Asymptotic properties of the estimator for a finite mixture of exponential dispersion models

This paper is concerned with a class of exponential dispersion distributions. We particularly focused on the mixture models, which represent an extension of the Gaussian distribution. It should be noted that the parameters estimation of mixture distributions is an important task in statistical processing. In order to estimate the parameters vector, we proposed a formulation of the Expectation-Maximization algorithm (EM) under exponential dispersion mixture distributions. Also, we developed a hybrid algorithm called Expectation-Maximization and Method of moments algorithm (EMM). Under mild regularity, several convergence results of the EMM algorithm were obtained. Through simulation studies, the robustness of the EMM was proved and the strong consistency of the EMM sequence appeared when the data set size and the number of iterations tend to infinity.

Download Full-text

Autonomous feature type selection based on environment using expectation maximization in self-localization

International Journal of Advanced Robotic Systems ◽

10.1177/1729881418814701 ◽

2018 ◽

Vol 15 (6) ◽

pp. 172988141881470

Author(s):

Nezih Ergin Özkucur ◽

H Levent Akın

Keyword(s):

Expectation Maximization ◽

Autonomous Robots ◽

Expectation Maximization Algorithm ◽

Sensory Information ◽

Ground Truth ◽

Local Environment ◽

Localization Algorithm ◽

Data Set ◽

Public Data ◽

The Individual

Self-localization in autonomous robots is one of the fundamental issues in the development of intelligent robots, and processing of raw sensory information into useful features is an integral part of this problem. In a typical scenario, there are several choices for the feature extraction algorithm, and each has its weaknesses and strengths depending on the characteristics of the environment. In this work, we introduce a localization algorithm that is capable of capturing the quality of a feature type based on the local environment and makes soft selection of feature types throughout different regions. A batch expectation–maximization algorithm is developed for both discrete and Monte Carlo localization models, exploiting the probabilistic pose estimations of the robot without requiring ground truth poses and also considering different observation types as blackbox algorithms. We tested our method in simulations, data collected from an indoor environment with a custom robot platform and a public data set. The results are compared with the individual feature types as well as naive fusion strategy.

Download Full-text

An Expectation Maximization Algorithm to Model Failure Times by Continuous-Time Markov Chains

Mathematical Problems in Engineering ◽

10.1155/2010/242567 ◽

2010 ◽

Vol 2010 ◽

pp. 1-16 ◽

Cited By ~ 4

Author(s):

Qihong Duan ◽

Zhiping Chen ◽

Dengfu Zhao

Keyword(s):

Markov Chain ◽

Expectation Maximization ◽

Continuous Time ◽

Failure Time ◽

Expectation Maximization Algorithm ◽

Failure Time Data ◽

Time Data ◽

Failure Rate Function ◽

Data Set ◽

Triangular Matrices

In many applications, the failure rate function may present a bathtub shape curve. In this paper, an expectation maximization algorithm is proposed to construct a suitable continuous-time Markov chain which models the failure time data by the first time reaching the absorbing state. Assume that a system is described by methods of supplementary variables, the device of stage, and so on. Given a data set, the maximum likelihood estimators of the initial distribution and the infinitesimal transition rates of the Markov chain can be obtained by our novel algorithm. Suppose that there aremtransient states in the system and that there arenfailure time data. The devised algorithm only needs to compute the exponential ofm×mupper triangular matrices forO(nm2)times in each iteration. Finally, the algorithm is applied to two real data sets, which indicates the practicality and efficiency of our algorithm.

Download Full-text

Asymptotic properties and expectation-maximization algorithm for maximum likelihood estimates of the parameters from Weibull-Logarithmic model

Applied Mathematics-A Journal of Chinese Universities ◽

10.1007/s11766-016-3391-2 ◽

2016 ◽

Vol 31 (4) ◽

pp. 425-438 ◽

Cited By ~ 3

Author(s):

Wen-hao Gui ◽

Huai-nian Zhang

Keyword(s):

Maximum Likelihood ◽

Expectation Maximization ◽

Asymptotic Properties ◽

Expectation Maximization Algorithm ◽

Maximum Likelihood Estimates ◽

Logarithmic Model

Download Full-text

Route identification in the National Football League

Journal of Quantitative Analysis in Sports ◽

10.1515/jqas-2019-0047 ◽

2020 ◽

Vol 16 (2) ◽

pp. 121-132

Author(s):

Dani Chu ◽

Matthew Reyers ◽

James Thomson ◽

Lucas Yifan Wu

Keyword(s):

Basis Function ◽

Expectation Maximization ◽

Bernstein Polynomial ◽

National Football League ◽

Expectation Maximization Algorithm ◽

Polynomial Basis ◽

Tracking Data ◽

Data Set ◽

Curve Clustering ◽

Bernstein Polynomial Basis

AbstractTracking data in the National Football League (NFL) is a sequence of spatial-temporal measurements that varies in length depending on the duration of the play. In this paper, we demonstrate how model-based curve clustering of observed player trajectories can be used to identify the routes run by eligible receivers on offensive passing plays. We use a Bernstein polynomial basis function to represent cluster centers, and the Expectation Maximization algorithm to learn the route labels for each of the 33,967 routes run on the 6963 passing plays in the data set. With few assumptions and no pre-existing labels, we are able to closely recreate the standard route tree from our algorithm. We go on to suggest ideas for new potential receiver metrics that account for receiver deployment and movement common throughout the league. The resulting route labels can also be paired with film to enable streamlined queries of game film.

Download Full-text