Use of Relative Entropy Statistics in Contingency Tables
Chapter from the book:
Akoğul,
S.
&
Tuna,
E.
(eds.)
2024.
Academic Studies with Current Econometric and Statistical Applications.
Synopsis
There are various information theoretic divergence measures used for determining associations between nominal variables. Among them, Shannon mutual information statistic is especially appealing, since its sampling properties are well-known. Although Shannon mutual information is more frequently used, Rényi and Tsallis mutual informations, as envelopes of various tools, provide much higher flexibility than Shannon mutual information. Indeed, Shannon mutual information is a special case of Kullback-Leibler divergence, Rényi, and Tsallis mutual informations. In this study, large sampling properties of Shannon, Rényi, Tsallis mutual information statistics are considered as well as Pearson, Tschuprow, Sakoda, Cramér, Hellinger, and Bhattacharyya measures. In simulations, the normality of most of the statistics, and the higher positive correlation coefficients between all these tools are observed. Their sampling variabilities are compared. Then by using Rényi and Tsallis mutual information statistics, correlation coefficients are estimated for 8 different scenarios, and 3 bivariate normal distributions.
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Copyright (c) 2024 Serkan Akoğul, Elif Tuna; Eda Yalçın Kayacan, Tuncay Moralı, Serkan Akoğul, Mert Veznikli, Zehra Zeynep Şahinbaşoğlu, Elif Bahadır, Şevval Gökçen, Elif Tuna, Mehmet Şamil Güneş, Nida Oruç, Doğan Yıldız, Gizem Aydın, Mehmet Yalçın, Aylin Uçan, Nuran Çakır Yıldız, İbrahim Demir, Furkan Metin, Metin Aytaç, Turgay Altun, Mehmet Şaban Uçarı, Onur Şentürk, Cem Baş, Atıf Evren, Erhan Ustaoğlu, Büşra Şahin, Muzaffer Göztaş, Doğan Yıldız, Arda Tekin, Boran Toktay, Ahmet Can Günay, Harun Yazgan, Neslihan G. İnan, Ozan Kocadağlı, Selim Serin, Gülder Kemalbay, Ümmü Şahin Şener, Ersin Şener