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We present a local density estimator based on first order statistics. To estimate the density at a point, $x$, the original sample is divided into subsets and the average minimum sample distance to $x$ over all such subsets is used to…
Density estimation is an interdisciplinary topic at the intersection of statistics, theoretical computer science and machine learning. We review some old and new techniques for bounding the sample complexity of estimating densities of…
Let $\textbf{X} = (X_1,\ldots, X_p)$ be a stochastic vector having joint density function $f_{\textbf{X}}(x)$ with partitions $\textbf{X}_1 = (X_1,\ldots, X_k)$ and $\textbf{X}_2 = (X_{k+1},\ldots, X_p)$. A new method for estimating the…
We investigate the modeling and the numerical solution of machine learning problems with prediction functions which are linear combinations of elements of a possibly infinite-dimensional dictionary. We propose a novel flexible composite…
We consider the problem of estimating the density $g$ of identically distributed variables $X\_i$, from a sample $Z\_1, ..., Z\_n$ where $Z\_i=X\_i+\sigma\epsilon\_i$, $i=1, ..., n$ and $\sigma \epsilon\_i$ is a noise independent of $X\_i$…
Conditional Density Estimation (CDE) models deal with estimating conditional distributions. The conditions imposed on the distribution are the inputs of the model. CDE is a challenging task as there is a fundamental trade-off between model…
Examples with bound information on the regression function and density abound in many real applications. We propose a novel approach for estimating such functions by incorporating the prior knowledge on the bounds. Specially, a Gaussian…
We propose local polynomial estimators for the conditional mean of a continuous response when only pooled response data are collected under different pooling designs. Asymptotic properties of these estimators are investigated and compared.…
We give a highly efficient "semi-agnostic" algorithm for learning univariate probability distributions that are well approximated by piecewise polynomial density functions. Let $p$ be an arbitrary distribution over an interval $I$ which is…
This paper investigates the bias and the weak Bahadur representation of a local polynomial estimator of the conditional quantile function and its derivatives. The bias and Bahadur remainder term are studied uniformly with respect to the…
We study the distribution of hard-, soft-, and adaptive soft-thresholding estimators within a linear regression model where the number of parameters k can depend on sample size n and may diverge with n. In addition to the case of known…
Regression problems are traditionally analyzed via univariate characteristics like the regression function, scale function and marginal density of regression errors. These characteristics are useful and informative whenever the association…
In this article we perform an asymptotic analysis of parallel Bayesian logspline density estimators. Such estimators are useful for the analysis of datasets that are partitioned into subsets and stored in separate databases without the…
Conditional density estimation (CDE) models can be useful for many statistical applications, especially because the full conditional density is estimated instead of traditional regression point estimates, revealing more information about…
Conditional density estimation (density regression) estimates the distribution of a response variable y conditional on covariates x. Utilizing a partition model framework, a conditional density estimation method is proposed using logistic…
This paper investigates the size performance of Wald tests for CAViaR models (Engle and Manganelli, 2004). We find that the usual estimation strategy on test statistics yields inaccuracies. Indeed, we show that existing density estimation…
We study the estimation, in Lp-norm, of density functions defined on [0,1]^d. We construct a new family of kernel density estimators that do not suffer from the so-called boundary bias problem and we propose a data-driven procedure based on…
We describe a method to computationally estimate the probability density function of a univariate random variable by applying the maximum entropy principle with some local conditions given by Gaussian functions. The estimation errors and…
We develop a new method for generating prediction sets that combines the flexibility of conformal methods with an estimate of the conditional distribution $P_{Y \mid X}$. Existing methods, such as conformalized quantile regression and…
We study regression discontinuity designs when covariates are included in the estimation. We examine local polynomial estimators that include discrete or continuous covariates in an additive separable way, but without imposing any…