scholarly journals Jackknife empirical likelihood: small bandwidth, sparse network and high-dimensional asymptotics

Biometrika ◽  
2020 ◽  
Author(s):  
Yukitoshi Matsushita ◽  
Taisuke Otsu
Keyword(s):  
Empirical Likelihood ◽  
Goodness Of Fit ◽  
Unified Framework ◽  
Inference Problem ◽  
Semiparametric Inference ◽  
Sparse Network ◽  
Inference Problems ◽  
Instrumental Variable Regression ◽  
Small Bandwidth ◽  
Jackknife Empirical Likelihood

Summary This article aims to shed light on inference problems for statistical models under alternative or nonstandard asymptotic frameworks from the perspective of the jackknife empirical likelihood. Examples include small-bandwidth asymptotics for semiparametric inference and goodness-of-fit testing, sparse-network asymptotics, many-covariates asymptotics for regression models, and many-weak-instruments asymptotics for instrumental variable regression. We first establish Wilks’ theorem for the jackknife empirical likelihood statistic in a general semiparametric inference problem under the conventional asymptotics. We then show that the jackknife empirical likelihood statistic may lose asymptotic pivotalness in the above nonstandard asymptotic frameworks, and argue that this phenomenon can be understood in terms of the emergence of Efron & Stein (1981)’s bias of the jackknife variance estimator at first order. Finally, we propose a modification of the jackknife empirical likelihood to recover asymptotic pivotalness under both conventional and nonstandard asymptotics. Our modification works for all of the above examples and provides a unified framework for investigating nonstandard asymptotic problems.

scholarly journals Approximate Bayesian Computation for Discrete Spaces

Entropy ◽  
2021 ◽  
Vol 23 (3) ◽  
pp. 312
Author(s):  
Ilze A. Auzina ◽  
Jakub M. Tomczak
Keyword(s):  
Approximate Bayesian Computation ◽  
Likelihood Function ◽  
Real Life ◽  
Random Variables ◽  
Bayesian Computation ◽  
Inference Problem ◽  
Markov Kernel ◽  
Inference Problems ◽  
Binary Neural Network ◽  
Approximate Bayesian

Many real-life processes are black-box problems, i.e., the internal workings are inaccessible or a closed-form mathematical expression of the likelihood function cannot be defined. For continuous random variables, likelihood-free inference problems can be solved via Approximate Bayesian Computation (ABC). However, an optimal alternative for discrete random variables is yet to be formulated. Here, we aim to fill this research gap. We propose an adjusted population-based MCMC ABC method by re-defining the standard ABC parameters to discrete ones and by introducing a novel Markov kernel that is inspired by differential evolution. We first assess the proposed Markov kernel on a likelihood-based inference problem, namely discovering the underlying diseases based on a QMR-DTnetwork and, subsequently, the entire method on three likelihood-free inference problems: (i) the QMR-DT network with the unknown likelihood function, (ii) the learning binary neural network, and (iii) neural architecture search. The obtained results indicate the high potential of the proposed framework and the superiority of the new Markov kernel.

Relational Chase Procedures Interpreted as Resolution with Paramodulation1

1991 ◽  
Vol 15 (2) ◽  
pp. 123-138
Author(s):  
Joachim Biskup ◽  
Bernhard Convent
Keyword(s):  
Alternative Interpretation ◽  
Order Logic ◽  
First Order Logic ◽  
Inference Problem ◽  
First Order ◽  
Inference Problems ◽  
The One ◽  
The Relationship ◽  
Theoretical Foundations ◽  
Insight Into

In this paper the relationship between dependency theory and first-order logic is explored in order to show how relational chase procedures (i.e., algorithms to decide inference problems for dependencies) can be interpreted as clever implementations of well known refutation procedures of first-order logic with resolution and paramodulation. On the one hand this alternative interpretation provides a deeper insight into the theoretical foundations of chase procedures, whereas on the other hand it makes available an already well established theory with a great amount of known results and techniques to be used for further investigations of the inference problem for dependencies. Our presentation is a detailed and careful elaboration of an idea formerly outlined by Grant and Jacobs which up to now seems to be disregarded by the database community although it definitely deserves more attention.

An Empirical Likelihood Goodness-of-Fit Test for Diffusions

2002 ◽  
pp. 259-281 ◽  
Author(s):  
Song Xi Chen ◽  
Wolfgang Härdle ◽  
Torsten Kleinow
Keyword(s):  
Empirical Likelihood ◽  
Goodness Of Fit ◽  
Goodness Of Fit Test

Bayesian jackknife empirical likelihood

Biometrika ◽  
2019 ◽  
Vol 106 (4) ◽  
pp. 981-988
Author(s):  
Y Cheng ◽  
Y Zhao
Keyword(s):  
Bayesian Inference ◽  
Empirical Likelihood ◽  
Small Sample ◽  
New Approach ◽  
U Statistics ◽  
Posterior Inference ◽  
Jackknife Empirical Likelihood ◽  
General Tool ◽  
Control Study ◽  
Better Than

Summary Empirical likelihood is a very powerful nonparametric tool that does not require any distributional assumptions. Lazar (2003) showed that in Bayesian inference, if one replaces the usual likelihood with the empirical likelihood, then posterior inference is still valid when the functional of interest is a smooth function of the posterior mean. However, it is not clear whether similar conclusions can be obtained for parameters defined in terms of $U$-statistics. We propose the so-called Bayesian jackknife empirical likelihood, which replaces the likelihood component with the jackknife empirical likelihood. We show, both theoretically and empirically, the validity of the proposed method as a general tool for Bayesian inference. Empirical analysis shows that the small-sample performance of the proposed method is better than its frequentist counterpart. Analysis of a case-control study for pancreatic cancer is used to illustrate the new approach.

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