Related papers: Nonparametric methods for volatility density estim…
The estimation of entropy rates for stationary discrete-valued stochastic processes is a well studied problem in information theory. However, estimating the entropy rate for stationary continuous-valued stochastic processes has not received…
Unlinked regression, in which covariates and responses are observed separately without known correspondence, has recently gained increasing attention. Deconvolution, on the other hand, is a fundamental and challenging problem in…
Let $X_1,..., X_n$ be i.i.d.\ copies of a random variable $X=Y+Z,$ where $ X_i=Y_i+Z_i,$ and $Y_i$ and $Z_i$ are independent and have the same distribution as $Y$ and $Z,$ respectively. Assume that the random variables $Y_i$'s are…
We consider the problem of estimating the density of observations taking values in classical or nonclassical spaces such as manifolds and more general metric spaces. Our setting is quite general but also sufficiently rich in allowing the…
For highly skewed or fat-tailed distributions, mean or median-based methods often fail to capture the central tendencies in the data. Despite being a viable alternative, estimating the conditional mode given certain covariates (or mode…
Spectral methods have greatly advanced the estimation of latent variable models, generating a sequence of novel and efficient algorithms with strong theoretical guarantees. However, current spectral algorithms are largely restricted to…
The paper develops new methods of non-parametric estimation a compound Poisson distribution. Such a problem arise, in particular, in the inference of a Levy process recorded at equidistant time intervals. Our key estimator is based on…
The partially observed linear Gaussian system of stochastic differential equations with low noise in observations is considered. A kernel-type estimators are used for estimation of the quadratic variation of the derivative of the limit of…
This paper deals with the nonparametric density estimation of the regression error term assuming its independence with the covariate. The difference between the feasible estimator which uses the estimated residuals and the unfeasible one…
This paper addresses the deconvolution problem of estimating a square-integrable probability density from observations contaminated with additive measurement errors having a known density. The estimator begins with a density estimate of the…
We describe nonparametric deconvolution models (NDMs), a family of Bayesian nonparametric models for collections of data in which each observation is the average over the features from heterogeneous particles. For example, these types of…
Density deconvolution deals with the estimation of the probability density function $f$ of a random signal from $n\geq1$ data observed with independent and known additive random noise. This is a classical problem in statistics, for which…
The spectral density function describes the second-order properties of a stationary stochastic process on $\mathbb{R}^d$. This paper considers the nonparametric estimation of the spectral density of a continuous-time stochastic process…
This paper provides a semiparametric model of estimating states of the volatility defined as the squared diffusion coefficient of a stochastic differential equation. Without assuming any functional form of the volatility function, we…
In the framework of shape constrained estimation, we review methods and works done in convex set estimation. These methods mostly build on stochastic and convex geometry, empirical process theory, functional analysis, linear programming,…
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…
The development of wavelet theory has in recent years spawned applications in signal processing, in fast algorithms for integral transforms, and in image and function representation methods. This last application has stimulated interest in…
Non-linear latent variable models have become increasingly popular in a variety of applications. However, there has been little study on theoretical properties of these models. In this article, we study rates of posterior contraction in…
In this paper we propose a new method of joint nonparametric estimation of probability density and its support. As is well known, nonparametric kernel density estimator has "boundary bias problem" when the support of the population density…
In many real applications, the distribution of measurement error could vary with each subject or even with each observation so the errors are heteroscedastic. In this paper, we propose a fast algorithm using a simulation-extrapolation…