Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
1.5. Notes and References
Aronszajn, N. (1950), Theory of reproducing kernels, Trans. Amer. Math. Soc. 68, 337–404.
Parzen, E. (1959), Statistical inference on time series by Hilbert space methods, I, in: Time series analysis papers, E. Parzen, ed., pp. 251–382, Holden-Day, San Francisco, 1967.
Vakhania, N. N., Tarieladze, V. I., and Chobanyan, S. A. (1987), Probability distributions on Banach spaces, Reidel, Dordrecht.
Wahba, G. (1990), Spline models for observational data, CBSM-NSF Regional Conf. Ser. Appl. Math. 59, SIAM, Philadelphia.
Atteia, M. (1992), Hilbertian kernels and spline functions, North-Holland, Amsterdam.
Loève, M. (1948), Fonctions aléatoires du second ordre, supplement to: Processus stochastiques et mouvement Brownien, Lévy, P., pp. 299–353, Gauthier-Villars, Paris.
Hájek, J. (1962), On linear statistical problems in stochastic processes, Czech. Math. J. 12, 404–440.
3.6. Notes and References
Atteia, M. (1992), Hilbertian kernels and spline functions, North-Holland, Amsterdam.
Kimeldorf, G. S., and Wahba, G. (1970a), A correspondence between Bayesian estimation on stochastic processes and smoothing by splines, Ann. Math. Statist. 41, 495–502.
Kimeldorf, G. S., and Wahba, G. (1970b), Spline functions and stochastic processes, Sankhyā Ser. A 32, 173–180.
Micchelli, C. A., and Rivlin, T. J. (1985), Lectures on optimal recovery, in: Numerical analysis Lancaster 1984, P. R. Turner, ed., pp. 21–93, Lect. Notes in Math. 1129, Springer-Verlag, Berlin.
Wasilkowski, G. W., and Woźniakowski, H. (1986), Average case optimal algorithms in Hilbert spaces, J. Approx. Theory 47, 17–25.
Wahba, G. (1990), Spline models for observational data, CBSM-NSF Regional Conf. Ser. Appl. Math. 59, SIAM, Philadelphia.
Mardia, K. V., Kent, J. T., Goodall, C. R., and Little, J. A. (1996), Kriging and splines with derivative information, Biometrika 83, 207–221.
Lee, D., and Wasilkowski, G. W. (1986), Approximation of linear functionals on a Banach space with a Gaussian measure, J. Complexity 2, 12–43.
Traub, J. F., Wasilkowski, G. W., and Woźniakowski, H. (1988), Information-based complexity, Academic Press, New York.
Kimeldorf, G. S., and Wahba, G. (1970a), A correspondence between Bayesian estimation on stochastic processes and smoothing by splines, Ann. Math. Statist. 41, 495–502.
Eubank, R. L. (1988), Spline smoothing and nonparametric regression, Dekker, New York.
Wahba, G. (1990), Spline models for observational data, CBSM-NSF Regional Conf. Ser. Appl. Math. 59, SIAM, Philadelphia.
Plaskota, L. (1996), Noisy information and computational complexity, Cambridge Univ. Press, Cambridge.
Zhensykbaev, A. A. (1983), Extremality of monosplines of minimal deficiency, Math. USSR Izvestiya 21, 461–482.
Micchelli, C. A., and Rivlin, T. J. (1985), Lectures on optimal recovery, in: Numerical analysis Lancaster 1984, P. R. Turner, ed., pp. 21–93, Lect. Notes in Math. 1129, Springer-Verlag, Berlin.
Traub, J. F., Wasilkowski, G. W., and Woźniakowski, H. (1988), Information-based complexity, Academic Press, New York.
Korneichuk, N. P. (1991), Exact constants in approximation theory, Cambridge Univ. Press, Cambridge.
Bojanov, B. D., Hakopian, H. A., and Sahakian, A. A. (1993), Spline functions and multivariate interpolations, Kluwer, Dordrecht.
Sacks, J., and Ylvisaker, D. (1966), Designs for regression with correlated errors, Ann. Math. Statist. 37, 68–89.
Sacks, J., and Ylvisaker, D. (1970b), Statistical design and integral approximation, in: Proc. 12th Bienn. Semin. Can. Math. Congr., R. Pyke, ed., pp. 115–136, Can. Math. Soc., Montreal.
Eubank, R. L., Smith, P. L., and Smith, P. W. (1981), Uniqueness and eventual uniqueness of optimal designs in some time series models, Ann. Statist. 9, 486–493.
Eubank, R. L., Smith, P. L., and Smith, P. W. (1982), A note on optimal and asymptotically optimal designs for certain time series models, Ann. Statist. 10, 1295–1301.
Müller-Gronbach, T. (1996), Optimal designs for approximating the path of a stochastic process, J. Statist. Planning Inf. 49, 371–385.
4.4. Notes and References
Christensen, R. (1987), Plane answers to complex questions, Springer-Verlag, New York.
Christensen, R. (1991), Linear models for multivariate, time series, and spatial data, Springer-Verlag, New York.
Cressie, N. A. C. (1993), Statistics for spatial data, Wiley, New York.
Christensen, R. (1991), Linear models for multivariate, time series, and spatial data, Springer-Verlag, New York.
Hjort, N. L., and Omre, H. (1994), Topics in spatial statistics, Scand. J. Statist. 21, 289–357.
Sacks, J., and Ylvisaker, D. (1970b), Statistical design and integral approximation, in: Proc. 12th Bienn. Semin. Can. Math. Congr., R. Pyke, ed., pp. 115–136, Can. Math. Soc., Montreal.
Cambanis, S. (1985), Sampling designs for time series, in: Time series in the time domain, Handbook of Statistics, Vol. 5, E. J. Hannan, P. R. Krishnaiah, and M. M. Rao, eds., pp. 337–362, North-Holland, Amsterdam.
Näther, W. (1985), Effective observation of random fields, Teubner Verlagsgesellschaft, Leipzig.
Pilz, J. (1983), Bayesian estimation and experimental design in linear regression models, Teubner Verlagsgesellschaft, Leipzig.
O'Hagan, A. (1992), Some Bayesian numerical analysis, in: Bayesian statistics 4, J. M. Bernardo, J. O. Berger, A. P. Dawid, and A. F. M. Smith, eds., pp. 345–363, Oxford Univ. Press, Oxford.
Cambanis, S., and Masry, E. (1983), Sampling designs for the detection of signals in noise, IEEE Trans. Inform. Theory IT-29, 83–104.
Cambanis, S. (1985), Sampling designs for time series, in: Time series in the time domain, Handbook of Statistics, Vol. 5, E. J. Hannan, P. R. Krishnaiah, and M. M. Rao, eds., pp. 337–362, North-Holland, Amsterdam.
Fedorov, V. V. (1972), Theory of optimal experiments, Academic Press, New York.
Pukelsheim, F. (1993), Optimal design of experiments, Wiley, New York.
Editor information
Rights and permissions
Copyright information
© 2000 Springer-Verlag
About this chapter
Cite this chapter
Ritter, K. (2000). Second-order results for linear problems. In: Ritter, K. (eds) Average-Case Analysis of Numerical Problems. Lecture Notes in Mathematics, vol 1733. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0103937
Download citation
DOI: https://doi.org/10.1007/BFb0103937
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-67449-8
Online ISBN: 978-3-540-45592-9
eBook Packages: Springer Book Archive