Related papers: Generalized Estimating Equation for the Student-t …
Label Proportion Learning (LLP) addresses the classification problem where multiple instances are grouped into bags and each bag contains information about the proportion of each class. However, in practical applications, obtaining precise…
The assumption of normality in data has been considered in the field of statistical analysis for a long time. However, in many practical situations, this assumption is clearly unrealistic. It has recently been suggested that the use of…
In this paper, we study the maximum likelihood estimation of the parameters of the multivariate and matrix variate symmetric Laplace distributions through group actions. The multivariate and matrix variate symmetric Laplace distributions…
Mixtures of generalized normal distributions (MGND) have gained popularity for modelling datasets with complex statistical behaviours. However, the estimation of the shape parameter within the maximum likelihood framework is quite complex,…
The Renyi distribution ensuring the maximum of a Renyi entropy is investigated for a particular case of a power--law Hamiltonian. Both Lagrange parameters, $\alpha$ and $\beta$ can be excluded. It is found that $\beta$ does not depend on a…
We investigate stochastic comparisons between exponential family distributions and their mixtures with respect to the usual stochastic order, the hazard rate order, the reversed hazard rate order, and the likelihood ratio order. A general…
Suppose that the normal model is used for data $Y_1,\ldots,Y_n$, but that the true distribution is a t-distribution with location and scale parameters $\xi$ and $\sigma$ and $m$ degrees of freedom. The normal model corresponds to…
The generalised linear model (GLM) is a very important tool for analysing real data in biology, sociology, agriculture, engineering and many other application domain where the relationship between the response and explanatory variables may…
We study probability density functions that are log-concave. Despite the space of all such densities being infinite-dimensional, the maximum likelihood estimate is the exponential of a piecewise linear function determined by finitely many…
We consider a version of D. Price's model for the growth of a bibliographic network, where in each iteration a constant number of citations is randomly allocated according to a weighted combination of accidental (uniformly distributed) and…
In this paper, following standard arguments, the maximum Renyi entropy problem for the weighted case is analyzed. We verify that under some constrains on weight function, the Student-r and Student-t distributions maximize the weighted Renyi…
We show that the mean-model parameter is always orthogonal to the error distribution in generalized linear models. Thus, the maximum likelihood estimator of the mean-model parameter will be asymptotically efficient regardless of whether the…
The property of learning-curve monotonicity, highlighted in a recent series of work by Loog, Mey and Viering, describes algorithms which only improve in average performance given more data, for any underlying data distribution within a…
Recent advances in deep learning have brought to the fore models that can make multiple computational steps in the service of completing a task; these are capable of describ- ing long-term dependencies in sequential data. Novel recurrent…
In this paper, we consider maximum likelihood estimations of the degree of freedom parameter $\nu$, the location parameter $\mu$ and the scatter matrix $\Sigma$ of the multivariate Student-$t$ distribution. In particular, we are interested…
We study holonomic gradient decent for maximum likelihood estimation of exponential-polynomial distribution, whose density is the exponential function of a polynomial in the random variable. We first consider the case that the support of…
Generalized linear models play an essential role in a wide variety of statistical applications. This paper discusses an approximation of the likelihood in these models that can greatly facilitate computation. The basic idea is to replace a…
We consider the problem of upper bounding the expected log-likelihood sub-optimality of the maximum likelihood estimate (MLE), or a conjugate maximum a posteriori (MAP) for an exponential family, in a non-asymptotic way. Surprisingly, we…
We study the problem of modeling univariate distributions via their quantile functions. We introduce a flexible family of distributions whose quantile function is a linear combination of basis quantiles. Because the model is linear in its…
The properties of Maximum Likelihood estimator in mixed causal and noncausal models with a generalized Student's t error process are reviewed. Several known existing methods are typically not applicable in the heavy-tailed framework. To…