scholarly journals Asymptotic Properties for Methods Combining the Minimum Hellinger Distance Estimate and the Bayesian Nonparametric Density Estimate

Entropy ◽  
2018 ◽  
Vol 20 (12) ◽  
pp. 955 ◽  
Author(s):  
Yuefeng Wu ◽  
Giles Hooker
Keyword(s):  
Asymptotic Properties ◽  
Kernel Density ◽  
Hellinger Distance ◽  
Density Estimate ◽  
Parametric Family ◽  
Density Estimator ◽  
Posterior Density ◽  
Minimum Hellinger Distance ◽  
Von Mises ◽  
Nonparametric Density Estimate

In frequentist inference, minimizing the Hellinger distance between a kernel density estimate and a parametric family produces estimators that are both robust to outliers and statistically efficient when the parametric family contains the data-generating distribution. This paper seeks to extend these results to the use of nonparametric Bayesian density estimators within disparity methods. We propose two estimators: one replaces the kernel density estimator with the expected posterior density using a random histogram prior; the other transforms the posterior over densities into a posterior over parameters through minimizing the Hellinger distance for each density. We show that it is possible to adapt the mathematical machinery of efficient influence functions from semiparametric models to demonstrate that both our estimators are efficient in the sense of achieving the Cramér-Rao lower bound. We further demonstrate a Bernstein-von-Mises result for our second estimator, indicating that its posterior is asymptotically Gaussian. In addition, the robustness properties of classical minimum Hellinger distance estimators continue to hold.

Nonparametric \(\phi\)-Divergence Estimation and Test for Model Selection

2020 ◽  
Vol 15 (2) ◽  
pp. 2349-2369
Author(s):  
Jean de Dieu Nkurunziza ◽  
Freedath Djibril Moussa ◽  
Papa Ngom
Keyword(s):  
Model Selection ◽  
Asymptotic Properties ◽  
Kernel Density ◽  
Kernel Density Estimator ◽  
Density Estimator ◽  
Normal Test ◽  
Standard Normal

In this paper, we study a bias reduced kernel density estimator and derive a nonparametric \(\phi\)-divergence estimator based on this density estimator. We investigate the asymptotic properties of these two estimators and we formulate an asymptotically standard normal test for model selection.

scholarly journals Intra-urban differentials of congenital and acquired syphilis and syphilis in pregnant women in an urban area in northeastern Brazil

2021 ◽  
Author(s):  
Talita Araujo de Souza ◽  
Karen Kaline Teixeira ◽  
Reginaldo Lopes Santana ◽  
Cinthia Barros Penha ◽  
Arthur de Almeida Medeiros ◽  
...  
Keyword(s):  
Relative Risk ◽  
Pregnant Women ◽  
Congenital Syphilis ◽  
Kernel Density ◽  
Poisson Model ◽  
Northeastern Brazil ◽  
Smoothing Function ◽  
Density Estimator ◽  
Epidemic Disease ◽  
Peripheral Areas

Abstract Background Currently syphilis is considered an epidemic disease worldwide. The objective of this study was to identify intra-urban differentials in the occurrence of congenital and acquired syphilis and syphilis in pregnant women in the city of Natal, in northeast Brazil. Methods Cases of syphilis recorded by the municipal surveillance system from 1 January 2011 to 30 December 2018 were analysed. Spatial statistical analyses were performed using the kernel density estimator of the quadratic smoothing function (weighted). SaTScan software was applied for the calculation of risk based on a discrete Poisson model. Results There were 2163 cases of acquired syphilis, 738 cases of syphilis in pregnant women and 1279 cases of congenital syphilis. Kernel density maps showed that the occurrence of cases is more prevalent in peripheral areas and in areas with more precarious urban infrastructure. In 2011–2014 and 2015–2018, seven statistically significant clusters of acquired syphilis were identified. From 2011 to 2014, the most likely cluster had a relative risk of 3.54 (log likelihood ratio [LLR] 38 895; p<0.001) and from 2015 to 2018 the relative risk was 0.54 (LLR 69 955; p<0.001). Conclusions In the municipality of Natal, there was a clustered pattern of spatial distribution of syphilis, with some areas presenting greater risk for the occurrence of new cases.

scholarly journals Analysis of the spatial distribution of dengue cases in the city of Rio de Janeiro, 2011 and 2012

2017 ◽  
Vol 51 ◽  
Author(s):  
Silvia Carvalho ◽  
Mônica De Avelar Figueiredo Mafra Magalhães ◽  
Roberto De Andrade Medronho
Keyword(s):  
Information System ◽  
Spatial Distribution ◽  
Rio De Janeiro ◽  
Influencing Factor ◽  
Kernel Density ◽  
Severe Dengue ◽  
Automatic Process ◽  
Density Estimator ◽  
Macroeconomic Policies ◽  
The City

OBJECTIVE Analyze the spatial distribution of classical dengue and severe dengue cases in the city of Rio de Janeiro. METHODS Exploratory study, considering cases of classical dengue and severe dengue with laboratory confirmation of the infection in the city of Rio de Janeiro during the years 2011/2012. The georeferencing technique was applied for the cases notified in the Notification Increase Information System in the period of 2011 and 2012. For this process, the fields “street” and “number” were used. The ArcGis10 program’s Geocoding tool’s automatic process was performed. The spatial analysis was done through the kernel density estimator. RESULTS Kernel density pointed out hotspots for classic dengue that did not coincide geographically with severe dengue and were in or near favelas. The kernel ratio did not show a notable change in the spatial distribution pattern observed in the kernel density analysis. The georeferencing process showed a loss of 41% of classic dengue registries and 17% of severe dengue registries due to the address in the Notification Increase Information System form. CONCLUSIONS The hotspots near the favelas suggest that the social vulnerability of these localities can be an influencing factor for the occurrence of this aggravation since there is a deficiency of the supply and access to essential goods and services for the population. To reduce this vulnerability, interventions must be related to macroeconomic policies.

scholarly journals Robust Multisensor Image Matching Using Bayesian Estimated Mutual Information

2013 ◽  
Vol 2013 ◽  
pp. 1-11
Author(s):  
Lurong Shen ◽  
Xinsheng Huang ◽  
Yuzhuang Yan ◽  
Yongbin Zheng ◽  
Wanying Xu
Keyword(s):  
Mutual Information ◽  
Cost Saving ◽  
Image Matching ◽  
Prior Information ◽  
Kernel Density ◽  
Density Estimate ◽  
Kernel Density Estimate ◽  
Template Image ◽  
Matching Performance

Mutual information (MI) has been widely used in multisensor image matching, but it may lead to mismatch among images with messy background. However, additional prior information can be of great help in improving the matching performance. In this paper, a robust Bayesian estimated mutual information, named as BMI, for multisensor image matching is proposed. This method has been implemented by utilizing the gradient prior information, in which the prior is estimated by the kernel density estimate (KDE) method, and the likelihood is modeled according to the distance of orientations. To further improve the robustness, we restrict the matching within the regions where the corresponding pixels of template image are salient enough. Experiments on several groups of multisensor images show that the proposed method outperforms the standard MI in robustness and accuracy and is similar with Pluim’s method. However, our computation is far more cost saving.

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