Functionals of nonparametric maximum likelihood estimators

05/09/2022
by   Piet Groeneboom, et al.
0

Nonparametric maximum likelihood estimators (MLEs) in inverse problems often have non-normal limit distributions, like Chernoff's distribution. However, if one considers smooth functionals of the model, with corresponding functionals of the MLE, one gets normal limit distributions and faster rates of convergence. We demonstrate this for interval censoring models and a model for the incubation time of Covid-19. The usual approach in the latter models is to use parametric distributions, like Weibull and gamma distributions, which leads to inconsistent estimators. Smoothed bootstrap methods are discussed for choosing a bandwidth and constructing confidence intervals. The classical bootstrap, based on the nonparametric MLE itself, has been proved to be inconsistent in this situation.

READ FULL TEXT

Authors

page 1

page 2

page 3

page 4

08/28/2021

Nonparametric estimation of the incubation time distribution

We discuss nonparametric estimators of the distribution of the incubatio...
12/13/2019

R-estimators in GARCH models; asymptotics, applications and bootstrapping

The quasi-maximum likelihood estimation is a commonly-used method for es...
11/28/2021

An inverse Sanov theorem for curved exponential families

We prove the large deviation principle (LDP) for posterior distributions...
06/24/2022

On the validity of bootstrap uncertainty estimates in the Mallows-Binomial model

The Mallows-Binomial distribution is the first joint statistical model f...
03/01/2015

JUMP-Means: Small-Variance Asymptotics for Markov Jump Processes

Markov jump processes (MJPs) are used to model a wide range of phenomena...
09/29/2020

On Smooth Change-Point Location Estimation for Poisson Processes

We are interested in estimating the location of what we call "smooth cha...
01/28/2022

Generalized statistics: applications to data inverse problems with outlier-resistance

The conventional approach to data-driven inversion framework is based on...
This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.