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In this paper, we consider the alleviation of the boundary problem when the probability density function has bounded support. We apply Robbins-Monro's algorithm and Bernstein polynomials to construct a recursive density estimator. We study…

Statistics Theory · Mathematics 2019-04-16 Yousri SLAOUI , Asma JMAEI

In the context of a species sampling problem we discuss a non-parametric maximum likelihood estimator for the underlying probability mass function. The estimator is known in the computer science literature as the high profile estimator. We…

Statistics Theory · Mathematics 2018-01-12 Dragi Anevski , Richard D. Gill , Stefan Zohren

Westling and Carone (2020) proposed a framework for studying the large sample distributional properties of generalized Grenander-type estimators, a versatile class of nonparametric estimators of monotone functions. The limiting distribution…

Statistics Theory · Mathematics 2024-07-08 Matias D. Cattaneo , Michael Jansson , Kenichi Nagasawa

We consider Grenander type estimators for monotone functions $f$ in a very general setting, which includes estimation of monotone regression curves, monotone densities, and monotone failure rates. These estimators are defined as the…

Statistics Theory · Mathematics 2014-10-09 Cécile Durot , Hendrik P. Lopuhaä

Robust estimators, like the median of a point set, are important for data analysis in the presence of outliers. We study robust estimators for locationally uncertain points with discrete distributions. That is, each point in a data set has…

Discrete Mathematics · Computer Science 2018-03-14 Kevin Buchin , Jeff M. Phillips , Pingfan Tang

We study the problem of estimating the joint probability mass function (pmf) over two random variables. In particular, the estimation is based on the observation of $m$ samples containing both variables and $n$ samples missing one fixed…

Statistics Theory · Mathematics 2023-05-17 H. S. Melihcan Erol , Erixhen Sula , Lizhong Zheng

We investigate nonparametric estimation of a monotone baseline hazard and a decreasing baseline density within the Cox model. Two estimators of a nondecreasing baseline hazard function are proposed. We derive the nonparametric maximum…

Statistics Theory · Mathematics 2013-01-10 Hendrik P. Lopuhaä , Gabriela F. Nane

Standard maximum likelihood estimation cannot be applied to discrete energy-based models in the general case because the computation of exact model probabilities is intractable. Recent research has seen the proposal of several new…

Machine Learning · Computer Science 2012-02-20 Benjamin Marlin , Nando de Freitas

The discrete kernel method was developed to estimate count data distributions, distinguishing discrete associated kernels based on their asymptotic behaviour. This study investigates the class of discrete asymmetric kernels and their…

Methodology · Statistics 2017-02-07 Tristan Senga Kiessé

Based on the convex least-squares estimator, we propose two different procedures for testing convexity of a probability mass function supported on N with an unknown finite support. The procedures are shown to be asymptotically calibrated.

Statistics Theory · Mathematics 2017-01-17 Fadoua Balabdaoui , Cécile Durot , François Koladjo

Jittering estimators are nonparametric function estimators for mixed data. They extend arbitrary estimators from the continuous setting by adding random noise to discrete variables. We give an in-depth analysis of the jittering kernel…

Methodology · Statistics 2017-11-15 Thomas Nagler

We consider a complex-valued linear mixture model, under discrete weakly stationary processes. We recover latent components of interest, which have undergone a linear mixing. We study asymptotic properties of a classical unmixing estimator,…

Statistics Theory · Mathematics 2020-03-12 Niko Lietzén , Lauri Viitasaari , Pauliina Ilmonen

We consider the problem of mean estimation assuming only finite variance. We study a new class of mean estimators constructed by integrating over random noise applied to a soft-truncated empirical mean estimator. For appropriate choices of…

Statistics Theory · Mathematics 2019-06-26 Matthew J. Holland

This article introduces a method for estimating the smoothness of a stationary, isotropic Gaussian random field from irregularly spaced data. This involves novel constructions of higher-order quadratic variations and the establishment of…

Statistics Theory · Mathematics 2015-10-30 Wei-Liem Loh

We study the problem of online monotone density estimation, where density estimators must be constructed in a predictable manner from sequentially observed data. We propose two online estimators: an online analogue of the classical…

Machine Learning · Statistics 2026-05-25 Rohan Hore , Ruodu Wang , Aaditya Ramdas

We study the isotonic regression estimator over a general countable pre-ordered set. We obtain the limiting distribution of the estimator and study its properties. It is proved that, under some general assumptions, the limiting distribution…

Statistics Theory · Mathematics 2018-11-06 Dragi Anevski , Vladimir Pastukhov

We propose a new framework for imposing monotonicity constraints in a Bayesian nonparametric setting based on numerical solutions of stochastic differential equations. We derive a nonparametric model of monotonic functions that allows for…

Machine Learning · Statistics 2020-02-26 Ivan Ustyuzhaninov , Ieva Kazlauskaite , Carl Henrik Ek , Neill D. F. Campbell

We consider the Grenander estimator that is the maximum likelihood estimator for non-increasing densities. We prove uniform central limit theorems for certain subclasses of bounded variation functions and for H\"older balls of smoothness…

Statistics Theory · Mathematics 2015-06-29 Jakob Söhl

The telegraph process $\{X(t), t>0\}$, is supposed to be observed at $n+1$ equidistant time points $t_i=i\Delta_n,i=0,1,..., n$. The unknown value of $\lambda$, the underlying rate of the Poisson process, is a parameter to be estimated. The…

Probability · Mathematics 2007-06-13 stefano m. iacus , nakahiro yoshida

In this paper, we investigate the (in)-consistency of different bootstrap methods for constructing confidence intervals in the class of estimators that converge at rate $n^{1/3}$. The Grenander estimator, the nonparametric maximum…

Statistics Theory · Mathematics 2010-10-20 Bodhisattva Sen , Moulinath Banerjee , Michael Woodroofe