Insurance claim severity data are characterized by complex distributional phenomenons, where flexible density estimation tools such as the finite mixture models (FMM) necessary. However, maximum likelihood estimations (MLE) often produce unstable tail estimates for FMM. Motivated this challenge, article presents a weighted estimator (MWLE) robust of heavy-tailed Under some regularity conditions...

When an econometric structural equation includes two endogenous variables and their coefficients are normalized so that their sum of squares is 1, it is natural to express them as the sine and cosine of an angle. The Limited Information Maximum Likelihood (LIML) estimator of this angle when the error covariance matrix is known has constant variance. Of all estimators with constant variance the ...

Skew normal mixture models provide a more flexible framework than the popular normal mixtures for modelling heterogeneous data with asymmetric behaviors. Due to the unboundedness of likelihood function and the divergency of shape parameters, the maximum likelihood estimators of the parameters of interest are often not well defined, leading to dissatisfactory inferential process. We put forward ...

Maximum likelihood estimation (MLE) methods are widely used for evolutionary tree. As evolutionary tree is not a smooth parameter, the consistency of its MLE has been a topic of debate. It has been noted without proof that the classical proof of consistency by Wald holds for the MLE of evolutionary tree. Other proofs of consistency under various models were also proposed. Here we will discuss s...

Training Conditional Random Fields (CRFs) can be very slow for big data. In this paper, we present a new training method for CRFs called Empirical Training which is motivated by the concept of co-occurrence rate. We show that the standard training (unregularized) can have many maximum likelihood estimations (MLEs). Empirical training has a unique closed form MLE which is also a MLE of the stand...

Presented herein is a performance analysis of a maximum likelihood estimator for calculating small speckle motions. Such estimators are important in a variety of speckle techniques used in non-destructive evaluation. The analysis characterizes the performance (bias and RMS deviation) of the estimator as a function of the signal-to-noise ratio. This SNR parameter is a convenient surrogate for de...