Related papers: Cramer-Rao Bound for Estimation After Model Select…
We study the performance of estimators of a sparse nonrandom vector based on an observation which is linearly transformed and corrupted by additive white Gaussian noise. Using the reproducing kernel Hilbert space framework, we derive a new…
In this paper, we study the trace regression when a matrix of parameters B* is estimated via the convex relaxation of a rank-regularized regression or via regularized non-convex optimization. It is known that these estimators satisfy…
Recently, several high-resolution parameter estimation algorithms have been developed to exploit the structure of strictly second-order (SO) non-circular (NC) signals. They achieve a higher estimation accuracy and can resolve up to twice as…
We consider the fundamental problem of estimating the mean of a vector $y=X\beta+z$, where $X$ is an $n\times p$ design matrix in which one can have far more variables than observations, and $z$ is a stochastic error term--the so-called…
We present a methodology for model evaluation and selection where the sampling mechanism violates the i.i.d. assumption. Our methodology involves a formulation of the bias between the standard Cross-Validation (CV) estimator and the mean…
This paper provides a statistical analysis of high-dimensional batch Reinforcement Learning (RL) using sparse linear function approximation. When there is a large number of candidate features, our result sheds light on the fact that…
We consider the linear regression problem of estimating an unknown, deterministic parameter vector based on measurements corrupted by colored Gaussian noise. We present and analyze blind minimax estimators (BMEs), which consist of a bounded…
This paper addresses the real-time state estimation problem for dynamic systems while protecting exogenous inputs against adversaries, who may be honest-but-curious third parties or external eavesdroppers. The Cram\'er-Rao lower bound…
Statistical inference of multiple parameters often involves a preliminary parameter selection stage. The selection stage has an impact on subsequent estimation, for example by introducing a selection bias. The post-selection maximum…
Linear regression with measurement error in the covariates is a heavily studied topic, however, the statistics/econometrics literature is almost silent to estimating a multi-equation model with measurement error. This paper considers a…
We consider the problem of estimating a meta-model of an unknown regression model with non-Gaussian and non-bounded error. The meta-model belongs to a reproducing kernel Hilbert space constructed as a direct sum of Hilbert spaces leading to…
Asymptotic lower bounds for estimation play a fundamental role in assessing the quality of statistical procedures. In this paper we propose a framework for obtaining semi-parametric efficiency bounds for sparse high-dimensional models,…
This study explores the estimation of parameters in a matrix-valued linear regression model, where the $T$ responses $(Y_t)_{t=1}^T \in \mathbb{R}^{n \times p}$ and predictors $(X_t)_{t=1}^T \in \mathbb{R}^{m \times q}$ satisfy the…
This paper proposes a Lasso-type estimator for a high-dimensional sparse parameter identified by a single index conditional moment restriction (CMR). In addition to this parameter, the moment function can also depend on a nuisance function,…
Meta-backscatter system that utilizes meta-material sensors is a promising enabler for future environmental sensing, offering distinct advantages such as low cost, zero-power consumption, and robustness. Specifically, the electromagnetic…
Cross-validation (CV) is often used to select the regularization parameter in high dimensional problems. However, when applied to the sparse modeling method Lasso, CV leads to models that are unstable in high-dimensions, and consequently…
We consider the sparse regression model where the number of parameters $p$ is larger than the sample size $n$. The difficulty when considering high-dimensional problems is to propose estimators achieving a good compromise between…
The problem of estimating the parameters of a moving target in multiple-input multiple-output (MIMO) radar is considered and a new approach for estimating the moving target parameters by making use of the phase information associated with…
Post-selection inference is a statistical technique for determining salient variables after model or variable selection. Recently, selective inference, a kind of post-selection inference framework, has garnered the attention in the…
We consider the bridge linear regression modeling, which can produce a sparse or non-sparse model. A crucial point in the model building process is the selection of adjusted parameters including a regularization parameter and a tuning…