References

GENERALIZED DIVERGENCE CRITERIA FOR MODEL SELECTION BETWEEN RANDOM WALK AND AR(1) MODEL


[1] H. Akaike, An approximation to the density function, Ann. Inst. Statist. Math. Tokyo 6 (1954), 127-132.

[2] S. Bouzebda and I. Elhattab, Uniform-in-bandwidth consistency for kernel-type estimators of Shannon’s entropy, Electronic Journal of Statistics 5 (2011), 440-459.

[3] D. Bosq and J. P. Lecoutre, Théorie de l\\\'estimation fonctionnelle, Économie et Statistiques Avancées, Economica, Paris, 1987.

[4] J. Burbea and C. R. Rao, On the convexity of divergence measures based on entropy functions, IEEE Trans. Inform. Theory 28 (1982a), 489-495.

[5] J. Burbea and C. R. Rao, On the convexity of higher order
Jensen differences based on entropy functions, IEEE Trans. Inform. Theory 28 (1982b), 961-963.

[6] J. Burbea and C. R. Rao, Entropy differential metric distance and divergence measures in probability spaces: A unified approach, J. Multivariate Anal. 12 (1982c), 575-596.

[7] I. Csiszr, Information-type measures of differences of probability distributions and indirect observations, Studia Sci. Math. Hungarica 2 (1967), 299-318.

[8] P. Deheuvels, Uniform limit laws for kernel density estimators on possibly unbounded intervals, Stat. Ind. Technol. (2000), 477-492.

[9] P. Deheuvels and J. Einmahl, On the strong limiting behavior of local functionals of empirical processes based upon censored data, Ann. Prob. 24 (1996), 504-525.

[10] P. Deheuvels and D. M. Mason, General asymptotic confidence bands based on kernel-type function estimators, Stat. Inference Stoch. Process 7 (2004), 225-277.

[11] L. Devroye and L. Gyorfi, Nonparametric Density Estimation, Wiley Series in Probability and Mathematical Statistics: Tracts on Probability and Statistics, John Wiley & Sons Inc., New York, The L1 View, 1985.

[12] L. Devroye and G. Lugosi, Combinatorial Methods in density Estimation, Springer Series in Statistics, Springer-Verlag, New York, 2001.

[13] H. Dhaker, P. Ngom, P. Mendy and E. Deme, Uniform-in-bandwidth consistency for nonparametric estimation of divergence measures, arXiv:1406.6017.

[14] U. Einmahl and D. M. Mason, An empirical process approach to the uniform consistency of kernel-type function estimators, J. Theoret. Probab. 13 (2000), 1-37.

[15] H. Jeffreys, An invariant form for the prior probability in estimation problems, Proceedings of the Royal Society of London, Series A, Mathematical and Physical Sciences 186(1007) (1946), 453-461.

[16] S. Kullback and R. A. Leibler, On information and sufficiency, The Annals of Mathematical Statistics 22 (1951), 79-86.

[17] A. Lynda and F. Hocine, On the stability of the unit root test, Journal Afrika Statistika 5 (2010), 228-237.

[18] J. Marriott and P. Newbold, Bayesian comparison of ARIMA and stationary ARMA models, International Statistical Review 3 (1998), 323-336.

[19] M. L. Menendez, D. Morales, L. Pardo and I. Vajda, Divergence based estimation and testing of statistical models of classification, J. Multivariate Anal. 54 (1995), 329-354.

[20] D. B. Owen, Statistical Inference Based on Divergence Measures, Taylor & Francis Group, LLC, 2006.

[21] E. Parzen, On estimation of a probability density function and mode, Ann. Math. Statist. 33 (1962), 1065-1076.

[22] B. Póczos and J. Schneider, On the estimation of alpha-divergences, CMU, Auton Lab Technical Report.

http://www.cs.cmu.edu/bapoczos/articles/poczos11alphaTR.pdf

[23] B. L. S. Prakasa Rao, Nonparametric Functional Estimation, Probability and Mathematical Statistics, Academic Press Inc. [Harcourt Brace Jovanovich Publishers], New York, 1983.

[24] A. Rényi, On measures of entropy and information, In Fourth Berkeley Symposium on Mathematical Statistics and Probability, 1961.

[25] B. D. Sharma and D. P. Mittal, New non-additive measures of relative information, Journ. Comb. Inf. Syst. Sci. 2 (1977), 122-132.

[26] M. Rosenblatt, Remarks on some nonparametric estimates of a density function, Ann. Math. Statist. 27 (1956), 832-837.

[27] I. J. Taneja, On Generalized Information Measures and their Applications, Chapter in: Advances in Electronics and Electon Physics, Editor P. W. Hawkes 76 (1989), 327-413.