Spline Models for Observational Data (CBMS-NSF Regional Conference Series in Applied Mathematics)
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Описание:
As a student of Manny Parzen at Stanford Grace Wahba worked in the area of reproducing kernel Hilbert Space and cubic spline smoothing. Basically splines are special flexible functions that can be used to fit regression functions to date without assuming a linear or fixed degree polynomial. It is the pasting together of local polynomial functions (e.g. cubic functions) where the polynomial changes definitions at a set of points called the knots of the spline. To maintain a smoothness to the function the constraints are placed on the derivatives of the splines at the knors. This is intended to give them continuity and smoothness at the points of connection.In this monograph Grace Wahba describes how to construct and fit such splines to data. In so doing smoothness, goodness of fit and ability ot predict are the important attributes. Appropriate loss functions with smoothness constraints are used in the fit. The number and location of the knots can be fixed or it can ve determined based on the sample data. It is important to note that to determine whether the spline is a goof predictor techniques such as cross-validation are required.
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