Related papers: On an EM-based closed-form solution for 2 paramete…
Accurate estimates of item difficulty are essential for valid assessment and effective adaptive learning. However, for newly created tasks, response data are typically unavailable. Pretesting and expert judgement can be costly and slow,…
Maximum likelihood estimations for the parameters of extreme value distributions are discussed in this paper using fixed point iteration. The commonly used numerical approach for addressing this problem is the Newton-Raphson approach which…
In the paper, we introduce the maximum entropy estimator based on 2-dimensional empirical distribution of the observation sequence of hidden Markov model , when the sample size is big: in that case computing the maximum likelihood estimator…
We discuss the problem of parameter estimation in nonlinear stochastic differential equations based on sampled time series. A central message from the theory of integrating stochastic differential equations is that there exists in general…
We study an EM algorithm for estimating product-term regression models with missing data. The study of such problems in the likelihood tradition has thus far been restricted to an EM algorithm method using full numerical integration.…
Estimation of a single Bernoulli parameter using pooled sampling is among the oldest problems in the group testing literature. To carry out such estimation, an array of efficient estimators have been introduced covering a wide range of…
Some statistical models are specified via a data generating process for which the likelihood function cannot be computed in closed form. Standard likelihood-based inference is then not feasible but the model parameters can be inferred by…
The article considers parameter estimation constructing such as quasi-maximum likelyhood estimation and one step estimation in statistical models generated by solution of stochastic differential equation. It has been developed a software…
Bi-factor and second-order models based on copulas are proposed for item response data, where the items can be split into non-overlapping groups such that there is a homogeneous dependence within each group. Our general models include the…
Maximum likelihood estimators are proposed for the parameters and the densities in a semiparametric density ratio model in which the nonparametric baseline density is approximated by the Bernstein polynomial model. The EM algorithm is used…
This paper considers both the least squares and quasi-maximum likelihood estimation for the recently proposed scalable ARMA model, a parametric infinite-order vector AR model, and their asymptotic normality is also established. It makes…
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,…
Implicit probabilistic models are models defined naturally in terms of a sampling procedure and often induces a likelihood function that cannot be expressed explicitly. We develop a simple method for estimating parameters in implicit models…
The item response theory obtains the estimates and their confidence intervals for parameters of abilities of examinees and difficulties of problems by using the observed item response matrix consisting of 0/1 value elements. Many papers…
Item Response Theory (IRT) is a ubiquitous model for understanding humans based on their responses to questions, used in fields as diverse as education, medicine and psychology. Large modern datasets offer opportunities to capture more…
Consider a rectangular matrix describing some type of communication or transportation between a set of origins and a set of destinations, or a classification of objects by two attributes. The problem is to infer the entries of the matrix…
Over the past decades, there has been a surge of interest in studying low-dimensional structures within high-dimensional data. Statistical factor models $-$ i.e., low-rank plus diagonal covariance structures $-$ offer a powerful framework…
The Rasch model, a classical model in the item response theory, is widely used in psychometrics to model the relationship between individuals' latent traits and their binary responses to assessments or questionnaires. In this paper, we…
In this article the issues are discussed with the Bayesian approach, least-square fits, and most-likely fits. Trying to counter these issues, a method, based on weighted confidence, is proposed for estimating probabilities and other…
We present a new proof of the quantum Cramer-Rao bound for precision parameter estimation [1-3] and extend it to a more general class of measurement procedures. We analyze a generalized framework for parameter estimation that covers most…