Minimum Power Divergence Estimator Research Articles

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.

Composite likelihood methods: Rao-type tests based on composite minimum density power divergence estimator

This paper is aimed to present a robust extension of the classical Rao test statistic, in the context of composite likelihood ideas and methods. The Rao-type test statistics are defined on the basis of the composite minimum power divergence estimators instead of the composite maximum likelihood estimator. These Rao-type test statistics are used to test simple and composite null hypotheses. Their performance is evaluated in terms of a simulation study which concentrates to the robustness and the comparison of the Rao-type tests with the respective Wald-type tests considered in Castilla et al. (Entropy 20:18, 2018). The proposed here procedures are developed on the basis of the restricted composite minimum density power divergence estimators which are also discussed for the sake of completeness.

Improved transformation of ϕ-divergence goodness-of-fit test statistics based on minimum ϕ*-divergence estimator for GLIM of binary data

Generalized linear models of binary data including a logistic regression model and a probit model are considered. For testing the null hypothesis that the considered model is correct, the ϕ-divergence family of goodness-of-fit test statistics Cϕϕ* that is based on a minimum ϕ*-divergence estimator is considered. The family of statistics Cϕϕ* includes a power divergence family of statistics Ra,b that is based on a minimum power divergence estimator. The derivation of an expression of a continuous term of asymptotic expansion for the distribution of Cϕϕ* under the null hypothesis is shown. Using the expression, a transformed Cϕϕ* statistic that improves the speed of convergence to the chi-square limiting distribution of Cϕϕ* is obtained. In the case of Ra,b, it is numerically shown that the transformed statistics usually perform better than the original statistics with respect to speed of convergence to the chi-square limiting distribution and it is also numerically shown that the power of the transformed statistics is almost the same as that of the original statistics.

A new class of minimum power divergence estimators with applications to cancer surveillance

The annual percent change (APC) has been adopted as a useful measure for analyzing the changing trends of cancer mortality and incidence rates by the NCI SEER program. Difficulties, however, arise when comparing the sample APCs between two overlapping regions because of induced dependence (e.g., comparing the cancer mortality change rate of California with that of the national level). This paper deals with a new perspective for understanding the sample distribution of the test-statistics for comparing the APCs between overlapping regions. Our proposal allows for computational readiness and easy interpretability. We further propose a more general family of estimators, namely, the so-called minimum power divergence estimators, including the maximum likelihood estimators as a special case. Our simulation experiments support the superiority of the proposed estimator to the conventional maximum likelihood estimator. The proposed method is illustrated by the analysis of the SEER cancer mortality rates observed from 1991 to 2006.

Homogeneity/Heterogeneity Hypotheses for Standardized Mortality Ratios Based on Minimum Power‐divergence Estimators

This paper analyzes the power divergence estimators when homogeneity/heterogeneity hypotheses among standardized mortality ratios (SMRs) are taken into account. A Monte Carlo study shows that when the standard mortality rate is not external, that is it is estimated from the sample data, these estimators have a good performance even for small sample sets and in particular the minimum chi-square estimators have a better behavior compared to the classical maximum likelihood estimators. In order to make decisions under homogeneity/heterogeneity hypotheses of SMRs we propose some test-statistics which consider the minimum power divergence estimators. Through a numerical example focused on SMRs of melanoma mortality ratios in different regions of the US, a homogeneity/heterogeneity study is illustrated.

Ordinary and penalized minimum power-divergence estimators in two-way contingency tables

Basu and Basu (Statistica Sinica 8:841---860, 1998) have proposed an empty cell penalty for the minimum power-divergence estimators which can lead to improvements in the small sample properties of these estimators. In this paper, we study the small and moderate sample performances of the ordinary and penalized minimum power-divergence estimators in terms of efficiency and robustness for the log-linear models in two-way contingency tables under the assumptions of multinomial sampling. Calculations made by enumerating all possible sample combinations show that the penalized estimators are competitive with the ordinary estimators for the moderate samples and definitely better for the smallest sample considered for both efficiency and robustness under the considered models. The results also reveal that the bigger the main effects the more need for penalization.

New family of estimators for the loglinear model of quasi-independence based on power-divergence measures

In this paper, we study the minimum power-divergence estimator, introduced and studied by Cressie and Read [Cressie, N. and Read, T.R.C., 1984, Multinomial goodness-of-fit tests. Journal of the Royal Statistic Society, Series B, 46, 440–464.], in the loglinear model of quasi-independence. A simulation study illustrates that minimum chi-squared estimator and Cressie–Read estimator are good alternatives to the classical maximum-likelihood estimator for this problem. The estimator obtained for λ=2 is the most robust and efficient estimator among the family of the minimum power estimators.

Minimum power-divergence estimator in three-way contingency tables

Cressie et al. (2000; 2003) introduced and studied a new family of statistics, based on the φ-divergence measure, for solving the problem of testing a nested sequence of loglinear models. In that family of test statistics the parameters are estimated using the minimum φ-divergence estimator which is a generalization of the maximum likelihood estimator. In this paper we study the minimum power-divergence estimator (the most important family of minimum φ-divergence estimator) for a nested sequence of loglinear models in three-way contingency tables under assumptions of multinomial sampling. A simulation study illustrates that the minimum chi-squared estimator is simultaneously the most robust and efficient estimator among the family of the minimum power-divergence estimator.

On robustness and efficiency of minimum divergence estimators

We study the trade-off between efficiency and robustness of the estimators obtained by minimizing the divergence statistics and their adjoints, obtained by minimizing the asymmetric counterparts of the divergence statistics. In particular, it is shown that no minimum power-divergence estimator is better than the minimum Hellinger distance estimator in terms of both second-order efficiency and robustness.

Robust Estimation for Grouped Data

Here we investigate the robustness properties of the class of minimum power divergence estimators for grouped data. This class contains the classical maximum likelihood estimators for grouped data. We find that the bias of these estimators due to deviations from the assumed underlying model can be large. Therefore, we propose a more general class of estimators that allows us to construct robust procedures. By analogy with Hampel's theorem, we define optimal bounded influence function estimators, and by a simulation study, we show that under small model contaminations, these estimators are more stable than the classical estimators for grouped data. Finally, we apply our results to a particular real example.

Robust Estimation for Grouped Data

Abstract Here we investigate the robustness properties of the class of minimum power divergence estimators for grouped data. This class contains the classical maximum likelihood estimators for grouped data. We find that the bias of these estimators due to deviations from the assumed underlying model can be large. Therefore, we propose a more general class of estimators that allows us to construct robust procedures. By analogy with Hampel's theorem, we define optimal bounded influence function estimators, and by a simulation study, we show that under small model contaminations, these estimators are more stable than the classical estimators for grouped data. Finally, we apply our results to a particular real example.