Related papers: Optimal rates for finite mixture estimation
The nonparametric regression with a random design model is considered. We want to recover the regression function at a point x where the design density is vanishing or exploding. Depending on assumptions on the regression function local…
We prove minimax bounds for estimating Gaussian location mixtures on $\mathbb{R}^d$ under the squared $L^2$ and the squared Hellinger loss functions. Under the squared $L^2$ loss, we prove that the minimax rate is upper and lower bounded by…
We investigate the problem of jointly testing a pair of composite hypotheses and, depending on the test result, estimating a random parameter under distributional uncertainties. Specifically, it is assumed that the distribution of the data…
Suppose that univariate data are drawn from a mixture of two distributions that are equal up to a shift parameter. Such a model is known to be nonidentifiable from a nonparametric viewpoint. However, if we assume that the unknown mixed…
Finite mixture models have long been used across a variety of fields in engineering and sciences. Recently there has been a great deal of interest in quantifying the convergence behavior of the \emph{mixing measure}, a fundamental object…
Maximum likelihood estimation is a common method of estimating the parameters of the probability distribution from a given sample. This paper aims to introduce the maximum likelihood estimation in the framework of sublinear expectation. We…
We study the problem of estimating the joint probability mass function (pmf) over two random variables. In particular, the estimation is based on the observation of $m$ samples containing both variables and $n$ samples missing one fixed…
In this paper, we consider estimators for an additive functional of $\phi$, which is defined as $\theta(P;\phi)=\sum_{i=1}^k\phi(p_i)$, from $n$ i.i.d. random samples drawn from a discrete distribution $P=(p_1,...,p_k)$ with alphabet size…
Consider the communication-constrained estimation of discrete distributions under $\ell^p$ losses, where each distributed terminal holds multiple independent samples and uses limited number of bits to describe the samples. We obtain the…
We study the minimax optimal rates for estimating a range of Integral Probability Metrics (IPMs) between two unknown probability measures, based on $n$ independent samples from them. Curiously, we show that estimating the IPM itself between…
Many algorithms in machine learning and computational geometry require, as input, the intrinsic dimension of the manifold that supports the probability distribution of the data. This parameter is rarely known and therefore has to be…
We consider maximum likelihood estimation of finite mixture of uniform distributions. We prove that maximum likelihood estimator is strongly consistent, if the scale parameters of the component uniform distributions are restricted from…
Finite mixture models are widely used in econometric analyses to capture unobserved heterogeneity. This paper shows that maximum likelihood estimation of finite mixtures of parametric densities can suffer from substantial finite-sample bias…
In finite mixture models, apart from underlying mixing measure, true kernel density function of each subpopulation in the data is, in many scenarios, unknown. Perhaps the most popular approach is to choose some kernel functions that we…
Scientific explanation often requires inferring maximally predictive features from a given data set. Unfortunately, the collection of minimal maximally predictive features for most stochastic processes is uncountably infinite. In such…
We consider two nonparametric procedures for estimating a concave distribution function based on data corrupted with additive noise generated by a bounded decreasing density on $(0,\infty)$. For the maximum likelihood (ML) estimator and…
The basic goal of quantization for probability distribution is to reduce the number of values, which is typically uncountable, describing a probability distribution to some finite set and thus approximation of a continuous probability…
We provide a general framework for computing upper bounds on mixing times of finite Markov chains when its minimal ideal is left zero. Our analysis is based on combining results by Brown and Diaconis with our previous work on stationary…
Monge matrices and their permuted versions known as pre-Monge matrices naturally appear in many domains across science and engineering. While the rich structural properties of such matrices have long been leveraged for algorithmic purposes,…
We study the minimax estimation of $\alpha$-divergences between discrete distributions for integer $\alpha\ge 1$, which include the Kullback--Leibler divergence and the $\chi^2$-divergences as special examples. Dropping the usual…