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We investigate optimal subsampling for quantile regression. We derive the asymptotic distribution of a general subsampling estimator and then derive two versions of optimal subsampling probabilities. One version minimizes the trace of the…
Linear regression with normally distributed errors - including particular cases such as ANOVA, Student's t-test or location-scale inference - is a widely used statistical procedure. In this case the ordinary least squares estimator…
The direct Gaussian copula model with discrete marginal distributions is an appealing data-analytic tool but poses difficult computational challenges due to its intractable likelihood. A number of approximations/surrogates for the…
Scientific modeling applications often require estimating a distribution of parameters consistent with a dataset of observations - an inference task also known as source distribution estimation. This problem can be ill-posed, however, since…
We revisit the classical problem of estimating an unknown distribution from its samples by fitting a mixture model that minimizes cross-entropy loss. Framing the task as a stochastic convex optimization problem over the space of $ M…
In numerous instances, the generalized exponential distribution can be used as an alternative to the most widely used non-regular family of distributions: Weibull, gamma, lognormal with three-parameters when analyzing lifetime or any skewed…
A number of discrete time, finite population size models in genetics describing the dynamics of allele frequencies are known to converge (subject to suitable scaling) to a diffusion process in the infinite population limit, termed the…
This paper presents some results on the maximum likelihood (ML) estimation from incomplete data. Finite sample properties of conditional observed information matrices are established. They possess positive definiteness and the same Loewner…
We derive an optimal shrinkage sample covariance matrix (SCM) estimator which is suitable for high dimensional problems and when sampling from an unspecified elliptically symmetric distribution. Specifically, we derive the optimal (oracle)…
Linear Least Squares is a very well known technique for parameter estimation, which is used even when sub-optimal, because of its very low computational requirements and the fact that exact knowledge of the noise statistics is not required.…
With the growing availability of large-scale biomedical data, it is often time-consuming or infeasible to directly perform traditional statistical analysis with relatively limited computing resources at hand. We propose a fast subsampling…
High-dimensional data arise routinely in modern statistics, econometrics, finance, genomics, and machine learning. While a large body of existing methodology is developed under Gaussian or light-tailed assumptions, many real data sets…
This paper addresses the statistical problem of estimating the infinite-norm deviation from the empirical mean to the distribution mean for high-dimensional distributions on $\{0,1\}^d$, potentially with $d=\infty$. Unlike traditional…
The Wasserstein distance is a metric on a space of probability measures that has seen a surge of applications in statistics, machine learning, and applied mathematics. However, statistical aspects of Wasserstein distances are bottlenecked…
The Tully-Fisher relation is a vital distance indicator, but its precise inference is challenged by selection bias, statistical bias, and uncertain inclination corrections. This study presents a Bayesian framework that simultaneously…
Let $Z_1,\ldots,Z_n$ be i.i.d. isotropic random vectors in $\mathbb{R}^p$, and $T \subset \mathbb{R}^p$ be a compact set. A classical line of empirical process theory characterizes the size of the suprema of the quadratic process…
In the regression model with errors in variables, we observe $n$ i.i.d. copies of $(Y,Z)$ satisfying $Y=f_{\theta^0}(X)+\xi$ and $Z=X+\epsilon$ involving independent and unobserved random variables $X,\xi,\epsilon$ plus a regression…
We consider the problem of computing a positive definite $p \times p$ inverse covariance matrix aka precision matrix $\theta=(\theta_{ij})$ which optimizes a regularized Gaussian maximum likelihood problem, with the elastic-net regularizer…
The maximum likelihood threshold (MLT) of a graph $G$ is the minimum number of samples to almost surely guarantee existence of the maximum likelihood estimate in the corresponding Gaussian graphical model. We give a new characterization of…
We consider a problem in parametric estimation: given $n$ samples from an unknown distribution, we want to estimate which distribution, from a given one-parameter family, produced the data. Following Schulman and Vazirani, we evaluate an…