Maximum likelihood is by far the most popular general method of estimation. Its widespread acceptance is seen on the one hand in the very large body of research dealing with its theoretical properties, and on the other in the almost unlimited list of applications. To give a reasonably general definition of maximum likelihood estimates, let X = (X1, . . . , Xn) be a random vector of observations...

Researchers of uncommon diseases are often interested in assessing potential risk factors. Given the low incidence of disease, these studies are frequently case-control in design. Such a design allows a sufficient number of cases to be obtained without extensive sampling and can increase efficiency; however, these case-control samples are then biased since the proportion of cases in the sample ...

BACKGROUND We propose a mathematical model for multichannel assessment of the trial-to-trial variability of auditory evoked brain responses in magnetoencephalography (MEG). METHODS Following the work of de Munck et al., our approach is based on the maximum likelihood estimation and involves an approximation of the spatio-temporal covariance of the contaminating background noise by means of th...

In some models, both parametric and not, maximum likelihood estimation fails to be consistent. We investigate why the maximum likelihood method breaks down with some examples and notice the paradox that, in those same models, maximum likelihood estimation would have been consistent if the data had been measured with error. With this motivation we define doubly-smoothed maximum likelihood as a n...

Because of the presence of Jacobian terms, determinants which arose as a result of a transformation of variables, many common likelihood functions have singularities. This fact has several implications for maximum likelihood estimation. The most interesting of these is that singularities often correspond with economically meaningful restrictions, and they can be used to impose the latter. Sever...

The reconstruction of a species tree from genomic data faces a double hurdle. First, the (gene) tree describing the evolution of each gene may differ from the species tree, for instance, due to incomplete lineage sorting. Second, the aligned genetic sequences at the leaves of each gene tree provide merely an imperfect estimate of the topology of the gene tree. In this note, we demonstrate forma...

We introduce a new class of the slash distribution using the epsilon half normal distribution. The newly defined model extends the slashed half normal distribution and has more kurtosis than the ordinary half normal distribution. We study the characterization and properties including moments and some measures based on moments of this distribution. A simulation is conducted to investigate asympt...

Maximum likelihood estimation of the concentration parameter of von Mises-Fisher distributions involves inverting the ratio [Formula: see text] of modified Bessel functions and computational methods are required to invert these functions using approximative or iterative algorithms. In this paper we use Amos-type bounds for [Formula: see text] to deduce sharper bounds for the inverse function, d...

Targeted maximum likelihood estimation of a parameter of a data generating distribution, known to be an element of a semi-parametric model, involves constructing a parametric model through an initial density estimator with parameter ɛ representing an amount of fluctuation of the initial density estimator, where the score of this fluctuation model at ɛ = 0 equals the efficient influence curve/ca...

Systematic biases such as long branch attraction can mislead commonly relied upon model-based (i.e. maximum likelihood and Bayesian) phylogenetic methods when, as is usually the case with empirical data, there is model misspecification. We present PhyQuart, a new method for evaluating the three possible binary trees for any quartet of taxa. PhyQuart was developed through a process of reciprocal...