相关论文: Inference for local parameters in convexity constr…

We study theoretical properties of regularized robust M-estimators, applicable when data are drawn from a sparse high-dimensional linear model and contaminated by heavy-tailed distributions and/or outliers in the additive errors and…

In this paper, the estimation problem for sparse reduced rank regression (SRRR) model is considered. The SRRR model is widely used for dimension reduction and variable selection with applications in signal processing, econometrics, etc. The…

We consider the problem of estimating an unknown $\theta\in {\mathbb{R}}^n$ from noisy observations under the constraint that $\theta$ belongs to certain convex polyhedral cones in ${\mathbb{R}}^n$. Under this setting, we prove bounds for…

We study a functional linear regression model that deals with functional responses and allows for both functional covariates and high-dimensional vector covariates. The proposed model is flexible and nests several functional regression…

We consider estimation of a one-dimensional location parameter by means of M-estimators S_n with monotone influence curve psi. For growing sample size n, on suitably thinned out convex contamination ball BQ_n of shrinking radius r/sqrt(n)…

This paper presents a unified geometric framework for the statistical analysis of a general ill-posed linear inverse model which includes as special cases noisy compressed sensing, sign vector recovery, trace regression, orthogonal matrix…

Confidence sets play a fundamental role in statistical inference. In this paper, we consider confidence intervals for high dimensional linear regression with random design. We first establish the convergence rates of the minimax expected…

We consider a class of systems with time-varying parameters, which are written as linear regressions with bounded disturbances. The task is to estimate such parameters under the condition that the regressor is finitely exciting (FE).…

Minimax lower bounds are pessimistic in nature: for any given estimator, minimax lower bounds yield the existence of a worst-case target vector $\beta^*_{worst}$ for which the prediction error of the given estimator is bounded from below.…

In many applications, data come with a natural ordering. This ordering can often induce local dependence among nearby variables. However, in complex data, the width of this dependence may vary, making simple assumptions such as a constant…

In typical high dimensional statistical inference problems, confidence intervals and hypothesis tests are performed for a low dimensional subset of model parameters under the assumption that the parameters of interest are unconstrained.…

Statistical problems often involve linear equality and inequality constraints on model parameters. Direct estimation of parameters restricted to general polyhedral cones, particularly when one is interested in estimating low dimensional…

We address the problem of minimizing a convex smooth function $f(x)$ over a compact polyhedral set $D$ given a stochastic zeroth-order constraint feedback model. This problem arises in safety-critical machine learning applications, such as…

We consider the problem of constructing pointwise confidence intervals in the multiple isotonic regression model. Recently, [HZ19] obtained a pointwise limit distribution theory for the so-called block max-min and min-max estimators [FLN17]…

In this article, we consider the problem of estimating the index parameter $\alpha_0$ in the single index model $E[Y |X] = f_0(\alpha_0^T X)$ with $f_0$ the unknown ridge function defined on $\mathbb{R}$, $X$ a d-dimensional covariate and…

We explore a novel methodology for constructing confidence regions for parameters of linear models, using predictions from any arbitrary predictor. Our framework requires minimal assumptions on the noise and can be extended to functions…

We study the problem of distributed adaptive estimation over networks where nodes cooperate to estimate physical parameters that can vary over both space and time domains. We use a set of basis functions to characterize the space-varying…

Functional data analysis has been extensively conducted. In this study, we consider a partially functional model, under which some covariates are scalars and have linear effects, while some other variables are functional and have…

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…

This paper considers fixed effects (FE) estimation for linear panel data models under possible model misspecification when both the number of individuals, $n$, and the number of time periods, $T$, are large. We first clarify the probability…