Confidence Regions Near Singular Information and Boundary Points With Applications to Mixed Models

03/18/2021
by   Karl Oskar Ekvall, et al.
0

We propose confidence regions with asymptotically correct uniform coverage probability of parameters whose Fisher information matrix can be singular at important points of the parameter set. Our work is motivated by the need for reliable inference on scale parameters close or equal to zero in mixed models, which is obtained as a special case. The confidence regions are constructed by inverting a continuous extension of the score test statistic standardized by expected information, which we show exists at points of singular information under regularity conditions. Similar results have previously only been obtained for scalar parameters, under conditions stronger than ours, and applications to mixed models have not been considered. In simulations our confidence regions have near-nominal coverage with as few as n = 20 independent observations, regardless of how close to the boundary the true parameter is. It is a corollary of our main results that the proposed test statistic has an asymptotic chi-square distribution with degrees of freedom equal to the number of tested parameters, even if they are on the boundary of the parameter set.

READ FULL TEXT
POST COMMENT

Comments

There are no comments yet.

Authors

page 1

page 2

page 3

page 4

10/05/2018

Asymptotic Confidence Regions Based on the Adaptive Lasso with Partial Consistent Tuning

We construct confidence sets based on an adaptive Lasso estimator with c...
02/19/2019

Computation of the expected value of a function of a chi-distributed random variable

We consider the problem of numerically evaluating the expected value of ...
11/09/2020

Singular Sturm-Liouville Problems with Zero Potential (q=0) and Singular Slow Feature Analysis

A Sturm-Liouville problem (λ wy=(ry')'+qy) is singular if its domain is ...
09/11/2021

On Some Problems of Confidence Region Construction

The general problem of constructing confidence regions is unsolved in th...
02/24/2020

Confidence Sets and Hypothesis Testing in a Likelihood-Free Inference Setting

Parameter estimation, statistical tests and confidence sets are the corn...
10/01/2019

Regularity of the solution of the scalar Signorini problem in polygonal domains

The Signorini problem for the Laplace operator is considered in a genera...
11/09/2018

Median Confidence Regions in a Nonparametric Model

The problem of constructing confidence regions for the median in the non...
This week in AI

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