Analytic Estimator Densities for Common Parameters under Misspecified Models

Hingley, Peter

doi:10.1007/978-3-0348-7958-3_11

Cited by 2 publications

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“…One possible way to use the technique is via a robustness index (RI), when the parameters are common in the two models. Hingley [10] explains RI and gives an example of the comparison for a gamma data generating model and a negative exponential estimation model.…”

Section: Methods For Comparing Modelsmentioning

confidence: 99%

Distributions of Maximum Likelihood Estimators and Model Comparisons

Hingley¹,

Korsunsky²

2008

AIP Conference Proceedings

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Abstract-Experimental data need to be assessed for purposes of model identification, estimation of model parameters and consequences of misspecified model fits. Here the first and third factors are considered via analytic formulations for the distribution of the maximum likelihood estimates. When estimating this distribution with statistics, it is a tradition to invert the roles of population quantities and quantities that have been estimated from the observed sample. If the model is known, simulations, normal approximations and p*-formula methods can be used. However, exact analytic methods for describing the estimator density are recommended. One of the methods (TED) can be used when the data generating model differs from the estimation model, which allows for the estimation of common parameters across a suite of candidate models. Information criteria such as AIC can be used to pick a winning model. AIC is however approximate and generally only asymptotically correct. For fairly simple models, where expressions remain tractable, the exact estimator density under TED allows for comparisons between models. This is illustrated via a novel information criterion. Three linear models are compared and fitted to econometric data on patent filings.

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Section: Methods For Comparing Modelsmentioning

confidence: 99%

Distributions of Maximum Likelihood Estimators and Model Comparisons

Hingley¹,

Korsunsky²

2008

AIP Conference Proceedings

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“…Exact analytic probability density functions (PDFs) for MLEs under the lognormal EM will be obtained by using a technique for estimator densities (TED) [7] [8] [9]. On the other hand, only approximate forms are developed for the distribution of the arithmetic mean under a lognormal DGM.…”

Section: Introductionmentioning

confidence: 99%

Estimating the mean of a small sample under the two parameter lognormal distribution

Hingley

2018

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Lognormally distributed variables are found in biological, economic and other systems. Here the sampling distributions of maximum likelihood estimates (MLE) for parameters are developed when data are lognormally distributed and estimation is carried out either by the correct lognormal model or by the mis-specified normal distribution. This is designed as an aid to experimental design when drawing a small sample under an assumption that the population follows a normal distribution while in fact it follows a lognormal distribution. Distributions are derived analytically as far as possible by using a technique for estimator densities and are confirmed by simulations. For an independently and identically distributed lognormal sample, when a normal distribution is used for estimation then the distribution of the MLE of the mean is different to that for the MLE of the lognormal mean. The distribution is not known but can be well enough approximated by another lognormal. An analytic method for the distribution of the mis-specified normal variance uses computational convolution for a sample of size 2. The expected value of the mis-specified normal variance is also found as a way to give information about the effect of the model misspecification on inferences for the mean. The results are demonstrated on an example for a population distribution that is abstracted from a survey.

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Analytic Estimator Densities for Common Parameters under Misspecified Models

Cited by 2 publications

References 10 publications

Distributions of Maximum Likelihood Estimators and Model Comparisons

Distributions of Maximum Likelihood Estimators and Model Comparisons

Estimating the mean of a small sample under the two parameter lognormal distribution

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