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.

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.

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.

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 Computation of the Exact Fisher Information Matrix of a Multiple Input Single Output Time Series Models

2021 ◽  
Vol 2 (2) ◽  
pp. 1-11
Author(s):  
Emilie EPEKA MBAMBE ◽  
Angèle YULE SOTAZO ◽  
Jacques SABITI KISETA
Keyword(s):  
Time Series ◽  
Fisher Information ◽  
Fisher Information Matrix ◽  
Likelihood Function ◽  
Moving Average ◽  
Information Matrix ◽  
Time Series Models ◽  
Single Input Single Output ◽  
Single Output ◽  
Computational Procedures

Klein, Mélard, and Zahaf (1998) have proposed the computation of the exact Fisher information matrix of a large class of Gaussian time series models called the single-input-single-output (SISO) model, includes dynamic regression with autocorrelated errors and the transfer function model, with autoregressive moving average errors. For computing the Fisher information matrix of a SISO model, they introduced an algorithm based on a combination of two computational procedures: recursions for the covariance matrix of the derivatives of the state vector with respect to the parameters and the fast Kalman filter recursions used in the evaluation of the likelihood function. In this paper, we propose a generalization of this method for computing the Fisher information matrix of a MISO model.

scholarly journals PENDUGAAN DATA HILANG DENGAN METODE YATES DAN ALGORITMA EM PADA RANCANGAN LATTICE SEIMBANG

2015 ◽  
Vol 4 (2) ◽  
pp. 74
Author(s):  
MADE SUSILAWATI ◽  
KARTIKA SARI
Keyword(s):  
Missing Data ◽  
Em Algorithm ◽  
Basic Concept ◽  
Incomplete Data ◽  
Likelihood Function ◽  
Animal Husbandry ◽  
Lattice Design ◽  
The Em Algorithm ◽  
Missing Data Estimation ◽  
Data Estimation

Missing data often occur in agriculture and animal husbandry experiment. The missing data in experimental design makes the information that we get less complete. In this research, the missing data was estimated with Yates method and Expectation Maximization (EM) algorithm. The basic concept of the Yates method is to minimize sum square error (JKG), meanwhile the basic concept of the EM algorithm is to maximize the likelihood function. This research applied Balanced Lattice Design with 9 treatments, 4 replications and 3 group of each repetition. Missing data estimation results showed that the Yates method was better used for two of missing data in the position on a treatment, a column and random, meanwhile the EM algorithm was better used to estimate one of missing data and two of missing data in the position of a group and a replication. The comparison of the result JKG of ANOVA showed that JKG of incomplete data larger than JKG of incomplete data that has been added with estimator of data. This suggest  thatwe need to estimate the missing data.

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