Monitoring Parameter Change for Time Series Models of Counts Based on Minimum Density Power Divergence Estimator

In this study, we consider an online monitoring procedure to detect a parameter change for integer-valued generalized autoregressive heteroscedastic (INGARCH) models whose conditional density of present observations over past information follows one parameter exponential family distributions. For this purpose, we use the cumulative sum (CUSUM) of score functions deduced from the objective functions, constructed for the minimum power divergence estimator (MDPDE) that includes the maximum likelihood estimator (MLE), to diminish the influence of outliers. It is well-known that compared to the MLE, the MDPDE is robust against outliers with little loss of efficiency. This robustness property is properly inherited by the proposed monitoring procedure. A simulation study and real data analysis are conducted to affirm the validity of our method.

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Test for parameter change in the presence of outliers: the density power divergence-based approach

Journal of Statistical Computation and Simulation ◽

10.1080/00949655.2020.1842407 ◽

2020 ◽

pp. 1-24

Author(s):

Junmo Song ◽

Jiwon Kang

Keyword(s):

Parameter Change ◽

Density Power Divergence ◽

Power Divergence ◽

Test For Parameter Change

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Robust Estimation for Bivariate Poisson INGARCH Models

Entropy ◽

10.3390/e23030367 ◽

2021 ◽

Vol 23 (3) ◽

pp. 367

Author(s):

Byungsoo Kim ◽

Sangyeol Lee ◽

Dongwon Kim

Keyword(s):

Robust Estimation ◽

New South ◽

Estimation Method ◽

Real Data ◽

Regularity Conditions ◽

Density Power Divergence ◽

Asymptotically Normal ◽

South Wales ◽

Power Divergence ◽

Conditional Maximum

In the integer-valued generalized autoregressive conditional heteroscedastic (INGARCH) models, parameter estimation is conventionally based on the conditional maximum likelihood estimator (CMLE). However, because the CMLE is sensitive to outliers, we consider a robust estimation method for bivariate Poisson INGARCH models while using the minimum density power divergence estimator. We demonstrate the proposed estimator is consistent and asymptotically normal under certain regularity conditions. Monte Carlo simulations are conducted to evaluate the performance of the estimator in the presence of outliers. Finally, a real data analysis using monthly count series of crimes in New South Wales and an artificial data example are provided as an illustration.

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Beta regression in the presence of outliers – A wieldy Bayesian solution

Statistical Methods in Medical Research ◽

10.1177/0962280218814574 ◽

2018 ◽

Vol 28 (12) ◽

pp. 3729-3740

Author(s):

Janet van Niekerk ◽

Andriette Bekker ◽

Mohammad Arashi

Keyword(s):

Degrees Of Freedom ◽

Real Data ◽

Small Sample ◽

Major Influence ◽

Beta Regression ◽

Response Model ◽

Density Power Divergence ◽

Heavy Tailed ◽

Power Divergence ◽

Different Response

Real phenomena often leads to challenges in data. One of these is outliers or influential values. Especially in a small sample, these values can have a major influence on the modeling process. In the beta regression framework, this issue has been addressed mainly in two ways: the assumption of a different response model and the application of a minimum density power divergence estimation (MDPDE) procedure. In this paper, however, we propose a simple hierarchical Bayesian methodology in the context of a varying dispersion beta response model that is robust to outliers, as shown through an extensive simulation study and analysis of two real data sets. To robustify Bayesian modeling, a heavy-tailed Student's t prior with uniform degrees of freedom is adopted for the regression coefficients. This proposal results in a wieldy implementation procedure which avails practical use of the approach.

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A New Class of Robust Two-Sample Wald-Type Tests

The International Journal of Biostatistics ◽

10.1515/ijb-2017-0023 ◽

2018 ◽

Vol 14 (2) ◽

Cited By ~ 2

Author(s):

Abhik Ghosh ◽

Nirian Martin ◽

Ayanendranath Basu ◽

Leandro Pardo

Keyword(s):

Clinical Trials ◽

Hypothesis Testing ◽

Real Data ◽

Nuisance Parameters ◽

Medical Sciences ◽

Density Power Divergence ◽

Minimum Density ◽

New Class ◽

Composite Hypotheses ◽

Power Divergence

Abstract Parametric hypothesis testing associated with two independent samples arises frequently in several applications in biology, medical sciences, epidemiology, reliability and many more. In this paper, we propose robust Wald-type tests for testing such two sample problems using the minimum density power divergence estimators of the underlying parameters. In particular, we consider the simple two-sample hypothesis concerning the full parametric homogeneity as well as the general two-sample (composite) hypotheses involving some nuisance parameters. The asymptotic and theoretical robustness properties of the proposed Wald-type tests have been developed for both the simple and general composite hypotheses. Some particular cases of testing against one-sided alternatives are discussed with specific attention to testing the effectiveness of a treatment in clinical trials. Performances of the proposed tests have also been illustrated numerically through appropriate real data examples.

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The Censored Beta-Skew Alpha-Power Distribution

Symmetry ◽

10.3390/sym13071114 ◽

2021 ◽

Vol 13 (7) ◽

pp. 1114

Author(s):

Guillermo Martínez-Flórez ◽

Roger Tovar-Falón ◽

María Martínez-Guerra

Keyword(s):

Power Distribution ◽

Information Matrix ◽

Real Data ◽

Likelihood Method ◽

Data Sets ◽

Alpha Power ◽

Score Functions ◽

New Family ◽

Two Parameters ◽

Family Of Distributions

This paper introduces a new family of distributions for modelling censored multimodal data. The model extends the widely known tobit model by introducing two parameters that control the shape and the asymmetry of the distribution. Basic properties of this new family of distributions are studied in detail and a model for censored positive data is also studied. The problem of estimating parameters is addressed by considering the maximum likelihood method. The score functions and the elements of the observed information matrix are given. Finally, three applications to real data sets are reported to illustrate the developed methodology.

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Robust Regression with Density Power Divergence: Theory, Comparisons, and Data Analysis

Entropy ◽

10.3390/e22040399 ◽

2020 ◽

Vol 22 (4) ◽

pp. 399 ◽

Cited By ~ 2

Author(s):

Marco Riani ◽

Anthony C. Atkinson ◽

Aldo Corbellini ◽

Domenico Perrotta

Keyword(s):

Robust Regression ◽

Robust Statistics ◽

Estimation Method ◽

Estimation Procedure ◽

Breakdown Point ◽

Parameter Estimates ◽

Normal Density ◽

Density Power Divergence ◽

Numerical Minimization ◽

Power Divergence

Minimum density power divergence estimation provides a general framework for robust statistics, depending on a parameter α , which determines the robustness properties of the method. The usual estimation method is numerical minimization of the power divergence. The paper considers the special case of linear regression. We developed an alternative estimation procedure using the methods of S-estimation. The rho function so obtained is proportional to one minus a suitably scaled normal density raised to the power α . We used the theory of S-estimation to determine the asymptotic efficiency and breakdown point for this new form of S-estimation. Two sets of comparisons were made. In one, S power divergence is compared with other S-estimators using four distinct rho functions. Plots of efficiency against breakdown point show that the properties of S power divergence are close to those of Tukey’s biweight. The second set of comparisons is between S power divergence estimation and numerical minimization. Monitoring these two procedures in terms of breakdown point shows that the numerical minimization yields a procedure with larger robust residuals and a lower empirical breakdown point, thus providing an estimate of α leading to more efficient parameter estimates.

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