zbMATH — the first resource for mathematics

Quasi-regression. (English) Zbl 0993.65018
Summary: Quasi-regression is introduced for approximation of functions on the unit cube in \(s\) dimensions. It is computationally efficient, compared to kriging, for problems requiring a large number of function evaluations. This paper describes how to implement quasi-regression and shows how to estimate the approximation error using the same data used to build the approximation. Four example functions are investigated numerically.

65C60 Computational problems in statistics (MSC2010)
62J05 Linear regression; mixed models
65D05 Numerical interpolation
Full Text: DOI
[1] Caflisch, R.E.; Morokoff, W.; Owen, A.B., Valuation of mortgage backed securities using Brownian bridges to reduce effective dimension, J. comput. finance, 1, 27-46, (1997)
[2] Chan, T.F.; Golub, G.H.; LeVeque, R.J., Algorithms for computing the sample variance: analysis and recommendations, Amer. statist., 37, 242-247, (1983) · Zbl 0521.65098
[3] Chui, C.K.; Diamond, H., A natural formulation of quasi-interpolation by multivariate splines, Proc. amer. math. soc., 99, 643-646, (1987) · Zbl 0656.41005
[4] Currin, C.; Mitchell, T.; Morris, M.; Ylvisaker, D., Bayesian prediction of deterministic functions, with applications to the design and analysis of computer experiments, J. amer. statist. assoc., 86, 953-963, (1991)
[5] Diaconis, P., Bayesian numerical analysis, Statistical decision theory and related topics IV, (1988), Springer-Verlag New York, p. 163-176
[6] Efromovich, S., On orthogonal series estimators for random design nonparametric regression, Computing science and statistics. Proceedings of the 24rd symposium on the interface, (1992), p. 375-379
[7] Hickernell, F.J.; Wozniakowski, H., Integration and approximation in arbitrary dimensions, Adv. comput. math., 12, 25-58, (2000) · Zbl 0939.41004
[8] Journel, A.G.; Huijbregts, C.J., Mining geostatistics, (1979), Academic Press New York
[9] Koehler, J.; Owen, A., Computer experiments, (), 261-308 · Zbl 0919.62089
[10] Morris, M.D.; Mitchell, T.J.; Ylvisaker, D., Bayesian design and analysis of computer experiments: use of derivatives in surface prediction, Technometrics, 35, 243-255, (1993) · Zbl 0785.62025
[11] Niederreiter, H., Random number generation and quasi-Monte Carlo methods, (1992), SIAM Philadelphia · Zbl 0761.65002
[12] Owen, A.B., Scrambled net variance for integrals of smooth functions, Ann. statist., 25, 1541-1562, (1997) · Zbl 0886.65018
[13] Owen, A.B., A central limit theorem for Latin hypercube sampling, J. roy. statist. soc. ser. B, 54, 541-551, (1992) · Zbl 0776.62041
[14] Owen, A.B., Assessing linearity in high dimensions, Ann. statist., 28, 1-19, (2000) · Zbl 1106.65306
[15] Paskov, S.; Traub, J., Faster valuation of financial derivatives, J. portfolio manage., 22, 113-120, (1995)
[16] Ritter, K., Average case analysis of numerical problems, (1995), University of Erlangen
[17] Sacks, J.; Welch, W.J.; Mitchell, T.J.; Wynn, H.P., Design and analysis of computer experiments (c/r: P423-435), Statistical sci., 4, 409-423, (1989)
[18] Sloan, I.H.; Wozniakowski, H., When are quasi-Monte Carlo algorithms efficient for high dimensional integration?, J. complexity, 14, 1-33, (1998) · Zbl 1032.65011
[19] Zhou, Y., Adaptive importance sampling for integration, (1998), Stanford University
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.