The problem of ROC analysis without truth: the EM algorithm and the information matrix

2000 ◽  
Author(s):  
Sergey V. Beiden ◽  
Gregory Campbell ◽  
Kristen L. Meier ◽  
Robert F. Wagner
Keyword(s):  
Em Algorithm ◽  
Roc Analysis ◽  
Information Matrix ◽  
The Em Algorithm

FREQUENTIST INFERENCE IN INSURANCE RATEMAKING MODELS ADJUSTING FOR MISREPRESENTATION

2019 ◽  
Vol 49 (1) ◽  
pp. 117-146
Author(s):  
Rexford M. Akakpo ◽  
Michelle Xia ◽  
Alan M. Polansky
Keyword(s):  
Em Algorithm ◽  
Latent Variable ◽  
Medical Expenditure Panel Survey ◽  
Likelihood Function ◽  
Information Matrix ◽  
Analytical Form ◽  
Medical Expenditure ◽  
The Em Algorithm ◽  
Risk Effect ◽  
Frequentist Inference

AbstractIn insurance underwriting, misrepresentation represents the type of insurance fraud when an applicant purposely makes a false statement on a risk factor that may lower his or her cost of insurance. Under the insurance ratemaking context, we propose to use the expectation-maximization (EM) algorithm to perform maximum likelihood estimation of the regression effects and the prevalence of misrepresentation for the misrepresentation model proposed by Xia and Gustafson [(2016) The Canadian Journal of Statistics, 44, 198–218]. For applying the EM algorithm, the unobserved status of misrepresentation is treated as a latent variable in the complete-data likelihood function. We derive the iterative formulas for the EM algorithm and obtain the analytical form of the Fisher information matrix for frequentist inference on the parameters of interest for lognormal losses. We implement the algorithm and demonstrate that valid inference can be obtained on the risk effect despite the unobserved status of misrepresentation. Applying the proposed algorithm, we perform a loss severity analysis with the Medical Expenditure Panel Survey data. The analysis reveals not only the potential impact misrepresentation may have on the risk effect but also statistical evidence on the presence of misrepresentation in the self-reported insurance status.

scholarly journals Fisher information and statistical inference for phase-type distributions

2011 ◽  
Vol 48 (A) ◽  
pp. 277-293 ◽  
Author(s):  
Mogens Bladt ◽  
Luz Judith R. Esparza ◽  
Bo Friis Nielsen
Keyword(s):  
Em Algorithm ◽  
Statistical Inference ◽  
Fisher Information ◽  
Fisher Information Matrix ◽  
Likelihood Function ◽  
Information Matrix ◽  
The Em Algorithm ◽  
Phase Type ◽  
Phase Type Distributions ◽  
Newton Raphson

This paper is concerned with statistical inference for both continuous and discrete phase-type distributions. We consider maximum likelihood estimation, where traditionally the expectation-maximization (EM) algorithm has been employed. Certain numerical aspects of this method are revised and we provide an alternative method for dealing with the E-step. We also compare the EM algorithm to a direct Newton–Raphson optimization of the likelihood function. As one of the main contributions of the paper, we provide formulae for calculating the Fisher information matrix both for the EM algorithm and Newton–Raphson approach. The inverse of the Fisher information matrix provides the variances and covariances of the estimated parameters.

Statistical Inference in Evolutionary Models of DNA Sequences via the EM Algorithm

2005 ◽  
Vol 4 (1) ◽  
Author(s):  
Asger Hobolth ◽  
Jens Ledet Jensen
Keyword(s):  
Maximum Likelihood ◽  
Em Algorithm ◽  
Statistical Inference ◽  
Dna Sequences ◽  
Expectation Maximization ◽  
Continuous Time ◽  
Information Matrix ◽  
Evolutionary Models ◽  
Likelihood Estimator ◽  
The Em Algorithm

We describe statistical inference in continuous time Markov processes of DNA sequences related by a phylogenetic tree. The maximum likelihood estimator can be found by the expectation maximization (EM) algorithm and an expression for the information matrix is also derived. We provide explicit analytical solutions for the EM algorithm and information matrix.

scholarly journals Fisher information and statistical inference for phase-type distributions

2011 ◽  
Vol 48 (A) ◽  
pp. 277-293
Author(s):  
Mogens Bladt ◽  
Luz Judith R. Esparza ◽  
Bo Friis Nielsen
Keyword(s):  
Em Algorithm ◽  
Statistical Inference ◽  
Fisher Information ◽  
Fisher Information Matrix ◽  
Likelihood Function ◽  
Information Matrix ◽  
The Em Algorithm ◽  
Phase Type ◽  
Phase Type Distributions ◽  
Newton Raphson

This paper is concerned with statistical inference for both continuous and discrete phase-type distributions. We consider maximum likelihood estimation, where traditionally the expectation-maximization (EM) algorithm has been employed. Certain numerical aspects of this method are revised and we provide an alternative method for dealing with the E-step. We also compare the EM algorithm to a direct Newton–Raphson optimization of the likelihood function. As one of the main contributions of the paper, we provide formulae for calculating the Fisher information matrix both for the EM algorithm and Newton–Raphson approach. The inverse of the Fisher information matrix provides the variances and covariances of the estimated parameters.

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