Journal ArticleDOI
The Effect of Sampling Rules on Likelihood Statistics
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In this paper, the distribution of the likelihood ratio statistic is considered for a number of systems of censoring and sequential stopping connected with Brownian motion, Poisson processes and survival analysis.Abstract:
Summary The distribution of the likelihood ratio statistic is considered for a number of systems of censoring and sequential stopping connected with Brownian motion, Poisson processes and survival analysis. The implications for the calculation of Bartlett adjustments are examined and the relation developed with an earlier general discussion of the higher-order distribution theory of maximum likelihood estimators and likelihood ratio statistics.read more
Citations
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Journal ArticleDOI
Saddlepoint Methods and Statistical Inference
TL;DR: In this article, the authors present a survey of second order asymptotic inference using the saddlepoint method, including Barndorff-Nielsen's approximation to the distribution of the maximum likelihood estimate, Bartlett factors for the likelihood ratio statistic and approximations to predictive and conditional likelihood.
Journal ArticleDOI
On the bias of maximum likelihood estimation following a sequential test
TL;DR: In this paper, the bias of maximum likelihood estimates calculated at the end of a sequential procedure is investigated, and a method of calculating an adjusted estimate with reduced bias is described, and an approximation to the standard error of the new estimate is provided.
Journal ArticleDOI
Practical Use of Higher Order Asymptotics for Multiparameter Exponential Families
Donald A. Pierce,Dawn Peters +1 more
TL;DR: In this article, the authors focus on tests and confidence intervals regarding a single parametric function which can be represented as a natural parameter of a full rank exponential family, and explore these approximations to exact conditional inferences.
Journal ArticleDOI
On bartlett and bartlett-type corrections francisco cribari-neto
TL;DR: This article reviewed the literature on Bartlett and Bartlett-type corrections to the likelihood ratio, score and Wald test statistics and compared the performance of three different types of corrections through simulation.
Journal ArticleDOI
Improved likelihood ratio statistics for exponential family nonlinear models
TL;DR: In this paper, a general formula for the expected likelihood ratio statistic for exponential family nonlinear models, corrected up to order n-1, where n is the sample size, is given.
References
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Book
Statistics of random processes
TL;DR: In this paper, the optimal linear non-stationary filtering, interpolation and extrapolation of Partially Observable Random Processes with a Countable Number of States (POMOS) was studied.
Book ChapterDOI
Properties of Sufficiency and Statistical Tests
TL;DR: In this article, the structure of small sample tests, whether these are related to problems of estimation and fiducial distributions, or are of the nature of tests of goodness of fit, is considered further.
Book
Nonlinear Renewal Theory in Sequential Analysis
TL;DR: Randomly Stopped Sequences Random Walks The Sequential Probability Ratio Test Nonlinear Renewal Theory Local Limit Theorems Open-Ended Tests Repeated Significance Tests Multiparameter Problems Estimation Following Sequential Testing Sequential Estimation as mentioned in this paper.