On full efficiency of the maximum composite likelihood estimator

AbstractMethods of estimating two-locus sample probabilities under a neutral model are extended in several ways. Estimation of sample probabilities is described when the ancestral or derived status of each allele is specified. In addition, probabilities for two-locus diploid samples are provided. A method for using these two-locus probabilities to test whether an observed level of linkage disequilibrium is unusually large or small is described. In addition, properties of a maximum-likelihood estimator of the recombination parameter based on independent linked pairs of sites are obtained. A composite-likelihood estimator, for more than two linked sites, is also examined and found to work as well, or better, than other available ad hoc estimators. Linkage disequilibrium in the Xq28 and Xq25 region of humans is analyzed in a sample of Europeans (CEPH). The estimated recombination parameter is about five times smaller than one would expect under an equilibrium neutral model.

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Large-sample confidence intervals of information-theoretic measures in linguistics

Journal of Research Design and Statistics in Linguistics and Communication Science ◽

10.1558/jrds.40134 ◽

2020 ◽

Vol 6 (1) ◽

pp. 19-54

Author(s):

Ryan Ka Yau Lai ◽

Youngah Do

Keyword(s):

Maximum Likelihood ◽

Corpus Linguistics ◽

Delta Method ◽

Confidence Bounds ◽

Likelihood Estimator ◽

Information Theoretic ◽

Leibler Divergence ◽

Information Theoretic Measures ◽

Data Points ◽

Measure Of Uncertainty

This article explores a method of creating confidence bounds for information-theoretic measures in linguistics, such as entropy, Kullback-Leibler Divergence (KLD), and mutual information. We show that a useful measure of uncertainty can be derived from simple statistical principles, namely the asymptotic distribution of the maximum likelihood estimator (MLE) and the delta method. Three case studies from phonology and corpus linguistics are used to demonstrate how to apply it and examine its robustness against common violations of its assumptions in linguistics, such as insufficient sample size and non-independence of data points.

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The Comparison Between the Bayes Estimator and the Maximum Likelihood Estimator of the Reliability Function for Negative Exponential Distribution

Ibn AL- Haitham Journal For Pure and Applied Science ◽

10.30526/2017.ihsciconf.1815 ◽

2018 ◽

pp. 439

Author(s):

Hazim Mansour Gorgees ◽

Bushra Abdualrasool Ali ◽

Raghad Ibrahim Kathum

Keyword(s):

Maximum Likelihood ◽

Maximum Likelihood Estimator ◽

Exponential Distribution ◽

Reliability Function ◽

Bayes Estimator ◽

Likelihood Estimator ◽

Monte Carlo Simulation Technique ◽

Negative Exponential Distribution ◽

Negative Exponential ◽

Better Than

In this paper, the maximum likelihood estimator and the Bayes estimator of the reliability function for negative exponential distribution has been derived, then a Monte –Carlo simulation technique was employed to compare the performance of such estimators. The integral mean square error (IMSE) was used as a criterion for this comparison. The simulation results displayed that the Bayes estimator performed better than the maximum likelihood estimator for different samples sizes.

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Transforming variables to central normality

Machine Learning ◽

10.1007/s10994-021-05960-5 ◽

2021 ◽

Author(s):

Jakob Raymaekers ◽

Peter J. Rousseeuw

Keyword(s):

Maximum Likelihood ◽

Maximum Likelihood Estimator ◽

Simulation Study ◽

Real Data ◽

Data Sets ◽

Transformation Parameter ◽

Likelihood Estimator ◽

Extensive Simulation ◽

Highly Sensitive

AbstractMany real data sets contain numerical features (variables) whose distribution is far from normal (Gaussian). Instead, their distribution is often skewed. In order to handle such data it is customary to preprocess the variables to make them more normal. The Box–Cox and Yeo–Johnson transformations are well-known tools for this. However, the standard maximum likelihood estimator of their transformation parameter is highly sensitive to outliers, and will often try to move outliers inward at the expense of the normality of the central part of the data. We propose a modification of these transformations as well as an estimator of the transformation parameter that is robust to outliers, so the transformed data can be approximately normal in the center and a few outliers may deviate from it. It compares favorably to existing techniques in an extensive simulation study and on real data.

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