Small-sample results for maximum-likelihood estimation in branching processes

1982 ◽  
Vol 10 (4) ◽  
pp. 271-276 ◽  
Author(s):  
Jean-Pierre Dion ◽  
Gilbert Labelle ◽  
Alain Latour
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Branching Processes ◽  
Likelihood Estimation ◽  
Small Sample

The Pricing Problem

1987 ◽  
Vol 1 (3) ◽  
pp. 349-366
Author(s):  
Jaxk H. Reeves ◽  
Ashim Mallik ◽  
William P. McCormick
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
High Efficiency ◽  
Asymptotic Properties ◽  
Likelihood Estimation ◽  
Small Sample ◽  
Sequential Procedure ◽  
Pricing Scheme ◽  
Simulation Results ◽  
Small Sample Sizes

A sequential procedure to select optimal prices based on maximum likelihood estimation is considered. Asymptotic properties of the pricing scheme and the concommitant estimation problem are examined. For small sample sizes, simulation results show that the proposed procedure has high efficiency relative to the best procedure when the parameter is known.

Maximum Likelihood Estimation for MA(1) Processes with a Root on or near the Unit Circle

1996 ◽  
Vol 12 (1) ◽  
pp. 1-29 ◽  
Author(s):  
Richard A. Davis ◽  
William T.M. Dunsmuir
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Unit Circle ◽  
Asymptotic Distribution ◽  
Moving Average ◽  
Likelihood Estimation ◽  
Small Sample ◽  
Practical Significance ◽  
True Parameter ◽  
Small Sample Sizes

This paper considers maximum likelihood estimation for the moving average parameter θ in an MA(1) model when θ is equal to or close to 1. A derivation of the limit distribution of the estimate θLM, defined as the largest of the local maximizers of the likelihood, is given here for the first time. The theory presented covers, in a unified way, cases where the true parameter is strictly inside the unit circle as well as the noninvertible case where it is on the unit circle. The asymptotic distribution of the maximum likelihood estimator subMLE is also described and shown to differ, but only slightly, from that of θLM. Of practical significance is the fact that the asymptotic distribution for either estimate is surprisingly accurate even for small sample sizes and for values of the moving average parameter considerably far from the unit circle.

scholarly journals Z-Tests in Multinomial Probit Models under Simulated Maximum Likelihood Estimation: Some Small Sample Properties

2010 ◽  
Vol 230 (5) ◽  
Author(s):  
Andreas Ziegler
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Likelihood Estimation ◽  
Small Sample ◽  
Multinomial Probit ◽  
Test Statistics ◽  
Simulated Maximum Likelihood ◽  
Probit Models ◽  
Small Sample Properties ◽  
Ghk Simulator

SummaryThis paper analyzes small sample properties of several versions of z-tests in multinomial probit models under simulated maximum likelihood estimation. Our Monte Carlo experiments show that z-tests on utility function coefficients provide more robust results than z-tests on variance covariance parameters. As expected, both the number of observations and the number of random draws in the incorporated Geweke-Hajivassiliou-Keane (GHK) simulator have on average a positive impact on the conformities between the shares of type I errors and the nominal significance levels. Furthermore, an increase of the number of observations leads to an expected decrease of the shares of type II errors, whereas the number of random draws in the GHK simulator surprisingly has no significant effect in this respect. One main result of our study is that the use of the robust version of the simulated z-test statistics is not systematically more favorable than the use of other versions. However, the application of the z-test statistics that exclusively include the Hessian matrix of the simulated loglikelihood function to estimate the information matrix often leads to substantial computational problems.

Maximum likelihood estimation for branching processes with immigration

1981 ◽  
Vol 13 (3) ◽  
pp. 498-509 ◽  
Author(s):  
B. R. Bhat ◽  
S. R. Adke
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Continuous Time ◽  
Strong Consistency ◽  
Branching Process ◽  
Branching Processes ◽  
Maximum Likelihood Estimators ◽  
Likelihood Estimation ◽  
Asymptotic Distributions ◽  
Branching Process With Immigration

This paper establishes the strong consistency of the maximum likelihood estimators of the parameters of discrete- and continuous-time Markov branching processes with immigration. The asymptotic distributions of the maximum likelihood estimators of the parameters of a Galton–Watson branching process with immigration are also obtained.

Maximum likelihood estimation for branching processes with immigration

1981 ◽  
Vol 13 (03) ◽  
pp. 498-509 ◽  
Author(s):  
B. R. Bhat ◽  
S. R. Adke
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Continuous Time ◽  
Strong Consistency ◽  
Branching Process ◽  
Branching Processes ◽  
Maximum Likelihood Estimators ◽  
Likelihood Estimation ◽  
Asymptotic Distributions ◽  
Branching Process With Immigration

This paper establishes the strong consistency of the maximum likelihood estimators of the parameters of discrete- and continuous-time Markov branching processes with immigration. The asymptotic distributions of the maximum likelihood estimators of the parameters of a Galton–Watson branching process with immigration are also obtained.

Sign in / Sign up

Export Citation Format

Share Document