Estimation of the variance for the multitype Galton–Watson process

1982 ◽  
Vol 19 (2) ◽  
pp. 408-414 ◽  
Author(s):  
K. Nanthi
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimator ◽  
Likelihood Estimator ◽  
Asymptotic Results ◽  
Variance Matrix ◽  
Individual Offspring ◽  
Watson Process ◽  
Asymptotic Variances

This paper is concerned with the estimation of the variance for the multitype Galton-Watson process X = {Xn = (Xn(1),…, Xn(p)); n ≧ 0}. Two estimators for the variance matrix are obtained and asymptotic results for the estimators are given. The first is a maximum likelihood estimator based upon knowledge of individual offspring sizes, the second estimator is based on parent-offspring type combination counts only. Estimators for the asymptotic variances of the Asmussen and Keiding estimator and Becker estimator are also proposed.

Estimation of the variance for the multitype Galton–Watson process

1982 ◽  
Vol 19 (02) ◽  
pp. 408-414
Author(s):  
K. Nanthi
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimator ◽  
Likelihood Estimator ◽  
Asymptotic Results ◽  
Variance Matrix ◽  
Individual Offspring ◽  
Watson Process ◽  
Asymptotic Variances

This paper is concerned with the estimation of the variance for the multitype Galton-Watson process X = {X n = (X n (1),…, X n (p)); n ≧ 0}. Two estimators for the variance matrix are obtained and asymptotic results for the estimators are given. The first is a maximum likelihood estimator based upon knowledge of individual offspring sizes, the second estimator is based on parent-offspring type combination counts only. Estimators for the asymptotic variances of the Asmussen and Keiding estimator and Becker estimator are also proposed.

Tuning of GPS aided attitude estimation using evolutionary algorithms

2016 ◽  
Vol 4 (1) ◽  
pp. 23-42 ◽  
Author(s):  
Shashi Poddar ◽  
Sajjad Hussain ◽  
Sanketh Ailneni ◽  
Vipan Kumar ◽  
Amod Kumar
Keyword(s):  
Maximum Likelihood ◽  
Evolutionary Algorithms ◽  
Maximum Likelihood Estimator ◽  
Inertial Sensors ◽  
Optimization Technique ◽  
Attitude Estimation ◽  
Measurement Noise ◽  
Likelihood Estimator ◽  
Content Type ◽  
Variance Matrix

Purpose – The purpose of this paper is to solve the problem of tuning of EKF parameters (process and measurement noise co-variance matrices) designed for attitude estimation using Global Positioning System (GPS) aided inertial sensors by employing a Human Opinion Dynamics (HOD)-based optimization technique and modifying the technique using maximum likelihood estimators and study its performance as compared to Particle Swarm Optimization (PSO) and manual tuning. Design/methodology/approach – A model for the determination of attitude of flight vehicles using inertial sensors and GPS measurement is designed and experiments are carried out to collect raw sensor and reference data. An HOD-based model is utilized to estimate the optimized process and measurement noise co-variance matrix. Added to it, few modifications are proposed in the HOD model by utilizing maximum likelihood estimator and finally the results obtained by the proposed schemes analysed. Findings – Analysis of the results shows that utilization of evolutionary algorithms for tuning is a significant improvement over manual tuning and both HOD and PSO-based methods are able to achieve the same level of accuracy. However, the HOD methods show better convergence and is easier to implement in terms of tuning parameters. Also, utilization of maximum likelihood estimator shows better search during initial iterations which increases the robustness of the algorithm. Originality/value – The paper is unique in its sense that it utilizes a HOD-based model to solve tuning problem of EKF for attitude estimation.

The Comparison Between the Bayes Estimator and the Maximum Likelihood Estimator of the Reliability Function for Negative Exponential Distribution

2018 ◽  
pp. 439
Author(s):  
Hazim Mansour Gorgees ◽  
Bushra Abdualrasool Ali ◽  
Raghad Ibrahim Kathum
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimator ◽  
Exponential Distribution ◽  
Reliability Function ◽  
Bayes Estimator ◽  
Likelihood Estimator ◽  
Monte Carlo Simulation Technique ◽  
Negative Exponential Distribution ◽  
Negative Exponential ◽  
Better Than

     In this paper, the maximum likelihood estimator and the Bayes estimator of the reliability function for negative exponential distribution has been derived, then a Monte –Carlo simulation technique was employed to compare the performance of such estimators. The integral mean square error (IMSE) was used as a criterion for this comparison. The simulation results displayed that the Bayes estimator performed better than the maximum likelihood estimator for different samples sizes.

scholarly journals Transforming variables to central normality

2021 ◽  
Author(s):  
Jakob Raymaekers ◽  
Peter J. Rousseeuw
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimator ◽  
Simulation Study ◽  
Real Data ◽  
Data Sets ◽  
Transformation Parameter ◽  
Likelihood Estimator ◽  
Extensive Simulation ◽  
Highly Sensitive

AbstractMany real data sets contain numerical features (variables) whose distribution is far from normal (Gaussian). Instead, their distribution is often skewed. In order to handle such data it is customary to preprocess the variables to make them more normal. The Box–Cox and Yeo–Johnson transformations are well-known tools for this. However, the standard maximum likelihood estimator of their transformation parameter is highly sensitive to outliers, and will often try to move outliers inward at the expense of the normality of the central part of the data. We propose a modification of these transformations as well as an estimator of the transformation parameter that is robust to outliers, so the transformed data can be approximately normal in the center and a few outliers may deviate from it. It compares favorably to existing techniques in an extensive simulation study and on real data.

Covariance matrix of the bias-corrected maximum likelihood estimator in generalized linear models

2013 ◽  
Vol 55 (3) ◽  
pp. 643-652
Author(s):  
Gauss M. Cordeiro ◽  
Denise A. Botter ◽  
Alexsandro B. Cavalcanti ◽  
Lúcia P. Barroso
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimator ◽  
Covariance Matrix ◽  
Generalized Linear Models ◽  
Linear Models ◽  
Likelihood Estimator

Large deviations and Berry–Esseen inequalities for estimators in nonhomogeneous diffusion driven by fractional Brownian motion

2020 ◽  
Vol 28 (3) ◽  
pp. 183-196
Author(s):  
Kouacou Tanoh ◽  
Modeste N’zi ◽  
Armel Fabrice Yodé
Keyword(s):  
Differential Equation ◽  
Brownian Motion ◽  
Maximum Likelihood ◽  
Large Deviations ◽  
Stochastic Differential Equation ◽  
Fractional Brownian Motion ◽  
Maximum Likelihood Estimator ◽  
Bayes Estimator ◽  
Likelihood Estimator

AbstractWe are interested in bounds on the large deviations probability and Berry–Esseen type inequalities for maximum likelihood estimator and Bayes estimator of the parameter appearing linearly in the drift of nonhomogeneous stochastic differential equation driven by fractional Brownian motion.

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