A discrete statistical model is a subset of probability simplex. Its maximum likelihood estimator (MLE) retraction from that simplex onto the model. We characterize all models for which this rational function. This contribution via real algebraic geometry rests on results Horn uniformization due to Huh and Kapranov. present an algorithm constructing with MLE, we demonstrate it range instances. ...

Multicollinearity negatively affects the efficiency of maximum likelihood estimator (MLE) in both linear and generalized models. The Kibria Lukman (KLE) was developed as an alternative to MLE handle multicollinearity for regression model. In this study, we proposed Logistic Kibria-Lukman (LKLE) logistic We theoretically established superiority condition new over MLE, ridge (LRE), Liu (LLE), Liu...

The two-parameter Weibull distribution is the predominant distribution in reliability and lifetime data analysis. The classical approach for estimating the scale [Formula: see text] and shape [Formula: see text] parameters employs the maximum likelihood estimation (MLE) method. However, most MLE based-methods resort to numerical or graphical techniques due to the lack of closed-form expressions...

The maximum likelihood estimator (MLE) is generally asymptotically consistent but is susceptible to overfitting. To combat this problem, regularization methods which reduce the variance at the cost of (slightly) increasing the bias are often employed in practice. In this paper, we present an alternative variance reduction (regularization) technique that quantizes the MLE estimates as a post pro...

Hidden Markov models were successfully applied in various fields of time series analysis, especially for analyzing ion channel recordings. The maximum likelihood estimator (MLE) has recently been proven to be asymptotically normally distributed. Here, we investigate finite sample properties of the MLE and of different types of likelihood ratio tests (LRTs) by means of simulation studies. The ML...

Here, we present a method that can improve the z-tracking accuracy of the recently invented TSUNAMI (Tracking of Single particles Using Nonlinear And Multiplexed Illumination) microscope. This method utilizes a maximum likelihood estimator (MLE) to determine the particle's 3D position that maximizes the likelihood of the observed time-correlated photon count distribution. Our Monte Carlo simula...

Markov chain Monte Carlo methods can be used to approximate the intractable normalizing constants that arise in likelihood calculations for many exponential family random graph models for networks. However, in practice, the resulting approximations degrade as parameter values move away from the value used to define the Markov chain. Here, we introduce a method of moving toward a maximum likelih...

This paper introduces a Monte Carlo method for maximum likelihood inference in the context of discretely observed diffusion processes. The method gives unbiased and a.s. continuous estimators of the likelihood function for a family of diffusion models and its performance in numerical examples is computationally efficient. It uses a recently developed technique for the exact simulation of diffus...

Determinantal point processes (DPPs) have wide-ranging applications in machine learning, where they are used to enforce the notion of diversity in subset selection problems. Many estimators have been proposed, but surprisingly the basic properties of the maximum likelihood estimator (MLE) have received little attention. The difficulty is that it is a non-concave maximization problem, and such f...

We discuss some inference problems associated with the fractional Ornstein-Uhlenbeck (fO-U) process driven by the fractional Brownian motion (fBm). In particular, we are concerned with the estimation of the drift parameter, assuming that the Hurst parameter H is known and is in [1/2, 1). Under this setting we compute the distributions of the maximum likelihood estimator (MLE) and the minimum co...