multiple-input multiple-output (MIMO) systems with one-bit quantization at the receiver side. Despite its optimality and significance in estimation theory,…
The term ``empirical predictor'' refers to a two-stage predictor of a linear combination of fixed and random effects. In the first stage, a predictor is obtained but it involves unknown parameters; thus, in the second stage, the unknown…
In this paper, by using the representation theorem for sublinear expectations, we give a simple proof to obtain two inequalities about the sample mean for independent random vectors under sublinear expectations.
We present large sample results for partitioning-based least squares nonparametric regression, a popular method for approximating conditional expectation functions in statistics, econometrics, and machine learning. First, we obtain a…
The linear minimum mean squared error (LMMSE) estimator is the best linear estimator for a Bayesian linear inverse problem with respect to the mean squared error. It arises as the solution operator to a Tikhonov-type regularized inverse…
In this paper, we consider the explicit expressions of the normwise condition number for the scaled total least squares problem. Some techniques are introduced to simplify the expression of the condition number, and some new results are…
We consider the problem of sequentially learning to estimate, in the mean squared error (MSE) sense, a Gaussian $K$-vector of unknown covariance by observing only $m < K$ of its entries in each round. We propose two MSE estimators, and…
In this paper, we consider the normalized least squares estimator of the parameter in a mildly stationary first-order autoregressive (AR(1)) model with dependent errors which are modeled as a mildly stationary AR(1) process. By martingale…
Consider the minimum mean-square error (MMSE) of estimating an arbitrary random variable from its observation contaminated by Gaussian noise. The MMSE can be regarded as a function of the signal-to-noise ratio (SNR) as well as a functional…