TY - BOOK ID - 1323615 TI - Spline models for observational data PY - 1990 VL - 59 SN - 0898712440 9780898712445 PB - Philadelphia (Pa.): Society for industrial and applied mathematics DB - UniCat KW - Numerical approximation theory KW - Spline theor KW - Mathematical statistics KW - Statistique mathématique KW - Spline theory KW - 519.6 KW - 681.3*G12 KW - Spline functions KW - Approximation theory KW - Interpolation KW - Computational mathematics. Numerical analysis. Computer programming KW - Approximation: chebyshev; elementary function; least squares; linear approximation; minimax approximation and algorithms; nonlinear and rational approximation; spline and piecewise polynomial approximation (Numerical analysis) KW - Mathematical statistics. KW - Spline theory. KW - 681.3*G12 Approximation: chebyshev; elementary function; least squares; linear approximation; minimax approximation and algorithms; nonlinear and rational approximation; spline and piecewise polynomial approximation (Numerical analysis) KW - 519.6 Computational mathematics. Numerical analysis. Computer programming KW - Statistique mathématique KW - Mathematics KW - Statistical inference KW - Statistics, Mathematical KW - Statistics KW - Probabilities KW - Sampling (Statistics) KW - Statistical methods UR - https://www.unicat.be/uniCat?func=search&query=sysid:1323615 AB - This book serves well as an introduction into the more theoretical aspects of the use of spline models. It develops a theory and practice for the estimation of functions from noisy data on functionals. The simplest example is the estimation of a smooth curve, given noisy observations on a finite number of its values. Convergence properties, data based smoothing parameter selection, confidence intervals, and numerical methods are established which are appropriate to a number of problems within this framework. Methods for including side conditions and other prior information in solving ill posed inverse problems are provided. Data which involves samples of random variables with Gaussian, Poisson, binomial, and other distributions are treated in a unified optimization context. Experimental design questions, i.e., which functionals should be observed, are studied in a general context. Extensions to distributed parameter system identification problems are made by considering implicitly defined functionals. ER -