Related papers: Least product relative error estimation for functi…
We consider the problem of estimating functionals of discrete distributions, and focus on tight nonasymptotic analysis of the worst case squared error risk of widely used estimators. We apply concentration inequalities to analyze the random…
Nonlinear function estimation is core to modern machine learning applications. In this paper, to perform nonlinear function estimation, we reduce a nonlinear inverse problem to a linear one using a polynomial kernel expansion. These kernels…
We propose a general method for constructing confidence intervals and statistical tests for single or low-dimensional components of a large parameter vector in a high-dimensional model. It can be easily adjusted for multiplicity taking…
We consider the problem of low probability estimation: given a machine learning model and a formally-specified input distribution, how can we estimate the probability of a binary property of the model's output, even when that probability is…
We analyze a stochastic approximation algorithm for decision-dependent problems, wherein the data distribution used by the algorithm evolves along the iterate sequence. The primary examples of such problems appear in performative prediction…
In linear regression we wish to estimate the optimum linear least squares predictor for a distribution over $d$-dimensional input points and real-valued responses, based on a small sample. Under standard random design analysis, where the…
In this paper we study the asymptotic theory for samples problem based on the functional empirical process (fep), this new method is called general samples problem. We suggest this method to develop the full theory of estimation of means,…
We define two minimum distance estimators for dependent data by minimizing some approximated Maximum Mean Discrepancy distances between the true empirical distribution of observations and their assumed (parametric) model distribution. When…
We investigate the problem of jointly testing two hypotheses and estimating a random parameter based on data that is observed sequentially by sensors in a distributed network. In particular, we assume the data to be drawn from a Gaussian…
We study optimal estimation when the likelihood may be misspecified. Building on tools from the theory of decision-making under uncertainty, we analyze a class of axiomatically grounded optimality criteria which nests several existing…
We consider the problem of fitting the parameters of a high-dimensional linear regression model. In the regime where the number of parameters $p$ is comparable to or exceeds the sample size $n$, a successful approach uses an…
We study the problem of signal source localization using received signal strength measurements. We begin by presenting verifiable geometric conditions for sensor deployment that ensure the model's asymptotic localizability. Then we…
In this paper we estimate the mean-variance portfolio in the high-dimensional case using the recent results from the theory of random matrices. We construct a linear shrinkage estimator which is distribution-free and is optimal in the sense…
Linear thresholding models postulate that the conditional distribution of a response variable in terms of covariates differs on the two sides of a (typically unknown) hyperplane in the covariate space. A key goal in such models is to learn…
Model selection criteria are one of the most important tools in statistics. Proofs showing a model selection criterion is asymptotically optimal are tailored to the type of model (linear regression, quantile regression, penalized…
We study the problem of parameter estimation for reflected stochastic processes driven by a standard Brownian motion. The estimator is obtained using nonlinear least squares method based on discretely observed processes. Under some certain…
This paper derives the nonparametric maximum likelihood estimator (NPMLE) of a distribution function from observations which are subject to both bias and censoring. The NPMLE is obtained by a simple EM algorithm which is an extension of the…
By means of two simple convexity arguments we are able to develop a general method for proving consistency and asymptotic normality of estimators that are defined by minimisation of convex criterion functions. This method is then applied to…
Many statistical applications involve models for which it is difficult to evaluate the likelihood, but from which it is relatively easy to sample. Approximate Bayesian computation is a likelihood-free method for implementing Bayesian…
In sparse linear regression, the SLOPE estimator generalizes LASSO by penalizing different coordinates of the estimate according to their magnitudes. In this paper, we present a precise performance characterization of SLOPE in the…