Information measures of kernel estimation

References

• Abramson, I. S. (1982). On bandwidth variation in kernel estimates-a square root law. The Annals of Statistics 10:1217–1223.
   Web of Science ®Google Scholar
• Asadi, M., Ebrahimi, N., Soofi, E. S. (2005). Dynamic generalized information measures. Statistics and Probability Letters 71:85–98.
   Web of Science ®Google Scholar
• Blumentritt, T., Schmid, F. (2012). Mutual information as a measure of multivariate association: Analytical properties and statistical estimation. Journal of Statistical Computation and Simulation 82(9):1257–1274.
   Web of Science ®Google Scholar
• Bowman, A., Hall, P., Prvan, T. (1998). Bandwidth selection for the smoothing of distribution functions. Biometrika 85:799–808.
   Web of Science ®Google Scholar
• Briët, J., Harremoës, P. (2009). Properties of classical and quantum Jensen-Shannon divergence. Phys. Rev. A 79: 052311.
   Web of Science ®Google Scholar
• Ebrahimi, N., Jalali, N. Y., Soofi, E. S. (2014). Comparison, utility, and partition of dependence under absolutely continuous and singular distributions. Journal of Multivariate Analysis 131:32–50.
   Web of Science ®Google Scholar
• Ebrahimi, N., Maasoumi, E., Soofi, E. S. (1999). Ordering univariate distributions by entropy and variance. Journal of Econometrics 90:317–366.
   Web of Science ®Google Scholar
• Ebrahimi, N., Soofi, E. S., Soyer, R. (2008). Multivariate maximum entropy identification, transformation, and dependence. Journal of Multivariate Analysis 99:1217–1231.
   Web of Science ®Google Scholar
• Ebrahimi, N., Soofi, E. S., Soyer, R. (2010). Information measures in perspective. International Statistical Review 78:383–412.
   Web of Science ®Google Scholar
• Granger, C. W. J., Lin, J. L. (1994). Using the mutual information coefficient to identify lags in nonlinear models. The Journal of Time Series Analysis 15(4):371–384.
   Google Scholar
• Granger, C. W. J., Maasoumi, E., Racine, J. S. (2004). A dependence metric for possibly nonlinear processes. Journal of Time Series Analysis 25(5):649–669.
   Web of Science ®Google Scholar
• Hall, P. (1987). On Kullback-Leibler loss and density estimation. Annals of Statistics 15(4):1491–1519.
   Web of Science ®Google Scholar
• Hall, P. (1990). Akaike’s information criterion and Kullback-Leibler loss for histogram density estimation. Probability Theory and Related Fields 85:449–467.
   Web of Science ®Google Scholar
• Hall, P., Morton, S. C. (1993). On the estimation of entropy. Annals of the Institute of Statistical Mathematics 45(1):69–88.
   Web of Science ®Google Scholar
• Hall, P., Sheather, S. J., Jones, M. C., Marron, J. S. (1991). On optimal data-based bandwidth selection in kernel density estimation. Biometrika 78(2):263–269.
   Web of Science ®Google Scholar
• Hodges, J., Lehmann, E. (1956). The efficiency of some nonparameteric competitors of the t-test. Annals of Mathematical Statistics 27(2):324–335.
   Google Scholar
• Itzkovitz, S., Hodis, E., Segal, E. (2010). Overlapping codes within protein-coding sequences. Genome Research 20: 1582–1589.
   PubMed Web of Science ®Google Scholar
• Joe, H. (1989). Relative entropy measures of multivariate dependence. Journal of the American Statistical Association 84:157–164.
   Web of Science ®Google Scholar
• Klingenstein, S., Hitchcock, T., DeDeo, S. (2014). The civilizing process in London’s Old Bailey. Proceedings of the National Academy of Sciences 111:9419–9424.
   PubMed Web of Science ®Google Scholar
• Kullback, S. (1959). Information Theory and Statistics. New York: Wiley (reprinted in 1968 by Dover).
   Google Scholar
• Lin, J. (1991). Divergence measures based on the Shannon entropy. IEEE Transactions on Information Theory IT-37(1): 145–151.
   Web of Science ®Google Scholar
• Lindley, D. V. (1956). On the measure of information provided by an experiment. Annals of Mathematical Statistics 27: 986–1005.
   Google Scholar
• Maasoumi, E. (1986). The measurement and decomposition of multi-dimensional inequality. Econometrica 54(4):991–997.
   Web of Science ®Google Scholar
• Nadaraya, E. A. (1964). Some new estimates for distribution functions. Theory of Probability and its Applications 9:497–500.
   Google Scholar
• Parzen, E. (1962). On estimation of a probability density function and mode. The Annals of Mathematical Statistics 33:1065–1076.
   Google Scholar
• Robinson, P. M. (1991). Consistent nonparametric entropy-based testing. Review of Economic Studies 58:437–453.
   Web of Science ®Google Scholar
• Rosenblatt, M. (1956). Remarks on some nonparametric estimates of a density function. The Annals of Mathematical Statistics 27:832–837.
   Google Scholar
• Shannon, C. E. (1948). A mathematical theory of communication. Bell System Technical Journal 27:379–423, 625–656.
   Web of Science ®Google Scholar
• Silverman, B. W. (1986). Density Estimation for Statistics and Data Analysis. New York: Chapman and Hall.
   Google Scholar
• Sims, G., Jun, S., Wu, G., Kim, S. (2009). Alignment-free genome comparison with feature frequency profiles (FFP) and optimal resolutions. Proceedings of the National Academy of Sciences 106:2677–2682.
   PubMed Web of Science ®Google Scholar
• van Erven, T., Harremoës, P. (2014). Rényi divergence and Kullback-Leibler divergence. IEEE Transactions on Information Theory 60:3797–3820.
   Web of Science ®Google Scholar
• Zellner, A. (1971). An Introduction to Bayesian Inference in Econometrics. New York: Wiley.
   Google Scholar