scholarly journals AN EM ALGORITHM FOR FITTING A NEW CLASS OF MIXED EXPONENTIAL REGRESSION MODELS WITH VARYING DISPERSION

2020 ◽  
Vol 50 (2) ◽  
pp. 555-583 ◽  
Author(s):  
George Tzougas ◽  
Dimitris Karlis
Keyword(s):  
Regression Models ◽  
Real Data ◽  
Dispersion Parameters ◽  
Ml Estimation ◽  
Exponential Models ◽  
Exponential Regression ◽  
Natural Choice ◽  
Type Algorithm ◽  
Varying Dispersion ◽  
Heavy Tailed

AbstractRegression modelling involving heavy-tailed response distributions, which have heavier tails than the exponential distribution, has become increasingly popular in many insurance settings including non-life insurance. Mixed Exponential models can be considered as a natural choice for the distribution of heavy-tailed claim sizes since their tails are not exponentially bounded. This paper is concerned with introducing a general family of mixed Exponential regression models with varying dispersion which can efficiently capture the tail behaviour of losses. Our main achievement is that we present an Expectation-Maximization (EM)-type algorithm which can facilitate maximum likelihood (ML) estimation for our class of mixed Exponential models which allows for regression specifications for both the mean and dispersion parameters. Finally, a real data application based on motor insurance data is given to illustrate the versatility of the proposed EM-type algorithm.

scholarly journals EM Estimation for the Poisson-Inverse Gamma Regression Model with Varying Dispersion: An Application to Insurance Ratemaking

Risks ◽  
2020 ◽  
Vol 8 (3) ◽  
pp. 97
Author(s):  
George Tzougas
Keyword(s):  
Regression Model ◽  
Negative Binomial ◽  
A Priori ◽  
Type I ◽  
Dispersion Parameters ◽  
Ml Estimation ◽  
Inverse Gamma ◽  
Binomial Type ◽  
Varying Dispersion ◽  
Heavy Tailed

This article presents the Poisson-Inverse Gamma regression model with varying dispersion for approximating heavy-tailed and overdispersed claim counts. Our main contribution is that we develop an Expectation-Maximization (EM) type algorithm for maximum likelihood (ML) estimation of the Poisson-Inverse Gamma regression model with varying dispersion. The empirical analysis examines a portfolio of motor insurance data in order to investigate the efficiency of the proposed algorithm. Finally, both the a priori and a posteriori, or Bonus-Malus, premium rates that are determined by the Poisson-Inverse Gamma model are compared to those that result from the classic Negative Binomial Type I and the Poisson-Inverse Gaussian distributions with regression structures for their mean and dispersion parameters.

scholarly journals A Discrete Gamma Model Approach to Flexible Count Regression Analysis: Maximum Likelihood Inference

2021 ◽  
Author(s):  
Chénagnon Frédéric Tovissodé ◽  
Romain Lucas Glèlè Kakaï
Keyword(s):  
Regression Analysis ◽  
Maximum Likelihood ◽  
Sample Size ◽  
Regression Models ◽  
Dispersion Model ◽  
Real Data ◽  
Small Samples ◽  
Simple Method ◽  
Ml Estimation ◽  
Nominal Level

Most existing flexible count regression models allow only approximate inference. Balanced discretization is a simple method to produce a mean-parametrizable flexible count distribution starting from a continuous probability distribution. This makes easy the definition of flexible count regression models allowing exact inference under various types of dispersion (equi-, under- and overdispersion). This study describes maximum likelihood (ML) estimation and inference in count regression based on balanced discrete gamma (BDG) distribution and introduces a likelihood ratio based latent equidispersion (LE) test to identify the parsimonious dispersion model for a particular dataset. A series of Monte Carlo experiments were carried out to assess the performance of ML estimates and the LE test in the BDG regression model, as compared to the popular Conway-Maxwell-Poisson model (CMP). The results show that the two evaluated models recover population effects even under misspecification of dispersion related covariates, with coverage rates of asymptotic 95% confidence interval approaching the nominal level as the sample size increases. The BDG regression approach, nevertheless, outperforms CMP regression in very small samples (n = 15 − 30), mostly in overdispersed data. The LE test proves appropriate to detect latent equidispersion, with rejection rates converging to the nominal level as the sample size increases. Two applications on real data are given to illustrate the use of the proposed approach to count regression analysis.

scholarly journals Robust Algorithms for Change-Point Regressions Using the t-Distribution

Mathematics ◽  
2021 ◽  
Vol 9 (19) ◽  
pp. 2394
Author(s):  
Kang-Ping Lu ◽  
Shao-Tung Chang
Keyword(s):  
Change Point ◽  
Regression Models ◽  
Degrees Of Freedom ◽  
Real Data ◽  
Fuzzy Classification ◽  
Robust Algorithms ◽  
Data Contamination ◽  
Heavy Tailed Distributions ◽  
Heavy Tailed ◽  
T Distribution

Regression models with change-points have been widely applied in various fields. Most methodologies for change-point regressions assume Gaussian errors. For many real data having longer-than-normal tails or atypical observations, the use of normal errors may unduly affect the fit of change-point regression models. This paper proposes two robust algorithms called EMT and FCT for change-point regressions by incorporating the t-distribution with the expectation and maximization algorithm and the fuzzy classification procedure, respectively. For better resistance to high leverage outliers, we introduce a modified version of the proposed method, which fits the t change-point regression model to the data after moderately pruning high leverage points. The selection of the degrees of freedom is discussed. The robustness properties of the proposed methods are also analyzed and validated. Simulation studies show the effectiveness and resistance of the proposed methods against outliers and heavy-tailed distributions. Extensive experiments demonstrate the preference of the t-based approach over normal-based methods for better robustness and computational efficiency. EMT and FCT generally work well, and FCT always performs better for less biased estimates, especially in cases of data contamination. Real examples show the need and the practicability of the proposed method.

scholarly journals Scaled Consistent Estimation of Regression Parameters in Frailty Models

2018 ◽  
Vol 5 (338) ◽  
pp. 133-142 ◽  
Author(s):  
Tadeusz Bednarski ◽  
Magdalena Skolimowska-Kulig
Keyword(s):  
Regression Models ◽  
Asymptotic Properties ◽  
Likelihood Estimation ◽  
Case Analysis ◽  
Real Data ◽  
Estimation Of Parameters ◽  
Consistent Estimation ◽  
Exponential Regression ◽  
Regression Parameters ◽  
Exponential Regression Model

A computationally attractive method of estimation of parameters for a class of frailty regression models is discussed. The method uses maximum likelihood estimation for the classical exponential regression model. Scaled Fisher consistency is shown to hold and a simulation study indicating good asymptotic properties of the method, as well as real data case analysis, are presented.

Robust Fuzzy Clustering Algorithms for Change-Point Regression Models

2020 ◽  
Vol 28 (05) ◽  
pp. 701-725
Author(s):  
Kang-Ping Lu ◽  
Shao-Tung Chang
Keyword(s):  
Change Point ◽  
Regression Models ◽  
Clustering Algorithms ◽  
Real Data ◽  
Robust Algorithms ◽  
Heavy Tailed Distributions ◽  
Regression Parameters ◽  
Fuzzy C Means Clustering ◽  
M Estimation ◽  
Heavy Tailed

This article presents a robust fuzzy procedure for estimating change-point regression models. We propose incorporating the fuzzy change-point algorithm with the M-estimation technique for robust estimations. The fuzzy c partitions concept is embedded into the change-point regression model so the fuzzy c-regressions and fuzzy c-means clustering can be employed to obtain the estimates of change-points and regression parameters. The M estimation with a robust criterion is used to make the estimators robust to the presence of outliers and heavy-tailed distributions. We create two robust algorithms named FCH and FCT by using Huber’s and Tukey’s functions as the robust criterion respectively. Extensive experiments with numerical and real examples are provided for demonstrating the effectiveness and the superiority of the proposed algorithms. The experimental results show the proposed algorithms are resistant to atypical observations and outperform the existing methods. The proposed FCH and FCT are generally comparable but FCT performs better in the presence of extremely high leverage outliers and heavy-tailed distributions. Real data applications show the practical usefulness of the proposed method.

scholarly journals Mixed Poisson Regression Models with Varying Dispersion Arising from Non-Conjugate Mixing Distributions

Algorithms ◽  
2021 ◽  
Vol 15 (1) ◽  
pp. 16
Author(s):  
George Tzougas ◽  
Natalia Hong ◽  
Ryan Ho
Keyword(s):  
Life Insurance ◽  
Poisson Regression ◽  
Regression Models ◽  
Likelihood Estimation ◽  
Dispersion Parameters ◽  
Modelling Framework ◽  
Mixing Distributions ◽  
Insurance Portfolio ◽  
Varying Dispersion ◽  
Different Levels

In this article we present a class of mixed Poisson regression models with varying dispersion arising from non-conjugate to the Poisson mixing distributions for modelling overdispersed claim counts in non-life insurance. The proposed family of models combined with the adopted modelling framework can provide sufficient flexibility for dealing with different levels of overdispersion. For illustrative purposes, the Poisson-lognormal regression model with regression structures on both its mean and dispersion parameters is employed for modelling claim count data from a motor insurance portfolio. Maximum likelihood estimation is carried out via an expectation-maximization type algorithm, which is developed for the proposed family of models and is demonstrated to perform satisfactorily.

scholarly journals MIXED CAUSAL-NONCAUSAL AR PROCESSES AND THE MODELLING OF EXPLOSIVE BUBBLES

2019 ◽  
Vol 35 (6) ◽  
pp. 1234-1270 ◽  
Author(s):  
Sébastien Fries ◽  
Jean-Michel Zakoian
Keyword(s):  
Conditional Distribution ◽  
Stable Distribution ◽  
Financial Time Series ◽  
Domain Of Attraction ◽  
Real Data ◽  
Autoregressive Processes ◽  
Financial Time ◽  
Causal Representation ◽  
Heavy Tailed ◽  
Non Gaussian

Noncausal autoregressive models with heavy-tailed errors generate locally explosive processes and, therefore, provide a convenient framework for modelling bubbles in economic and financial time series. We investigate the probability properties of mixed causal-noncausal autoregressive processes, assuming the errors follow a stable non-Gaussian distribution. Extending the study of the noncausal AR(1) model by Gouriéroux and Zakoian (2017), we show that the conditional distribution in direct time is lighter-tailed than the errors distribution, and we emphasize the presence of ARCH effects in a causal representation of the process. Under the assumption that the errors belong to the domain of attraction of a stable distribution, we show that a causal AR representation with non-i.i.d. errors can be consistently estimated by classical least-squares. We derive a portmanteau test to check the validity of the estimated AR representation and propose a method based on extreme residuals clustering to determine whether the AR generating process is causal, noncausal, or mixed. An empirical study on simulated and real data illustrates the potential usefulness of the results.

scholarly journals Relationships between test positivity rate, total laboratory confirmed cases of malaria, and malaria incidence in high burden settings of Uganda: an ecological analysis

2021 ◽  
Vol 20 (1) ◽  
Author(s):  
Jaffer Okiring ◽  
Adrienne Epstein ◽  
Jane F. Namuganga ◽  
Victor Kamya ◽  
Asadu Sserwanga ◽  
...  
Keyword(s):  
Regression Models ◽  
Malaria Incidence ◽  
Temporal Changes ◽  
Linear Regression Models ◽  
High Burden ◽  
Exponential Regression ◽  
Malaria Morbidity ◽  
Laboratory Test Results ◽  
Combining Data ◽  
Catchment Areas

Abstract Background Malaria surveillance is critical for monitoring changes in malaria morbidity over time. National Malaria Control Programmes often rely on surrogate measures of malaria incidence, including the test positivity rate (TPR) and total laboratory confirmed cases of malaria (TCM), to monitor trends in malaria morbidity. However, there are limited data on the accuracy of TPR and TCM for predicting temporal changes in malaria incidence, especially in high burden settings. Methods This study leveraged data from 5 malaria reference centres (MRCs) located in high burden settings over a 15-month period from November 2018 through January 2020 as part of an enhanced health facility-based surveillance system established in Uganda. Individual level data were collected from all outpatients including demographics, laboratory test results, and village of residence. Estimates of malaria incidence were derived from catchment areas around the MRCs. Temporal relationships between monthly aggregate measures of TPR and TCM relative to estimates of malaria incidence were examined using linear and exponential regression models. Results A total of 149,739 outpatient visits to the 5 MRCs were recorded. Overall, malaria was suspected in 73.4% of visits, 99.1% of patients with suspected malaria received a diagnostic test, and 69.7% of those tested for malaria were positive. Temporal correlations between monthly measures of TPR and malaria incidence using linear and exponential regression models were relatively poor, with small changes in TPR frequently associated with large changes in malaria incidence. Linear regression models of temporal changes in TCM provided the most parsimonious and accurate predictor of changes in malaria incidence, with adjusted R2 values ranging from 0.81 to 0.98 across the 5 MRCs. However, the slope of the regression lines indicating the change in malaria incidence per unit change in TCM varied from 0.57 to 2.13 across the 5 MRCs, and when combining data across all 5 sites, the R2 value reduced to 0.38. Conclusions In high malaria burden areas of Uganda, site-specific temporal changes in TCM had a strong linear relationship with malaria incidence and were a more useful metric than TPR. However, caution should be taken when comparing changes in TCM across sites.

scholarly journals Transition models for count data: a flexible alternative to fixed distribution models

2021 ◽  
Author(s):  
Moritz Berger ◽  
Gerhard Tutz
Keyword(s):  
Count Data ◽  
Regression Models ◽  
Negative Binomial ◽  
Real Data ◽  
Distribution Models ◽  
Explanatory Variables ◽  
Excess Zeros ◽  
Proposed Model ◽  
Transition Models ◽  
Fixed Distribution

AbstractA flexible semiparametric class of models is introduced that offers an alternative to classical regression models for count data as the Poisson and Negative Binomial model, as well as to more general models accounting for excess zeros that are also based on fixed distributional assumptions. The model allows that the data itself determine the distribution of the response variable, but, in its basic form, uses a parametric term that specifies the effect of explanatory variables. In addition, an extended version is considered, in which the effects of covariates are specified nonparametrically. The proposed model and traditional models are compared in simulations and by utilizing several real data applications from the area of health and social science.

On the ML Estimation of the Correlation Parameter in Generalized Exponential Models

2011 ◽  
Author(s):  
Helmut Waldl ◽  
Theodore E. Simos ◽  
George Psihoyios ◽  
Ch. Tsitouras ◽  
Zacharias Anastassi
Keyword(s):  
Ml Estimation ◽  
Correlation Parameter ◽  
Exponential Models
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