When the spatial sample size is extremely large, which occurs in many environmental and ecological studies, operations on the large covariance matrix are a numerical challenge. Covariance tapering is a technique to alleviate the numerical challenges. Under the assumption that data are collected along a line in a bounded region, we investigate how the tapering affects the asymptotic efficiency o...

Fosdick and Raftery (2012) revisited the classical problem of inference for a bivariate normal correlation coefficient ρ when the variances are known. They considered several frequentist and Bayesian estimators, the former including the maximum likelihood estimator (MLE), but did not obtain the standard errors of these estimators or confidence intervals for ρ. Here we present a new variance-sta...

This article considers the nonparametric maximum likelihood estimator (MLE) for the joint distribution function of an interval censored survival time and a continuous mark variable. We derive a new explicit formula for the MLE that has both computational and theoretical advantages. Using this formula and the mark specific cumulative hazard function of Huang & Louis (1998), we derive the almost ...

We introduce a new class of distributions called the epsilon–positive family, which can be viewed as generalization with positive support. The construction family is motivated by ideas behind generation skew using symmetric kernels. This has special cases exponential, Weibull, log–normal, log–logistic and gamma distributions, it provides an alternative for analyzing reliability survival data. A...

Solution 1: The goal of MLE is to estimate optimal values for each of the model’s parameters by maximizing the likelihood of the data given the parameters. MLE provides an answer to the question “which model instance best fits the data?” when “best fits” is defined as “gives the most evidence for”. If θ is a particular assignment of values to the model’s parameters and y represents the observed...

This article concerns the study of the asymptotic properties of the maximum likelihood estimator (MLE) for the general hidden semi-Markov model (HSMM) with backward recurrence time dependence. By transforming the general HSMM into a general hidden Markov model, we prove that under some regularity conditions, the MLE is strongly consistent and asymptotically normal. We also provide useful expres...

Recent research has demonstrated that the rotor angle stability can be assessed by identifying the sign of the system’s maximal Lyapunov exponent (MLE). A positive (negative) MLE implies unstable (stable) rotor angle dynamics. However, because the MLE may fluctuate between positive and negative values for a long time after a severe disturbance, it is difficult to determine the system stability ...

OBJECTIVES The Mikania laevigata extract (MLE) (popularly known in Brazil as "guaco") possesses anti-inflammatory properties. In the present study we tested the effects of MLE in a periodontitis experimental model in rats. We also investigated possible mechanisms underlying such effects. MATERIAL AND METHODS Periodontal disease was induced by a ligature placed around the mandibular first mola...