Asymptotics and representation of cubic splines
نویسندگان
چکیده
منابع مشابه
Constrained Interpolation via Cubic Hermite Splines
Introduction In industrial designing and manufacturing, it is often required to generate a smooth function approximating a given set of data which preserves certain shape properties of the data such as positivity, monotonicity, or convexity, that is, a smooth shape preserving approximation. It is assumed here that the data is sufficiently accurate to warrant interpolation, rather than least ...
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The asymptotic behavior of penalised spline estimators is studied in the univariate case. B-splines are used and a penalty is placed on mth order differences of the coefficients. The number of knots is assumed to converge to ∞ as the sample size increases. We show that penalised splines behave similarly to Nadaraya-Watson kernel estimators with an “equivalent” kernels depending upon m. The equi...
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The asymptotic behaviour of penalized spline estimators is studied in the univariate case. We use B -splines and a penalty is placed on mth-order differences of the coefficients. The number of knots is assumed to converge to infinity as the sample size increases. We show that penalized splines behave similarly to Nadaraya-Watson kernel estimators with ‘equivalent’ kernels depending upon m. The ...
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ژورنال
عنوان ژورنال: Journal of Approximation Theory
سال: 1976
ISSN: 0021-9045
DOI: 10.1016/0021-9045(76)90077-0