Related papers: Multivariate Density Estimation via Adaptive Parti…
This paper introduces a high-dimensional binary variate model that accommodates nonstationary covariates and factors, and studies their asymptotic theory. This framework encompasses scenarios where single indices are nonstationary or…
In this paper, we study the problem of adaptive estimation of the spectral density of a stationary Gaussian process. For this purpose, we consider a wavelet-based method which combines the ideas of wavelet approximation and estimation by…
We present large sample results for partitioning-based least squares nonparametric regression, a popular method for approximating conditional expectation functions in statistics, econometrics, and machine learning. First, we obtain a…
The model interpretation is essential in many application scenarios and to build a classification model with a ease of model interpretation may provide useful information for further studies and improvement. It is common to encounter with a…
Motivated by studies in biological sciences to detect differentially expressed genes, a semiparametric two-component mixture model with one known component is being studied in this paper. Assuming the density of the unknown component to be…
Theoretical guarantees are established for a standard estimator in a semi-parametric finite mixture model, where each component density is modeled as a product of univariate densities under a conditional independence assumption. The focus…
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…
Nonparametric density estimation is an unsupervised learning problem. In this work we propose a two-step procedure that casts the density estimation problem in the first step into a supervised regression problem. The advantage is that we…
Partition-wise models offer a flexible approach for modeling complex and multidimensional data that are capable of producing interpretable results. They are based on partitioning the observed data into regions, each of which is modeled with…
The Mutual Information (MI) is an often used measure of dependency between two random variables utilized in information theory, statistics and machine learning. Recently several MI estimators have been proposed that can achieve parametric…
Reliable density estimation is fundamental for numerous applications in statistics and machine learning. In many practical scenarios, data are best modeled as mixtures of component densities that capture complex and multimodal patterns.…
We introduce the Binless Multidimensional Thermodynamic Integration (BMTI) method for nonparametric, robust, and data-efficient density estimation. BMTI estimates the logarithm of the density by initially computing log-density differences…
This article is devoted to nonlinear approximation and estimation via piecewise polynomials built on partitions into dyadic rectangles. The approximation rate is studied over possibly inhomogeneous and anisotropic smoothness classes that…
In this paper, we study the nonparametric maximum likelihood estimator (MLE) of a convex hazard function. We show that the MLE is consistent and converges at a local rate of $n^{2/5}$ at points $x_0$ where the true hazard function is…
Divergence estimators based on direct approximation of density-ratios without going through separate approximation of numerator and denominator densities have been successfully applied to machine learning tasks that involve distribution…
Density Estimation is one of the central areas of statistics whose purpose is to estimate the probability density function underlying the observed data. It serves as a building block for many tasks in statistical inference, visualization,…
This paper explores Maximum Likelihood in parametric models in the context of Sanov type Large Deviation Probabilities. MLE in parametric models under weighted sampling is shown to be associated with the minimization of a specific…
Given a sample from a discretely observed multidimensional compound Poisson process, we study the problem of nonparametric estimation of its jump size density $r_0$ and intensity $\lambda_0$. We take a nonparametric Bayesian approach to the…
We consider the problem of estimating parameters of stochastic differential equations (SDEs) with discrete-time observations that are either completely or partially observed. The transition density between two observations is generally…
This paper studies the minimax rate of nonparametric conditional density estimation under a weighted absolute value loss function in a multivariate setting. We first demonstrate that conditional density estimation is impossible if one only…