
Distributionally Robust Parametric Maximum Likelihood Estimation
We consider the parameter estimation problem of a probabilistic generati...
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Singularity structures and impacts on parameter estimation in finite mixtures of distributions
Singularities of a statistical model are the elements of the model's par...
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Estimation of the Number of Components of NonParametric Multivariate Finite Mixture Models
We propose a novel estimator for the number of components (denoted by M)...
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Multivariate, Heteroscedastic Empirical Bayes via Nonparametric Maximum Likelihood
Multivariate, heteroscedastic errors complicate statistical inference in...
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Entropybased test for generalized Gaussian distributions
In this paper, we provide the proof of L^2 consistency for the kth neare...
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Combining multiple imputation with raking of weights in the setting of nearlytrue models
Raking of weights is one approach to using data from the full cohort in ...
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A Tutorial on Multivariate kStatistics and their Computation
This document aims to provide an accessible tutorial on the unbiased est...
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A robust multivariate linear nonparametric maximum likelihood model for ties
Statistical analysis in applied research, across almost every field (e.g., biomedical, economics, computer science, and psychological) makes use of samples upon which the explicit error distribution of the dependent variable is unknown or, at best, difficult to linearly model. Yet, these assumptions are extremely common. Unknown distributions are of course biased when incorrectly specified, compromising the generalisability of our interpretations – the linearly unbiased Euclidean distance is very difficult to correctly identify upon finite samples and therefore results in an estimator which is neither unbiased nor maximally informative when incorrectly applied. The alternative common solution to the problem however, the use of nonparametric statistics, has its own fundamental flaws. In particular, these flaws revolve around the problem of orderstatistics and the estimation in the presence of ties, which often removes the introduction of multiple independent variables and the estimation of interactions. We introduce a competitor to the Euclidean norm, the Kemeny norm, which we prove to be a valid Banach space, and construct a multivariate linear expansion of the KendallTheilSen estimator, which performs without compromising the parameter space extensibility, and establish its linear maximum likelihood properties. Empirical demonstrations upon both simulated and empirical data shall be used to demonstrate these properties, such that the new estimator is nearly equivalent in power for the glm upon Gaussian data, but grossly superior for a vast array of analytic scenarios, including finite ordinal sumscore analysis, thereby aiding in the resolution of replication in the Applied Sciences.
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