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Journal articles on the topic 'Hellinger's distance'

Author: Grafiati

Published: 4 June 2021

Last updated: 15 February 2022

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1

McIntyre, Lauren M., and B. S. Weir. "Hardy-Weinberg Testing for Continuous Data." Genetics 147, no. 4 (December 1, 1997): 1965–75. http://dx.doi.org/10.1093/genetics/147.4.1965.

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Abstract Estimation of allelic and genotypic distributions for continuous data using kernel density estimation is discussed and illustrated for some variable number of tandem repeat data. These kernel density estimates provide a useful representation of data when only some of the many variants at a locus are present in a sample. Two Hardy-Weinberg test procedures are introduced for continuous data: a continuous chi-square test with test statistic TCCS and a test based on Hellinger's distance with test statistic TCCS. Simulations are used to compare the powers of these tests to each other and to the powers of a test of intraclass correlation TIC, as well as to the power of Fisher's exact test TFET applied to discretized data. Results indicate that the power of TCCS is better than that of THD but neither is as powerful as TFET. The intraclass correlation test does not perform as well as the other tests examined in this article.

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2

Wu, Jingjing, and Rohana J. Karunamuni. "Profile Hellinger distance estimation." Statistics 49, no. 4 (August 12, 2014): 711–40. http://dx.doi.org/10.1080/02331888.2014.946928.

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3

Si-Ma, Ling-Han, Jian Zhang, Bin-Qiang Wang, and Yan-Yu Zhang. "Hellinger-Distance-Optimal Space Constellations." IEEE Communications Letters 21, no. 4 (April 2017): 765–68. http://dx.doi.org/10.1109/lcomm.2017.2650234.

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4

Wu, Jingjing, and Rohana J. Karunamuni. "On minimum Hellinger distance estimation." Canadian Journal of Statistics 37, no. 4 (December 2009): 514–33. http://dx.doi.org/10.1002/cjs.10042.

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5

Pitrik, József, and Dániel Virosztek. "Quantum Hellinger distances revisited." Letters in Mathematical Physics 110, no. 8 (March 10, 2020): 2039–52. http://dx.doi.org/10.1007/s11005-020-01282-0.

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6

Withers, Christopher S., and Saralees Nadarajah. "METHODS FOR SYMMETRIZING RANDOM VARIABLES." Probability in the Engineering and Informational Sciences 24, no. 4 (August 19, 2010): 549–59. http://dx.doi.org/10.1017/s0269964810000173.

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Let X be a random variable with nonsymmetric density p(x). We give the symmetric density q(x) closest to it in the sense of Kulback–Liebler and Hellinger distances. (All symmetries are around zero.) For the first distance, we show that q(x) is proportional to the geometric mean of p(x) and p(−x). For example, a symmetrized shifted exponential is a centered uniform, and a symmetrized shifted gamma is a centered beta random variable. For the second distance, q(x) is proportional to the square of the arithmetic mean of p(x)1/2 and p(−x)1/2. Sample versions are also given for each. We also give the optimal random function f such that f(X) is symmetrically distributed and minimizes |f(X)−X|. Finally, we show how to optimize the Hellinger distance for vector X subject to supersymmetry and for scalar X subject to being monotone about zero in each half-line.

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7

Kadjo, Roger, Ouagnina Hili, and Aubin N'dri. "Minimum Hellinger Distance Estimation of a Univariate GARCH Process." Journal of Mathematics Research 9, no. 3 (May 28, 2017): 80. http://dx.doi.org/10.5539/jmr.v9n3p80.

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In this paper, we determine the Minimum Hellinger Distance estimator of a stationary GARCH process. We construct an estimator of the parameters based on the minimum Hellinger distance method. Under conditions which ensure the $\phi$-mixing of the GARCH process, we establish the almost sure convergence and the asymptotic normality of the estimator.

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8

Hili, Ouagnina. "Hellinger distance estimation of SSAR models." Statistics & Probability Letters 53, no. 3 (June 2001): 305–14. http://dx.doi.org/10.1016/s0167-7152(01)00086-4.

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9

Shemyakin, Arkady. "Hellinger Distance and Non-informative Priors." Bayesian Analysis 9, no. 4 (December 2014): 923–38. http://dx.doi.org/10.1214/14-ba881.

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10

Kitsos, C., and T. Toulias. "Hellinger Distance Between Generalized Normal Distributions." British Journal of Mathematics & Computer Science 21, no. 2 (January 10, 2017): 1–16. http://dx.doi.org/10.9734/bjmcs/2017/32229.

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11

Bhatia, Rajendra, Stephane Gaubert, and Tanvi Jain. "Matrix versions of the Hellinger distance." Letters in Mathematical Physics 109, no. 8 (January 14, 2019): 1777–804. http://dx.doi.org/10.1007/s11005-019-01156-0.

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12

Karunamuni, Rohana J., and Jingjing Wu. "One-step minimum Hellinger distance estimation." Computational Statistics & Data Analysis 55, no. 12 (December 2011): 3148–64. http://dx.doi.org/10.1016/j.csda.2011.06.029.

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13

Ryu, Kwon Moo, Young Jin Han, and Young Hoon Joo. "Multiple Moving Object Tracking Method Using Hellinger Distance." Transactions of The Korean Institute of Electrical Engineers 69, no. 5 (May 31, 2020): 729–37. http://dx.doi.org/10.5370/kiee.2020.69.5.729.

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14

LI, Wei-wei, and Xiu-yi JIA. "Feature selection algorithm based on Hellinger distance." Journal of Computer Applications 30, no. 6 (June 23, 2010): 1530–32. http://dx.doi.org/10.3724/sp.j.1087.2010.01530.

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15

Valkeila, Esko, and Ljudmilla Vostrikova. "An integral representation for the Hellinger distance." MATHEMATICA SCANDINAVICA 58 (June 1, 1986): 239. http://dx.doi.org/10.7146/math.scand.a-12144.

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16

Kang, Joonsung. "Minimum Hellinger distance estimation for correlated errors." Journal of the Korean Data And Information Science Society 30, no. 1 (January 31, 2019): 219–31. http://dx.doi.org/10.7465/jkdi.2019.30.1.219.

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17

Wu, Jingjing, and Rohana J. Karunamuni. "Efficient Hellinger distance estimates for semiparametric models." Journal of Multivariate Analysis 107 (May 2012): 1–23. http://dx.doi.org/10.1016/j.jmva.2012.01.007.

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18

Karlis, Dimitris, and Evdokia Xekalaki. "Minimum Hellinger distance estimation for Poisson mixtures." Computational Statistics & Data Analysis 29, no. 1 (November 1998): 81–103. http://dx.doi.org/10.1016/s0167-9473(98)00047-4.

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19

Harris, Ian R., and Ayanendranath Basu. "Hellinger distance as a penalized log likelihood." Communications in Statistics - Simulation and Computation 23, no. 4 (January 1994): 1097–113. http://dx.doi.org/10.1080/03610919408813219.

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20

Hili, Ouagnina. "Hellinger distance estimation of nonlinear dynamical systems." Statistics & Probability Letters 63, no. 2 (June 2003): 177–84. http://dx.doi.org/10.1016/s0167-7152(03)00080-4.

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21

Sengar, H., Haining Wang, D. Wijesekera, and S. Jajodia. "Detecting VoIP Floods Using the Hellinger Distance." IEEE Transactions on Parallel and Distributed Systems 19, no. 6 (June 2008): 794–805. http://dx.doi.org/10.1109/tpds.2007.70786.

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22

Zhang, Yue, and Shunlong Luo. "Quantifying non-Gaussianity via the Hellinger distance." Theoretical and Mathematical Physics 204, no. 2 (August 2020): 1046–58. http://dx.doi.org/10.1134/s0040577920080061.

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23

Eslinger, Paul W., and Wayne A. Woodward. "Minimum hellinger distance estimation for normal models." Journal of Statistical Computation and Simulation 39, no. 1-2 (May 1991): 95–114. http://dx.doi.org/10.1080/00949659108811342.

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24

Boone, Edward L., Jason R. W. Merrick, and Matthew J. Krachey. "A Hellinger distance approach to MCMC diagnostics." Journal of Statistical Computation and Simulation 84, no. 4 (October 9, 2012): 833–49. http://dx.doi.org/10.1080/00949655.2012.729588.

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25

Marazzi, Alfio, and Victor J. Yohai. "Optimal robust estimates using the Hellinger distance." Advances in Data Analysis and Classification 4, no. 2-3 (June 4, 2010): 169–79. http://dx.doi.org/10.1007/s11634-010-0061-8.

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26

Agahi, Hamzeh. "A generalized Hellinger distance for Choquet integral." Fuzzy Sets and Systems 396 (October 2020): 42–50. http://dx.doi.org/10.1016/j.fss.2020.03.005.

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27

Woodward, Wayne A., Paul Whitney, and Paul W. Eslinger. "Minimum Hellinger distance estimation of mixture proportions." Journal of Statistical Planning and Inference 48, no. 3 (December 1995): 303–19. http://dx.doi.org/10.1016/0378-3758(95)00006-u.

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28

Dinh, Trung Hoa, Cong Trinh Le, Bich Khue Vo, and Trung-Dung Vuong. "Weighted Hellinger distance and in-betweenness property." Mathematical Inequalities & Applications, no. 1 (2021): 157–65. http://dx.doi.org/10.7153/mia-2021-24-11.

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29

Carvalho, Naiallen Carolyne Rodrigues Lima, Leonardo Sant’Anna Bins, and Sidnei João Siqueira Sant’Anna. "Analysis of Stochastic Distances and Wishart Mixture Models Applied on PolSAR Images." Remote Sensing 11, no. 24 (December 12, 2019): 2994. http://dx.doi.org/10.3390/rs11242994.

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This paper address unsupervised classification strategies applied to Polarimetric Synthetic Aperture Radar (PolSAR) images. We analyze the performance of complex Wishart distribution, which is a widely used model for multi-look PolSAR images, and the robustness of five stochastic distances (Bhattacharyya, Kullback-Leibler, Rényi, Hellinger and Chi-square) between Wishart distributions. Two unsupervised classification strategies were chosen: the Stochastic Clustering (SC) algorithm, which is based on the K-means algorithm but uses stochastic distance as the similarity metric, and the Expectation-Maximization (EM) algorithm for Wishart Mixture Model. With the aim of assessing the performance of all algorithms presented here, we performed a Monte Carlo simulation over a set of simulated PolSAR images. A second experiment was conducted using the study area of Tapajós National Forest and the surrounding area, in Brazilian Amazon Forest. The PolSAR images were obtained by the satellite PALSAR. The results, in both experiments, suggest that the EM algorithm and the SC with Hellinger and the SC with Bhattacharyya distance provide a better classification performance. We also analyze the initialization problem for SC and EM algorithms, and we demonstrate how the initial centroid choice influences the final classification result.

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30

Li, Zhen Xing, and Wei Hua Li. "Multitask Similarity Cluster." Advanced Materials Research 765-767 (September 2013): 1662–66. http://dx.doi.org/10.4028/www.scientific.net/amr.765-767.1662.

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Single task learning is widely used training in artificial neural network. Before, people usually see other tasks as noise in same learning machine. However, multitask learning, proposed by Rich Caruana, sees simultaneously training several correlated tasks is helpful to improve single tasks performance. In this paper, we propose a new neural network multitask similarity cluster. Combined with hellinger distance, multitask similarity cluster can estimate distances among clusters more accurate. Experimental results show multitask learning is helpful to improve performance of single task and multitask similarity cluster can get satisfactory result.

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31

SUETAKE, Noriaki, Go TANAKA, Hayato HASHII, and Eiji UCHINO. "Hellinger Distance-Based Parameter Tuning for ε-Filter." IEICE Transactions on Information and Systems E93-D, no. 9 (2010): 2647–50. http://dx.doi.org/10.1587/transinf.e93.d.2647.

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32

Kadjo, Roger, Ouagnina Hili, and Aubin N’dri. "MINIMUM HELLINGER DISTANCE ESTIMATION OF MULTIVARIATE GARCH PROCESSES." Far East Journal of Theoretical Statistics 54, no. 6 (December 12, 2018): 503–26. http://dx.doi.org/10.17654/ts054060503.

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33

Ying, Zhiliang. "Minimum Hellinger-Type Distance Estimation for Censored Data." Annals of Statistics 20, no. 3 (September 1992): 1361–90. http://dx.doi.org/10.1214/aos/1176348773.

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34

Chen, Jiahua, and J. D. Kalbfleisch. "Inverse Problems in Fractal Construction: Hellinger Distance Method." Journal of the Royal Statistical Society: Series B (Methodological) 56, no. 4 (November 1994): 687–700. http://dx.doi.org/10.1111/j.2517-6161.1994.tb02008.x.

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35

Cutler, Adele, and Olga I. Cordero-Braña. "Minimum Hellinger Distance Estimation for Finite Mixture Models." Journal of the American Statistical Association 91, no. 436 (December 1996): 1716–23. http://dx.doi.org/10.1080/01621459.1996.10476743.

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36

Marian, Paulina, and Tudor A. Marian. "Hellinger distance as a measure of Gaussian discord." Journal of Physics A: Mathematical and Theoretical 48, no. 11 (February 19, 2015): 115301. http://dx.doi.org/10.1088/1751-8113/48/11/115301.

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37

Bhatia, Rajendra, Stephane Gaubert, and Tanvi Jain. "Correction to: Matrix versions of the Hellinger distance." Letters in Mathematical Physics 109, no. 12 (October 11, 2019): 2779–81. http://dx.doi.org/10.1007/s11005-019-01228-1.

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38

Yang, Tao, Dongmei Fu, Xiaogang Li, and Kamil Říha. "Manifold regularized multiple kernel learning with Hellinger distance." Cluster Computing 22, S6 (March 16, 2018): 13843–51. http://dx.doi.org/10.1007/s10586-018-2106-2.

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39

González-Castro, Víctor, Rocío Alaiz-Rodríguez, and Enrique Alegre. "Class distribution estimation based on the Hellinger distance." Information Sciences 218 (January 2013): 146–64. http://dx.doi.org/10.1016/j.ins.2012.05.028.

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40

CORTES, CORINNA, MEHRYAR MOHRI, and ASHISH RASTOGI. "Lp DISTANCE AND EQUIVALENCE OF PROBABILISTIC AUTOMATA." International Journal of Foundations of Computer Science 18, no. 04 (August 2007): 761–79. http://dx.doi.org/10.1142/s0129054107004966.

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This paper presents an exhaustive analysis of the problem of computing the Lp distance of two probabilistic automata. It gives efficient exact and approximate algorithms for computing these distances for p even and proves the problem to be NP-hard for all odd values of p, thereby completing previously known hardness results. It further proves the hardness of approximating the Lp distance of two probabilistic automata for odd values of p. Similar techniques to those used for computing the Lp distance also yield efficient algorithms for computing the Hellinger distance of two unambiguous probabilistic automata both exactly and approximately. A problem closely related to the computation of a distance between probabilistic automata is that of testing their equivalence. This paper also describes an efficient algorithm for testing the equivalence of two arbitrary probabilistic automata A1 and A2 in time O(|Σ|(|A1| + |A2|)3), a significant improvement over the previously best reported algorithm for this problem.

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41

Wu, Yuefeng, and Giles Hooker. "Asymptotic Properties for Methods Combining the Minimum Hellinger Distance Estimate and the Bayesian Nonparametric Density Estimate." Entropy 20, no. 12 (December 11, 2018): 955. http://dx.doi.org/10.3390/e20120955.

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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.

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42

Luong, Andrew, Claire Bilodeau, and Christopher Blier-Wong. "Simulated Minimum Hellinger Distance Inference Methods for Count Data." Open Journal of Statistics 08, no. 01 (2018): 187–219. http://dx.doi.org/10.4236/ojs.2018.81012.

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43

N'dri, Aubin Yao, Ouagnina Hili, and Gueï Cyrille OKOU. "Hellinger Distance Estimation of Strongly Dependent Gaussian Random Fields." Afrika Statistika 14, no. 1 (January 1, 2019): 1937–50. http://dx.doi.org/10.16929/as/2019.1937.143.

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44

Ricotta, C. "Can we trust the chord (and the Hellinger) distance?" Community Ecology 20, no. 1 (April 2019): 104–6. http://dx.doi.org/10.1556/168.2019.20.1.11.

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45

Karunamuni, R. J., and J. Wu. "Minimum Hellinger distance estimation in a nonparametric mixture model." Journal of Statistical Planning and Inference 139, no. 3 (March 2009): 1118–33. http://dx.doi.org/10.1016/j.jspi.2008.07.004.

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46

Hili, Ouagnina. "Hellinger distance estimation of general bilinear time series models." Statistical Methodology 5, no. 2 (March 2008): 119–28. http://dx.doi.org/10.1016/j.stamet.2007.06.005.

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47

Sriram, T. N., and A. N. Vidyashankar. "Minimum Hellinger distance estimation for supercritical Galton–Watson processes." Statistics & Probability Letters 50, no. 4 (December 2000): 331–42. http://dx.doi.org/10.1016/s0167-7152(00)00112-7.

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48

Bissinger, Brett E., R. Lee Culver, and N. K. Bose. "Minimum Hellinger distance classification of passive underwater acoustic signals." Journal of the Acoustical Society of America 126, no. 4 (2009): 2183. http://dx.doi.org/10.1121/1.3248538.

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49

Tamura, Roy N., and Dennis D. Boos. "Minimum Hellinger Distance Estimation for Multivariate Location and Covariance." Journal of the American Statistical Association 81, no. 393 (March 1986): 223–29. http://dx.doi.org/10.1080/01621459.1986.10478264.

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50

Kanazawa, Yuichiro. "Hellinger distance and Akaike's information criterion for the histogram." Statistics & Probability Letters 17, no. 4 (July 1993): 293–98. http://dx.doi.org/10.1016/0167-7152(93)90205-w.

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