Related papers: Estimation of a functional single index model with…
Multivariate density estimation is a popular technique in statistics with wide applications including regression models allowing for heteroskedasticity in conditional variances. The estimation problems become more challenging when…
We introduce a nonparametric way to estimate the global probability density function for a random persistence diagram. Precisely, a kernel density function centered at a given persistence diagram and a given bandwidth is constructed. Our…
In the context of regressing a response $Y$ on a predictor $X$, we consider estimating the local modes of the distribution of $Y$ given $X=x$ when $X$ is prone to measurement error. We propose two nonparametric estimation methods, with one…
Recently nonparametric functional model with functional responses has been proposed within the functional reproducing kernel Hilbert spaces (fRKHS) framework. Motivated by its superior performance and also its limitations, we propose a…
Bayesian methods are developed for the multivariate nonparametric regression problem where the domain is taken to be a compact Riemannian manifold. In terms of the latter, the underlying geometry of the manifold induces certain symmetries…
We develop Bayesian models for density regression with emphasis on discrete outcomes. The problem of density regression is approached by considering methods for multivariate density estimation of mixed scale variables, and obtaining…
In this paper, we propose a robust profile estimation method for the parametric and nonparametric components of a single index model when the errors have a strongly unimodal density with unknown nuisance parameter. Under regularity…
Estimating density functionals of analog sources is an important problem in statistical signal processing and information theory. Traditionally, estimating these quantities requires either making parametric assumptions about the underlying…
In the context of estimating local modes of a conditional density based on kernel density estimators, we show that existing bandwidth selection methods developed for kernel density estimation are unsuitable for mode estimation. We propose…
To estimate accurately the parameters of a regression model, the sample size must be large enough relative to the number of possible predictors for the model. In practice, sufficient data is often lacking, which can lead to overfitting of…
A residual-based empirical distribution function is proposed to estimate the distribution function of the errors of a heteroskedastic nonparametric regression with responses missing at random based on completely observed data, and this…
We estimate the derivative of a probability density function defined on $[0,\infty)$. For this purpose, we choose the class of kernel estimators with asymmetric gamma kernel functions. The use of gamma kernels is fruitful due to the fact…
The performance of multivariate kernel density estimation (KDE) depends strongly on the choice of bandwidth matrix. The high computational cost required for its estimation provides a big motivation to develop fast and accurate methods. One…
Uncertainty estimation is an essential step in the evaluation of the robustness for deep learning models in computer vision, especially when applied in risk-sensitive areas. However, most state-of-the-art deep learning models either fail to…
In a large class of statistical inverse problems it is necessary to suppose that the transformation that is inverted is known. Although, in many applications, it is unrealistic to make this assumption, the problem is often insoluble without…
We explain how effective automatic probability density function estimates can be constructed using contemporary Bayesian inference engines such as those based on no-U-turn sampling and expectation propagation. Extensive simulation studies…
With the increasing availability of non-Euclidean data objects, statisticians are faced with the task of developing appropriate statistical methods for their analysis. For regression models in which the predictors lie in $\mathbb{R}^p$ and…
We consider regression models with parametric (linear or nonlinear) regression function and allow responses to be ``missing at random.'' We assume that the errors have mean zero and are independent of the covariates. In order to estimate…
Multivariate kernel density estimations have received much spate of interest. In addition to conventional methods of (non-)classical associated-kernels for (un)bounded densities and bandwidth selections, the multiple extended-beta kernel…
Single index model is a powerful yet simple model, widely used in statistics, machine learning, and other scientific fields. It models the regression function as $g(<a,x>)$, where a is an unknown index vector and x are the features. This…