Geodesic
Comparison of approaches to optimization of functional statistical modeling algorithms in the metric of the space~$\mathbf C$
Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 18 (2015) no. 2, pp. 219-234.

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Functional algorithms of the statistical modeling are designed to construct an approximation of the problem solution as function on a required domain. The approaches to construction of the upper error bound in the metrics of the space $\mathbf C$ with allowance for the degree of dependence of the estimates were devised for functional algorithms with different types of stochastic estimates in the nodes. Furthermore, there exists a universal approach applicable at any degree of dependence. The constructed upper error bound of the functional algorithm is used for choosing an optimal value of parameters, such as the number of grid nodes and the sample size. Optimality of the chosen parameters directly depends on the accuracy of the used upper error bound. The primary intent of the present paper is a comparison of universal approaches and those with allowance for the degree of dependence of the estimates. 
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E. V. Shkarupa. Comparison of approaches to optimization of functional statistical modeling algorithms in the metric of the space~$\mathbf C$. Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 18 (2015) no. 2, pp. 219-234. http://geodesic.mathdoc.fr/item/SJVM_2015_18_2_a8/

[1] Mikhailov G. A., Minimization of Computational Costs of Non-analogue Monte Carlo Methods, Series of Soviet East European Mathematics, 5, World Scientific, Singapore, 1991 | MR

[2] Mikhajlov G. A., Plotnikov M. Yu., “Otsenka “po probegu” dlya resheniya linejnogo i nelinejnogo uravneniya perenosa izlucheniya v tselom”, Dokl. AN SSSR, 337:2 (1994), 162–164 | MR

[3] Plotnikov M. Yu., “Using the weighted Monte Carlo method for solving nonlinear integral equations”, Russian J. Numer. Anal. Math. Modelling, 9:2 (1994), 121–147 | DOI | MR

[4] Vojtishek A. V., Prigarin S. M., “O funktsional'noj skhodimosti otsenok i modelej v metode Monte-Karlo”, Zhurn. vychisl. matem. i mat. fiziki, 32:10 (1992), 1641–1651 | MR | Zbl

[5] Voytishek A. V., “On the errors of discretely stochastic procedures in estimating globally the solution of an integral equation of the second kind”, Russian J. Numer. Anal. Math. Modelling, 11:1 (1996), 71–92 | MR | Zbl

[6] Shkarupa E. V., Voytishek A. V., “Optimization of discretely stochastic procedures for globally estimating the solution of an integral equation of the second kind”, Russian J. Numer. Anal. Math. Modelling, 12:6 (1997), 525–546 | MR | Zbl

[7] Shkarupa E. V., “Otsenka pogreshnosti i optimizatsiya metoda poligona chastot dlya global'nogo resheniya integral'nogo uravneniya vtorogo roda”, Zhurn. vychisl. matem. i mat. fiziki, 38:4 (1998), 612–627 | MR | Zbl

[8] Shkarupa E. V., “Otsenka pogreshnosti i optimizatsiya funktsional'nykh algoritmov bluzhdaniya po reshetke resheniya zadachi Dirikhle dlya uravneniya Gel'mgol'tsa”, Sib. mat. zhurnal, 44:5 (2003), 1163–1182 | MR | Zbl

[9] Shkarupa E. V., “Funktsional'nyj algoritm bluzhdaniya po reshetke dlya bigarmonicheskogo uravneniya. Otsenka pogreshnosti i optimizatsiya”, Sib. zhurn. vychisl. matematiki (Novosibirsk), 8:2 (2005), 163–176 | Zbl

[10] Sabelfeld K. K., Shkarupa E. V., “Functional random walk on spheres algorithm for biharmonic equation: optimization and error estimation”, Monte Carlo Methods and Applications, 9:1 (2003), 51–65 | DOI | MR | Zbl

[11] Vojtishek A. V., “O dopustimom klasse vospolnenij dlya diskretno-stokhasticheskikh protsedur global'noj otsenki funktsij”, Sib. zhurn. vychisl. matematiki (Novosibirsk), 1:2 (1998), 119–134 | MR | Zbl

[12] Miloserdov V. V., Diskretno-stokhasticheskie chislennye algoritmy so splajn-vospolneniyami, Diss. $\dots$ kand. fiz.-mat. nauk: 01.01.07, Novosibirsk, 2006

[13] Miloserdov V. V., “Uslovnaya optimizatsiya diskretno-stokhasticheskikh chislennykh protsedur v sluchae primeneniya kubicheskikh splajnov”, Sib. zhurn. vychisl. matematiki (Novosibirsk), 9:2 (2006), 147–163 | Zbl

[14] Plotnikov M. Yu., Shkarupa E. V., “Estimation of the statistical error and the choice of parameters in the method of test particles”, Russian J. Numer. Anal. Math. Modelling, 27:2 (2012), 155–174 | DOI | MR

[15] Plotnikov M. Yu., Shkarupa E. V., “Selection of sampling numerical parameters for the DSMC method”, Computers Fluids, 58 (2012), 102–111 | DOI | MR

[16] Frolov A. S., Chentsov N. N., “O vychislenii metodom Monte-Karlo opredelennykh integralov, zavisyashchikh ot parametra”, Zhurn. vychisl. matem. i mat. fiziki, 2:4 (1962), 714–717 | MR | Zbl

[17] Prigarin S. M., “Nekotorye prilozheniya teoremy Dzhejna-Markusa v statisticheskom modelirovanii”, Teoriya i prilozheniya statisticheskogo modelirovaniya, VTs SO AN, Novosibirsk, 1990, 22–28

[18] Prigarin S. M., “O skhodimosti i optimizatsii funktsional'nykh otsenok metoda Monte-Karlo v prostranstvakh Soboleva”, Sib. zhurn. vychisl. matematiki (Novosibirsk), 2:1 (1999), 57–67 | Zbl

[19] Litbetter M., Rotsen Kh., Lindgren G., Ekstremumy sluchajnykh posledovatel'nostej i protsessov, Mir, M., 1989 | MR

[20] Sabel'fel'd K. K., Metody Monte-Karlo v kraevykh zadachakh, Nauka, M., 1989 | MR

[21] Mikhajlov G. A., Lukinov V. L., “Reshenie mnogomernogo raznostnogo bigarmonicheskogo uravneniya metodom Monte-Karlo”, Sib. mat. zhurnal, 42:5 (2001), 1125–1135 | MR | Zbl

[22] Timoshenko S. P., Voinovsky-Krieger S., Theory of Plates and Shells, McGraw-Hill Book Company, New York, 1959

[23] Mikhajlov G. A., Cheshkova A. F., “Reshenie raznostnoj zadachi Dirikhle dlya mnogomernogo uravneniya Gel'mgol'tsa metodom Monte-Karlo”, Zhurn. vychisl. matem. i mat. fiziki, 38:1 (1996), 99–106 | MR | Zbl