Related papers: On Generalized Likelihood Estimation Based on the …
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…
Reinforcement Learning with Verifiable Rewards (RLVR) strengthens LLM reasoning, but training often oscillates between {entropy collapse} and {entropy explosion}. We trace both hazards to the mean baseline used in value-free RL (e.g., GRPO…
Many common loss functions such as mean-squared-error, cross-entropy, and reconstruction loss are unnecessarily rigid. Under a probabilistic interpretation, these common losses correspond to distributions with fixed shapes and scales. We…
In real life, we frequently come across data sets that involve some independent explanatory variable(s) generating a set of ordinal responses. These ordinal responses may correspond to an underlying continuous latent variable, which is…
In this paper, we consider distributed maximum likelihood estimation (MLE) with dependent quantized data under the assumption that the structure of the joint probability density function (pdf) is known, but it contains unknown deterministic…
Generalized Linear Models are routinely used in data analysis. The classical procedures for estimation are based on Maximum Likelihood and it is well known that the presence of outliers can have a large impact on this estimator. Robust…
Precisely estimating out-of-sample upper quantiles is very important in risk assessment and in engineering practice for structural design to prevent a greater disaster. For this purpose, the generalized extreme value (GEV) distribution has…
The normality assumption on data set is very restrictive approach for modelling. The generalized form of normal distribution, named as an exponential power (EP) distribution, and its scale mixture form have been considered extensively to…
Estimating the unconstrained mean and covariance matrix is a popular topic in statistics. However, estimation of the parameters of $N_p(\mu,\Sigma)$ under joint constraints such as $\Sigma\mu = \mu$ has not received much attention. It can…
The paper offers a novel unified approach to studying the accuracy of parameter estimation by the quasi likelihood method. Important features of the approach are: (1) The underlying model {is not assumed to be parametric}. (2) No conditions…
Marginal maximum likelihood estimation (MMLE) in item response theory (IRT) is highly sensitive to aberrant responses, such as careless answering and random guessing, which can reduce estimation accuracy. To address this issue, this study…
In this letter, we revisit the problem of maximum likelihood estimation (MLE) of parameters of Gaussian Mixture Model (GMM) and show a new derivation for its parameters. The new derivation, unlike the classical approach employing the…
We propose a new approach for estimating the parameters of a probability distribution. It consists on combining two new methods of estimation. The first is based on the definition of a new distance measuring the difference between…
Likelihood ratios (LRs), which are commonly used for probabilistic data processing, are often estimated based on the frequency counts of individual elements obtained from samples. In natural language processing, an element can be a…
A new generator of univariate continuous distributions, with two additional parameters, called the Log-Lindley generated family is introduced. Some special distributions in the new family are presented. Some mathematical properties of the…
Given two populations from which independent binary observations are taken with parameters $p_1$ and $p_2$ respectively, estimators are proposed for the relative risk $p_1/p_2$, the odds ratio $p_1(1-p_2)/(p_2(1-p_1))$ and their logarithms.…
This paper addresses the estimation of parameters of a Bayesian network from incomplete data. The task is usually tackled by running the Expectation-Maximization (EM) algorithm several times in order to obtain a high log-likelihood…
The minimax robust hypothesis testing problem for the case where the nominal probability distributions are subject to both modeling errors and outliers is studied in twofold. First, a robust hypothesis testing scheme based on a relative…
Generalized linear models and the quasi-likelihood method extend the ordinary regression models to accommodate more general conditional distributions of the response. Nonparametric methods need no explicit parametric specification, and the…
We use the delta method and Stein's method to derive, under regularity conditions, explicit upper bounds for the distributional distance between the distribution of the maximum likelihood estimator (MLE) of a $d$-dimensional parameter and…