Related papers: Empirical MSE Minimization to Estimate a Scalar Pa…
Variance estimation in the linear model when $p > n$ is a difficult problem. Standard least squares estimation techniques do not apply. Several variance estimators have been proposed in the literature, all with accompanying asymptotic…
Expectile regression is a nice tool for investigating conditional distributions beyond the conditional mean. It is well-known that expectiles can be described with the help of the asymmetric least square loss function, and this link makes…
Nearly all estimators in statistical prediction come with an associated tuning parameter, in one way or another. Common practice, given data, is to choose the tuning parameter value that minimizes a constructed estimate of the prediction…
M-type smoothing splines are a broad class of spline estimators that include the popular least-squares smoothing spline but also spline estimators that are less susceptible to outlying observations and model-misspecification. However,…
Often it is not easy to choose between estimators, based on the estimated MSE and bias using simulation studies. Normality in small samples and a variance of the estimator, which is correct and easy to calculate using a single sample, give…
The mean square error (MSE)-optimal estimator is known to be the conditional mean estimator (CME). This paper introduces a parametric channel estimation technique based on Bayesian estimation. This technique uses the estimated channel…
The two-level normal hierarchical model (NHM) has played a critical role in the theory of small area estimation (SAE), one of the growing areas in statistics with numerous applications in different disciplines. In this paper, we address…
Optimization software enables the solution of problems with millions of variables and associated parameters. These parameters are, however, often uncertain and represented with an analytical description of the parameter's distribution or…
This paper considers the asymptotic theory of a semiparametric M-estimator that is generally applicable to models that satisfy a monotonicity condition in one or several parametric indexes. We call the estimator two-stage maximum score…
Statistical and structural modeling represent two distinct approaches to data analysis. In this paper, we propose a set of novel methods for combining statistical and structural models for improved prediction and causal inference. Our first…
We consider the problem of estimating the error variance in a general linear model when the error distribution is assumed to be spherically symmetric, but not necessary Gaussian. In particular we study the case of a scale mixture of…
Model averaging (MA) and ensembling play a crucial role in statistical and machine learning practice. When multiple candidate models are considered, MA techniques can be used to weight and combine them, often resulting in improved…
This paper considers sequential adaptive estimation of sparse signals under a constraint on the total sensing effort. The advantage of adaptivity in this context is the ability to focus more resources on regions of space where signal…
Applications of structural equation models (SEMs) are often restricted to linear associations between variables. Maximum likelihood (ML) estimation in non-linear models may be complex and require numerical integration. Furthermore, ML…
We consider the estimation problem for jointly stable random variables. Under two specific dependency models: a linear transformation of two independent stable variables and a sub-Gaussian symmetric $\alpha$-stable (S$\alpha$S) vector, we…
Misspecified models often provide useful information about the true data generating distribution. For example, if $y$ is a non-linear function of $x$ the least squares estimator $\hat{\beta}$ is an estimate of $\beta$, the slope of the best…
The maximum likelihood estimator (MLE) is pivotal in statistical inference, yet its application is often hindered by the absence of closed-form solutions for many models. This poses challenges in real-time computation scenarios,…
This paper studies selecting a subset of the system's output to minimize the state estimation mean square error (MSE). This results in the maximization problem of a set function defined on possible sensor selections subject to a cardinality…
Assume one observes independent categorical variables or, equivalently, one observes the corresponding multinomial variables. Estimating the distribution of the observed sequence amounts to estimating the expectation of the multinomial…
We consider the problem of sequentially choosing between a set of unbiased Monte Carlo estimators to minimize the mean-squared-error (MSE) of a final combined estimate. By reducing this task to a stochastic multi-armed bandit problem, we…