Efficient Likelihood Ratio Confidence Intervals using Constrained Optimization

2019 ◽  
Author(s):  
Gregor Reich ◽  
Kenneth L. Judd
Keyword(s):  
Constrained Optimization ◽  
Confidence Intervals ◽  
Likelihood Ratio

Exact likelihood ratio and score confidence intervals for the binomial proportion

2013 ◽  
Vol 12 (3) ◽  
pp. 120-128 ◽  
Author(s):  
Matthew C. Somerville ◽  
Rebekkah S. Brown
Keyword(s):  
Confidence Intervals ◽  
Likelihood Ratio ◽  
Binomial Proportion

scholarly journals On the Correction of the Asymptotic Distribution of the Likelihood Ratio Statistic If Nuisance Parameters Are Estimated Based on an External Source

2014 ◽  
Vol 10 (2) ◽  
Author(s):  
Marianne Jonker ◽  
Aad Van der Vaart
Keyword(s):  
Confidence Interval ◽  
Asymptotic Distribution ◽  
Confidence Intervals ◽  
Likelihood Ratio ◽  
Statistical Models ◽  
Likelihood Ratio Statistic ◽  
External Source ◽  
Nuisance Parameters ◽  
Testing Hypotheses

AbstractIn practice, nuisance parameters in statistical models are often replaced by estimates based on an external source, for instance if estimates were published before or a second dataset is available. Next these estimates are assumed to be known when the parameter of interest is estimated, a hypothesis is tested or confidence intervals are constructed. By this assumption, the level of the test is, in general, higher than supposed and the coverage of the confidence interval is too low. In this article, we derive the asymptotic distribution of the likelihood ratio statistic if the nuisance parameters are estimated based on a dataset that is independent of the data used for estimating the parameter of interest. This distribution can be used for correctly testing hypotheses and constructing confidence intervals. Four theoretical and practical examples are given as illustration.

Confidence Intervals for Weibull Fast-Fracture Parameters

2002 ◽  
Author(s):  
Mandar Chati ◽  
Curtis Johnson ◽  
Ahmet Kaya ◽  
Bjoern Schenk
Keyword(s):  
Confidence Interval ◽  
Confidence Intervals ◽  
Likelihood Ratio ◽  
Failure Modes ◽  
Bootstrap Method ◽  
Parametric Bootstrap ◽  
Nonparametric Bootstrap ◽  
Weibull Parameters ◽  
Fracture Data ◽  
Fast Fracture

Practical limits on number of specimens that can be tested lead to uncertainty in the estimated Weibull parameters. This paper presents an evaluation of four techniques for estimating confidence intervals for size-scaled Weibull parameters of monolithic ceramics. The techniques include normal approximation method, likelihood ratio technique, nonparametric bootstrap, and parametric bootstrap methods. For uncensored fast-fracture data, the confidence intervals for Weibull parameters are compared to the method used in ASTM Standard C1239. A simulation fracture experiment is conducted to evaluate the statistical characteristics, in particular coverage probability, of the four methods. For fast-fracture data with multiple failure modes, the statistical assessment of the confidence interval techniques for size-scaled Weibull parameters complement the existing literature. Overall, it was observed that the likelihood ratio technique and parametric bootstrap method perform very well. These techniques can also be extended for confidence interval estimation using fast-fracture data obtained from various geometry’s of test specimens and/or loading conditions (pooled data).

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