Nonparametric estimators for varextropy under $\alpha$-mixing condition with appliction in exponential AR(1) model

[1] Alizadeh, H. N., & Shafaei, M. N. (2023). Varentropy estimators with applications in testing uniformity. Journal of Statistical Computation and Simulation, 93, 2582-2599. https://doi.org/10.1080/00949655.2023.2196627

[2] Al-Labadi, L., Hamlili, M., & Ly, A. (2023). Bayesian estimation of variance-based information measures and their application to testing uniformity. axioms, 12(9) 887. https://doi.org/10.3390/axioms12090887

[3] Balakrishna, N. (2021). Non-Gaussian autoregressive-type time series. Springer Nature.

[4] Becerra, A., de la Rosa, J. I., Gonzaez, E., Pedroza, A. D., & Escalante, N. I. (2018). Training deep neural networks with non-uniform frame-level cost function for automatic speech recognition. Multimedia Tools and Applications, 77, 27231-27267. http://doi.org/10.1007/s11042-018-5917-5

[5] Csorg}o, M., & Revesz, P. (1981). Strong Approximations in Probability and Statistics. Probability and Mathematical Statistics. Academic Press, New York.

[6] Gneiting, T., & Raftery, A. E. (2007). Strictly proper scoring rules, prediction, and estimation. Journal of the American Statistical Association, 102, 359-378. https://doi.org/10.1198/016214506000001437

[7] Goodarzi, F., Amini, M., & Mohtashami Borzadaran, G. R. (2017). Characterizations of continuous distributions through inequalities involving the expected values of selected functions. Application of mathematics, 62(5), 493-507. https://doi.org/10.21136/AM.2017.0182-16

[8] Goodarzi, F. (2023). Characterizations of some discrete distributions and upper bounds on discrete residual varentropy. Journal of the Iranian Statistical Society, 21(2), 233-250. https://doi.org/10.22034/jirss.2022.706994

[9] Irshad, M. R., & Maya, R. (2022). Nonparametric estimation of past extropy under  -mixing dependence condition. Ricerche di Matematica, 71, 723-734. https://doi.org/10.1007/s11587-021-00570-8

[10] Kamari, O., & Buono, F. (2021). On extropy of past lifetime distribution. Ricerche di Matematica, 70, 505-515. https://doi.org/10.1007/s11587-020-00488-7

[11] Krishnan, A. S., Sunoj, S. M., & Nair, N. U. (2020). Some reliability properties of extropy for residual and past lifetime random variables. Journal of the Korean Statistical Society, 49, 457-474. https://doi.org/10.1007/s42952-019-00023-x

[12] Lad, F., San lippo, G., Argo, G. (2015). Extropy: complementary dual of entropy. Statistical Science, 30(1), 40-58. https://doi.org/10.1214/14-STS430

[13] Lewis, P. A. W. (1964). A branching poisson process model for the analysis of computer failure patterns. Journal of the Royal Statistical Society, B 26, 398-456. https://doi.org/10.1111/j.2517-6161.1964.tb00573.x

[14] Loynes, R. M. (1965). Extreme values in uniformly mixing stationary stochastic processes. The Annals of Mathematical Statistics, 36(3), 993-999. https://doi.org/10.1214/aoms/1177700071

[15] Maadani, S., Mohtashami Borzadaran, G. R., & Rezaei Roknabadi, A. H. (2022). Varentropy of order statistics and some stochastic comparisons. Communications in Statistics-Theory and Methods, 51, 6447-6460. https://doi.org/10.1080/03610926.2020.1861299

[16] Masry, E. (1986). Recursive probablity density estimation for weakly dependent stationary processes. IEEE Transactions on Information Theory, 32, 254-267. https://doi.org/10.1109/TIT.1986.1057163

[17] Masry, E., & Gyor , L. (1987). Strong consistency and rates for recursive probability density estimators of stationary processes. Journal of Multivariate Analysis, 22(1), 79-93. https://doi.org/10.1016/0047-259X(87)90077-7

[18] Maya, R., & Irshad, M. R. (2019). Kernel estimation of the residual extropy under -mixing dependence condition. South African Statistical Journal, 53, 65-72. https://doi.org/10.37920/sasj.2019.53.2.1

[19] Maya, R., & Irshad, M. R. (2022). Kernel estimation of Mathai-Haubold entropy and residual Mathai-Haubold entropy functions under  -Mixing dependence condition. American Journal of Mathematical and Management Sciences, 41, 148-159. https://doi.org/10.1080/01966324.2021.1935366

[20] Maya, R., Irshad, M. R., & Archana, K. (2023). Recursive and non-recursive kernel estimation of negative cumulative residual extropy under  -mixing dependence condition. Ricerche di Matematica, 72(1), 119-139. https://doi.org/10.1007/s11587-021-00605-0

21] Maya, R., Irshad, M. R., Bakouch, H., Krishnakumar, A., & Qarmalah, N. (2023).
Kernel estimation of the extropy function under  -mixing dependent data. Symmetry,
15(4), 796. https://doi.org/10.3390/sym15040796
[22] Philipp, W., & Pinzur, L. (1980). Almost sure approximation theorems for the multivariate
empirical process. Z. Wahrscheinlichkeitstheorie verw. Gebiete. 54, 1{13.
https://doi.org/10.1007/BF00535346
[23] Qiu, G., & Jia, K. (2018a). Extropy estimators with applications in
testing uniformity. Journal of Nonparametric Statistics, 30, 182-196.
https://doi.org/10.1080/10485252.2017.1404063
[24] Qiu, G., & Jia, K. (2018b). The residual extropy of order statistics. Statistics & Probability
Letters, 133, 15-22. https://doi.org/10.1016/j.spl.2017.09.014
[25] Rajesh, R., Rajesh, G., & Sunoj, S. M. (2022). Kernel estimation of extropy
function under length biased sampling. Statistics & Probability Letters, 181, 1-9.
https://doi.org/10.1016/j.spl.2021.109290
[26] Rosenblatt, M. (1956). A central limit theorem and a strong mixing condition. Proceedings
of the National Academy of Sciences, 42, 43-47. https://www.jstor.org/stable/89041
[27] Roussas, G. G. (1989). Some asymptotic properties of an estimate of the survival
function under dependence conditions. Statistics & Probability Letters, 8, 235-243.
https://doi.org/10.1016/0167-7152(89)90128-4
[28] Saadatmand, A., Nematollahi, A. R., Sadooghi-Alvandi, S. M. (2021). On the estimation
problem in AR(1) model with exponential innovations. Journal of Statistical Modelling:
Theory and Applications, 2, 51-62. https://doi.org/10.22034/jsmta.2021.2695
[29] Shannon, C. E. (1948), A mathematical theory of communication, Bell System Technical
Journal, 27, 379-423. https://doi.org/10.1002/j.1538-7305.1948.tb01338.x
[30] Song, K. S. (2001). Renyi information, loglikelihood and an intrinsic distribution
measure. Journal of Statistical Planning and Inference, 93, 51-69.
https://doi.org/10.1016/S0378-3758(00)00169-5
[31] Vaselabadi, N. M., Tahmasebi, S., Kazemi, M. R., & Buono, F. (2021). Results on varextropy
measure of random variables. Entropy, 23, 356. https://doi.org/10.3390/e23030356
[32] Wolverton, C., Wagner, T. J. (1969). Asymptotically optimal discriminant functions
for pattern classi cation. IEEE Transactions on Information Theorey, 15(2), 258-265.
https://doi.org/10.1109/TIT.1969.1054295
[33] Zamini, R., Goodarzi, F., & Hashemi, F. (2023). Some kernel estimators for varextropy
function under length-biased sampling. Communications in Statistics-Simulation and
Computation, 1-21. https://doi.org/10.1080/03610918.2023.2289354