On the Approximation of Maximum Deviation Spline Estimation of the Probability Density Gaussian Process
Affiliation(s)
1 Institute of Mathematics, National University of Uzbekistan, Tashkent, Uzbekistan. 2 Tashkent University of Information Technologies, Tashkent, Uzbekistan.
1 Institute of Mathematics, National University of Uzbekistan, Tashkent, Uzbekistan. 2 Tashkent University of Information Technologies, Tashkent, Uzbekistan.
ABSTRACT
In the paper, the deviation of the spline estimator for the unknown probability density is approximated with the Gauss process. It is also found zeros for the infimum of variance of the derivation from the approximating process.
In the paper, the deviation of the spline estimator for the unknown probability density is approximated with the Gauss process. It is also found zeros for the infimum of variance of the derivation from the approximating process.
Cite this paper
Muminov, M. and Soatov, K. (2015) On the Approximation of Maximum Deviation Spline Estimation of the Probability Density Gaussian Process. Open Journal of Statistics, 5, 334-339. doi: 10.4236/ojs.2015.54034.
Muminov, M. and Soatov, K. (2015) On the Approximation of Maximum Deviation Spline Estimation of the Probability Density Gaussian Process. Open Journal of Statistics, 5, 334-339. doi: 10.4236/ojs.2015.54034.
References
[1] Muminov, M.S. and Soatov, Kh. (2011) A Note on Spline Estimator of Unknown Probability Density Function. Open Journal of Statistics, 157-160.
http://dx.doi.org/10.4236/ojs.2011.13019 [2] Khashimov, Sh.A. and Muminov, M.S. (1987) The Limit Distribution of the Maximal Deviation of a Spline Estimate of a Probability Density. Journal of Mathematical Sciences, 38, 2411-2421. [3] Stechkin, S.B. and Subbotin, Yu.N. (1976) Splines in Computational Mathematics. Nauka, Moscow, 272p. [4] Hardy G.G., Littlewood, J.E. and Polio, G. (1948) Inequalities. Moscow. IL, 456 p.
http://dx.doi.org/10.1007/BF01095085 [5] Berman, S.M. (1974) Sojourns and Extremes of Gaussian Processes. Annals of Probability, 2, 999-1026.
http://dx.doi.org/10.1214/aop/1176996495 [6] Rudzkis, R.O. (1985) Probability of the Large Outlier of Nonstationary Gaussian Process. Lit. Math. Sb., XXV, 143-154. [7] Azais, J.-M. and Wschebor, M. (2009) Level Sets and Extrema of Random Processes and Fields, Wiley, Hoboken, 290p. [8] Muminov, M.S. (2010) On Approximation of the Probability of the Large Outlier of Nonstationary Gauss Process. Siberian Mathematical Journal, 51, 144-161.
http://dx.doi.org/10.1007/s11202-010-0015-6
[1] Muminov, M.S. and Soatov, Kh. (2011) A Note on Spline Estimator of Unknown Probability Density Function. Open Journal of Statistics, 157-160.
http://dx.doi.org/10.4236/ojs.2011.13019 [2] Khashimov, Sh.A. and Muminov, M.S. (1987) The Limit Distribution of the Maximal Deviation of a Spline Estimate of a Probability Density. Journal of Mathematical Sciences, 38, 2411-2421. [3] Stechkin, S.B. and Subbotin, Yu.N. (1976) Splines in Computational Mathematics. Nauka, Moscow, 272p. [4] Hardy G.G., Littlewood, J.E. and Polio, G. (1948) Inequalities. Moscow. IL, 456 p.
http://dx.doi.org/10.1007/BF01095085 [5] Berman, S.M. (1974) Sojourns and Extremes of Gaussian Processes. Annals of Probability, 2, 999-1026.
http://dx.doi.org/10.1214/aop/1176996495 [6] Rudzkis, R.O. (1985) Probability of the Large Outlier of Nonstationary Gaussian Process. Lit. Math. Sb., XXV, 143-154. [7] Azais, J.-M. and Wschebor, M. (2009) Level Sets and Extrema of Random Processes and Fields, Wiley, Hoboken, 290p. [8] Muminov, M.S. (2010) On Approximation of the Probability of the Large Outlier of Nonstationary Gauss Process. Siberian Mathematical Journal, 51, 144-161.
http://dx.doi.org/10.1007/s11202-010-0015-6