Related papers: f-divergence estimation and two-sample homogeneity…
Probability density estimation is a core problem of statistics and signal processing. Moment methods are an important means of density estimation, but they are generally strongly dependent on the choice of feasible functions, which severely…
We propose three test criteria each of which is appropriate for testing, respectively, the equivalence hypotheses of symmetry, of homogeneity, and of independence, with multivariate data. All quantities have the common feature of involving…
Maximum likelihood estimators are proposed for the parameters and the densities in a semiparametric density ratio model in which the nonparametric baseline density is approximated by the Bernstein polynomial model. The EM algorithm is used…
We investigate the problem of estimating a smooth invertible transformation f when observing independent samples X_1, ..., X_n ~ P \circ f, where P is a known measure. We focus on the two dimensional case where P and f are defined on R^2.…
The traditional kernel density estimator of an unknown density is by construction completely nonparametric, in the sense that it has no preferences and will work reasonably well for all shapes. The present paper develops a class of…
The estimation of a density profile from experimental data points is a challenging problem, usually tackled by plotting a histogram. Prior assumptions on the nature of the density, from its smoothness to the specification of its form, allow…
We consider the problem of estimating a density $f_X$ using a sample $Y_1,...,Y_n$ from $f_Y=f_X\star f_{\epsilon}$, where $f_{\epsilon}$ is an unknown density. We assume that an additional sample $\epsilon_1,...,\epsilon_m$ from…
The problem of binary hypothesis testing between two probability measures is considered. New sharp bounds are derived for the best achievable error probability of such tests based on independent and identically distributed observations.…
Two-sample testing is a fundamental problem in statistics. Despite its long history, there has been renewed interest in this problem with the advent of high-dimensional and complex data. Specifically, in the machine learning literature,…
We introduce a novel two-step approach for estimating a probability density function (pdf) given its samples, with the second and important step coming from a geometric formulation. The procedure involves obtaining an initial estimate of…
The ratio of two densities provides a direct characterization of their differences. We consider the two-sample comparison problem by estimating this ratio given i.i.d. observations from two distributions. To this end, we propose additive…
We consider the problem of testing the equality of conditional distributions of a response variable given a vector of covariates between two populations. Such a hypothesis testing problem can be motivated from various machine learning and…
In this article, we present a nonparametric method for the general two-sample problem involving functional random variables modelled as elements of a separable Hilbert space ${\cal H}$. First, we present a general recipe based on linear…
We consider goodness-of-fit tests for uniformity of a multinomial distribution by means of tests based on a class of symmetric statistics, defined as the sum of some function of cell-frequencies. We are dealing with an asymptotic regime,…
Integrating probability and non-probability samples is increasingly important, yet unknown sampling mechanisms in non-probability sources complicate identification and efficient estimation. We develop semiparametric theory for dual-frame…
When we use the normal mixture model, the optimal number of the components describing the data should be determined. Testing homogeneity is good for this purpose; however, to construct its theory is challenging, since the test statistic…
The asymptotic solution to the problem of comparing the means of two heteroscedastic populations, based on two random samples from the populations, hinges on the pivot underpinning the construction of the confidence interval and the test…
I consider two problems in machine learning and statistics: the problem of estimating the joint probability density of a collection of random variables, known as density estimation, and the problem of inferring model parameters when their…
Comparison of two univariate distributions based on independent samples from them is a fundamental problem in statistics, with applications in a wide variety of scientific disciplines. In many situations, we might hypothesize that the two…
We analyze four different approaches to estimate a multivariate probability density (or the log-density) and its first and second order derivatives. Two methods, local log-likelihood and local Hyv\"arinen score estimation, are in terms of…