In this paper we will compare the performance of two techniques (the Maximum Likelihood Estimation (MLJZ) and the Population Vector (PV)) for estimating the interpretation of neuronal activity in a population of neurons. Although such a comparison has been made before, so far only homogeneous distributions of receptive fields have been investigated. Since the performance of both methods depends...

Estimating equation approaches have been widely used in statistics inference. Important examples of estimating equations are the likelihood equations. Since its introduction by Sir R. A. Fisher almost a century ago, maximum likelihood estimation (MLE) is still the most popular estimation method used for fitting probability distribution to data, including fitting lifetime distributions with cens...

The introduced three parameter (position μ, scale Σ and shape γ) multivariate generalized Normal distribution (γ-GND) is based on a strong theoretical background and emerged from Logarithmic Sobolev Inequalities. It includes a number of well known distributions such as the multivariate Uniform, Normal, Laplace and the degenerated Dirac distributions. In this paper, the cumulative distribution, ...

Unsupervised learning of linguistic structure is a difficult problem. A common approach is to define a generative model and maximize the probability of the hidden structure given the observed data. Typically, this is done using maximum-likelihood estimation (MLE) of the model parameters. We show using part-of-speech tagging that a fully Bayesian approach can greatly improve performance. Rather ...

This paper deals with the problem of global parameter estimation in the Cox-IngersollRoss (CIR) model (Xt)t≥0. This model is frequently used in finance for example to model the evolution of short-term interest rates or as a dynamic of the volatility in the Heston model. In continuity with a recent work by Ben Alaya and Kebaier [1], we establish new asymptotic results on the maximum likelihood e...

This short communication uses a simple experiment to show that fitting to a power law distribution by using graphical methods based on linear fit on the log-log scale is biased and inaccurate. It shows that using maximum likelihood estimation (MLE) is far more robust. Finally, it presents a new table for performing the Kolmogorov-Smirnof test for goodness-of-fit tailored to power-law distributi...

Delft University of Technology and Vrije Universiteit Amsterdam, University of Washington and University of Washington We study nonparametric estimation of the sub-distribution functions for current status data with competing risks. Our main interest is in the nonparametric maximum likelihood estimator (MLE), and for comparison we also consider the ‘naive estimator’ of Jewell, Van der Laan and ...

We introduce a maximum Lq-likelihood estimation (MLqE) of mixture models using our proposed expectation maximization (EM) algorithm, namely the EM algorithm with Lq-likelihood (EM-Lq). Properties of the MLqE obtained from the proposed EMLq are studied through simulated mixture model data. Compared with the maximum likelihood estimation (MLE) which is obtained from the EM algorithm, the MLqE pro...

In this article, we combine results from the theory of linear exponential families, polyhedral geometry and algebraic geometry to provide analytic and geometric characterizations of log-linear models and maximum likelihood estimation. Geometric and combinatorial conditions for the existence of the Maximum Likelihood Estimate (MLE) of the cell mean vector of a contingency table are given for gen...

*Correspondence: [email protected] 2Department of Mathematics and Statistics, UNC Charlotte, 9201 University City Blvd, 28223 Charlotte, USA Full list of author information is available at the end of the article Abstract The maximum likelihood estimator (MLE) of Gini-Simpson’s diversity index (GS) is widely used but suffers from large bias when the number of species is large or infinite. We prop...