We consider n observations from the GARCH-type model: Z = UY, where U and Y are independent random variables. We aim to estimate density function Y where Y have a weighted distribution. We determine a sharp upper bound of the associated mean integrated square error. We also make use of the measure of expected true evidence, so as to determine when model leads to a crisis and causes data to be lost.
 R. Royall, “On the Probability of Observing Misleading Statistical Evidence,” Journal of the American Statistical Association, Vol. 95, No. 451, 2000, pp. 760-780. doi:10.1080/01621459.2000.10474264
 M. Emadi, J. Ahmadi and N. R. Arghami, “Comparing of Record Data and Random Observation Based on Statistical Evidence,” Statistical Papers, Vol. 48, No. 1, 2007, pp. 1-21. doi:10.1007/s00362-006-0313-z
 D. Modha and E. Masry, “Minimum Complexity Regression Estimation with Weakly Dependent Observations,” IEEE Transactions on Information Theory, Vol. 42, No. 6, 1996, pp. 2133-2145. doi:10.1109/18.556602
 A. Cohen, I. Daubechies, B. Jawerth and P. Vial, “Wavelets on the Interval and Fast Wavelet Transforms,” Applied and Computational Harmonic Analysis, Vol. 24, No. 1, 1993, pp. 54-81. doi:10.1006/acha.1993.1005
 M. Abbaszadeh, C. Chesneau and H. Doosti, “Nonparametric Estimation of Density under Bias and Multiplicative Censoring via Wavelet Methods,” Statistics and Probability Letters, Vol. 82, No. 5, 2012, pp. 932-941. doi:10.1016/j.spl.2012.01.016