Related papers: Tilting maximum Lq-Likelihood estimation for extre…
Maximum likelihood estimation is applied to the determination of an unknown quantum measurement. The measuring apparatus performs measurements on many different quantum states and the positive operator-valued measures governing the…
The occurrence of successive extreme observations can have an impact on society. In extreme value theory there are parameters to evaluate the effect of clustering of high values, such as the extremal index. The estimation of the extremal…
The maximum ${\log}_q$ likelihood estimation method is a generalization of the known maximum $\log$ likelihood method to overcome the problem for modeling non-identical observations (inliers and outliers). The parameter $q$ is a tuning…
A common approach for modeling extremes, such as peak flow or high temperatures, is the three-parameter Generalized Extreme-Value distribution. This is typically fit to extreme observations, here defined as maxima over disjoint blocks. This…
The last decade has seen max-stable processes emerge as a common tool for the statistical modeling of spatial extremes. However, their application is complicated due to the unavailability of the multivariate density function, and so…
In this article, we consider the parameter estimation of regression model with pth order autoregressive (AR(p)) error term. We use the Maximum Lq-likelihood (MLq) estimation method that is proposed by Ferrari and Yang (2010a), as a robust…
We propose regularization methods for linear models based on the $L_q$-likelihood, which is a generalization of the log-likelihood using a power function. Some heavy-tailed distributions are known as $q$-normal distributions. We find that…
This article introduces a robust hypothesis testing procedure: the Lq-likelihood-ratio-type test (LqRT). By deriving the asymptotic distribution of this test statistic, the authors demonstrate its robustness both analytically and…
The block maxima method is a classical and widely applied statistical method for time series extremes. It has recently been found that respective estimators whose asymptotics are driven by empirical means can be improved by using sliding…
The block maxima method in extreme value theory consists of fitting an extreme value distribution to a sample of block maxima extracted from a time series. Traditionally, the maxima are taken over disjoint blocks of observations.…
Maximum likelihood estimation is a valuable tool often applied to inverse problems in quantum theory. Estimation from small data sets can, however, have non unique solutions. We discuss this problem and propose to use Jaynes maximum entropy…
Maximum likelihood estimation is a common method of estimating the parameters of the probability distribution from a given sample. This paper aims to introduce the maximum likelihood estimation in the framework of sublinear expectation. We…
Maximum likelihood estimation is one of the most used methods in quantum state tomography, where the aim is to reconstruct the density matrix of a physical system from measurement results. One strategy to deal with positivity and unit trace…
We introduce the lookahead-bounded Q-learning (LBQL) algorithm, a new, provably convergent variant of Q-learning that seeks to improve the performance of standard Q-learning in stochastic environments through the use of ``lookahead'' upper…
The extreme value index is a fundamental parameter in univariate Extreme Value Theory (EVT). It captures the tail behavior of a distribution and is central in the extrapolation beyond observed data. Among other semi-parametric methods (such…
The pseudo-marginal (PM) approach is increasingly used for Bayesian inference in statistical models, where the likelihood is intractable but can be estimated unbiasedly. %Examples include random effect models, state-space models and data…
This expository note describes how to apply the method of maximum likelihood to estimate the parameters of the ``$q$-exponential'' distributions introduced by Tsallis and collaborators. It also describes the relationship of these…
Firth-type logistic regression has become a standard approach for the analysis of binary outcomes with small samples. Whereas it reduces the bias in maximum likelihood estimates of coefficients, bias towards 1/2 is introduced in the…
Empirical risk minimization (ERM) is typically designed to perform well on the average loss, which can result in estimators that are sensitive to outliers, generalize poorly, or treat subgroups unfairly. While many methods aim to address…
In multivariate or spatial extremes, inference for max-stable processes observed at a large collection of locations is among the most challenging problems in computational statistics, and current approaches typically rely on less expensive…