Related papers: Improved multivariate normal mean estimation with …
Say $X_1,X_2,\ldots$ are independent identically distributed Bernoulli random variables with mean $p$. This paper builds a new estimate $\hat p$ of $p$ that has the property that the relative error, $\hat p /p - 1$, of the estimate does not…
Both parametric distribution functions appearing in extreme value theory - the generalized extreme value distribution and the generalized Pareto distribution - have log-concave densities if the extreme value index gamma is in [-1,0].…
Reliable uncertainty estimates are an important tool for helping autonomous agents or human decision makers understand and leverage predictive models. However, existing approaches to estimating uncertainty largely ignore the possibility of…
We consider a high-dimensional mean estimation problem over a binary hidden Markov model, which illuminates the interplay between memory in data, sample size, dimension, and signal strength in statistical inference. In this model, an…
Covariance estimation and selection for multivariate datasets in a high-dimensional regime is a fundamental problem in modern statistics. Gaussian graphical models are a popular class of models used for this purpose. Current Bayesian…
In this paper, we consider the nonparametric estimation of the multivariate probability density function and its partial derivative with a support on $[0,\infty)$. To this end we use the class of kernel estimators with asymmetric gamma…
A sample covariance matrix $\boldsymbol{S}$ of completely observed data is the key statistic in a large variety of multivariate statistical procedures, such as structured covariance/precision matrix estimation, principal component analysis,…
A typical desideratum for quantifying the uncertainty from a classification model as a prediction set is class-conditional singleton set calibration. That is, such sets should map to the output of well-calibrated selective classifiers,…
In many applied fields incomplete covariate vectors are commonly encountered. It is well known that this can be problematic when making inference on model parameters, but its impact on prediction performance is less understood. We develop a…
This paper is devoted to the multivariate estimation of a vector of Poisson means. A novel loss function that penalises bad estimates of each of the parameters and the sum (or equivalently the mean) of the parameters is introduced. Under…
Let $\{X_n,n\ge1\}$ be a sequence of independent and identically distributed random variables, taking non-negative integer values, and call $X_n$ a $\delta$-record if $X_n>\max\{X_1,...,X_{n-1}\}+\delta$, where $\delta$ is an integer…
Performing statistical inference in high-dimension is an outstanding challenge. A major source of difficulty is the absence of precise information on the distribution of high-dimensional estimators. Here, we consider linear regression in…
This paper considers distributed M-estimation under heterogeneous distributions among distributed data blocks. A weighted distributed estimator is proposed to improve the efficiency of the standard "Split-And-Conquer" (SaC) estimator for…
It has been proposed that complex populations, such as those that arise in genomics studies, may exhibit dependencies among observations as well as among variables. This gives rise to the challenging problem of analyzing unreplicated…
I--MR charts commonly estimate the process standard deviation $\sigma$ via the span-2 average moving range divided by the unbiasing constant $d_2$; unlike the unbiased sample standard deviation ($S/c_4$), this estimator depends on ordering…
We study a novel class of affine invariant and consistent tests for normality in any dimension. The tests are based on a characterization of the standard $d$-variate normal distribution as the unique solution of an initial value problem of…
A multivariable measurement error model $AX \approx B$ is considered. Here $A$ and $B$ are input and output matrices of measurements and $X$ is a rectangular matrix of fixed size to be estimated. The errors in $[A,B]$ are row-wise…
In this paper, a nonparametric estimator is proposed for estimating the L1-median for multivariate conditional distribution when the covariates take values in an infinite dimensional space. The multivariate case is more appropriate to…
We consider the problem of using expert data with unobserved confounders for imitation and reinforcement learning. We begin by defining the problem of learning from confounded expert data in a contextual MDP setup. We analyze the…
The prediction of the variance-covariance matrix of the multivariate normal distribution is important in the multivariate analysis. We investigated Bayesian predictive distributions for Wishart distributions under the Kullback-Leibler…