Related papers: Adaptive estimation of a distribution function and…
The problem of finding the expected value of a statistic of a locally stable point process in a bounded region is addressed. We propose an adaptive importance sampling for solving the problem. In our proposal, we restrict the importance…
Recent results in compressed sensing showed that the optimal subsampling strategy should take into account the sparsity pattern of the signal at hand. This oracle-like knowledge, even though desirable, nevertheless remains elusive in most…
Density estimation and inference methods are widely used in empirical work. When the underlying distribution has compact support, conventional kernel-based density estimators are no longer consistent near or at the boundary because of their…
We consider the problem of estimating the unknown response function in the Gaussian white noise model. We first utilize the recently developed Bayesian maximum a posteriori "testimation" procedure of Abramovich et al. (2007) for recovering…
We propose communication-efficient distributed estimation and inference methods for the transelliptical graphical model, a semiparametric extension of the elliptical distribution in the high dimensional regime. In detail, the proposed…
Many randomized approximation algorithms operate by giving a procedure for simulating a random variable $X$ which has mean $\mu$ equal to the target answer, and a relative standard deviation bounded above by a known constant $c$. Examples…
This paper is concerned with Bayesian inferential methods for data from controlled branching processes that account for model robustness through the use of disparities. Under regularity conditions, we establish that estimators built on…
We propose a new method of estimation in high-dimensional linear regression model. It allows for very weak distributional assumptions including heteroscedasticity, and does not require the knowledge of the variance of random errors. The…
We propose a new randomized optimization method for high-dimensional problems which can be seen as a generalization of coordinate descent to random subspaces. We show that an adaptive sampling strategy for the random subspace significantly…
Sampling is a fundamental problem in computer science and statistics. However, for a given task and stream, it is often not possible to choose good sampling probabilities in advance. We derive a general framework for adaptively changing the…
As the most fundamental problem in statistics, robust location estimation has many prominent solutions, such as the trimmed mean, Winsorized mean, Hodges Lehmann estimator, Huber M estimator, and median of means. Recent studies suggest that…
It is shown that the variable bandwidth density estimator proposed by McKay (1993a and b) following earlier findings by Abramson (1982) approximates density functions in $C^4(\mathbb R^d)$ at the minimax rate in the supremum norm over…
Density estimation plays a fundamental role in many areas of statistics and machine learning. Parametric, nonparametric and semiparametric density estimation methods have been proposed in the literature. Semiparametric density models are…
In this work we study the {\it moment estimation} problem using weighted sampling. Given sample access to a set $A$ with $n$ weighted elements, and a parameter $t>0$, we estimate the $t$-th moment of $A$ given as $S_t=\sum_{a\in A} w(a)^t$.…
We derive rates of contraction of posterior distributions on nonparametric models resulting from sieve priors. The aim of the paper is to provide general conditions to get posterior rates when the parameter space has a general structure,…
We consider a multiplicative deconvolution problem, in which the density $f$ or the survival function $S^X$ of a strictly positive random variable $X$ is estimated nonparametrically based on an i.i.d. sample from a noisy observation $Y =…
We present a new a priori analysis of a class of collocation methods for parabolic PDEs that rely only on pointwise data of force term, boundary data, and initial data. Under Besov regularity assumptions, we characterize the optimal…
A finite dimensional abstract approximation and convergence theory is developed for estimation of the distribution of random parameters in infinite dimensional discrete time linear systems with dynamics described by regularly dissipative…
A new approach of obtaining stratified random samples from statistically dependent random variables is described. The proposed method can be used to obtain samples from the input space of a computer forward model in estimating expectations…
The analysis of the joint cumulative distribution function (CDF) with bivariate event time data is a challenging problem both theoretically and numerically. This paper develops a tensor spline-based sieve maximum likelihood estimation…