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Polynomial Splines and Data Approximation
"... The problem of data approximation is of great interest. There are a lot of approaches to solve this problem. One of them is a polynomial spline approximation. In this paper we propose a new algorithm for polynomial spline approximation based on nonsmooth optimization techniques. Numerical experiment ..."
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The problem of data approximation is of great interest. There are a lot of approaches to solve this problem. One of them is a polynomial spline approximation. In this paper we propose a new algorithm for polynomial spline approximation based on nonsmooth optimization techniques. Numerical
Weighted Integrals of Polynomial Splines
"... Summary. The construction of weighted splines by knot insertion techniques such as de Boor and Oslo type algorithms leads immediately to the problem of evaluating integrals of polynomial splines with respect to the positive measure possessing piecewise constant density. It is for such purposes that ..."
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Summary. The construction of weighted splines by knot insertion techniques such as de Boor and Oslo type algorithms leads immediately to the problem of evaluating integrals of polynomial splines with respect to the positive measure possessing piecewise constant density. It is for such purposes
Polynomial splines as examples of Chebyshevian splines
"... The results we present here concern geometrically continuous polynomial splines, in the sense that the left/right derivatives at the knots are linked by connection matrices. A classical sufficient condition for spaces of such splines to be suitable for either Approximation or Geometric Design is the ..."
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Cited by 2 (2 self)
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The results we present here concern geometrically continuous polynomial splines, in the sense that the left/right derivatives at the knots are linked by connection matrices. A classical sufficient condition for spaces of such splines to be suitable for either Approximation or Geometric Design
Polynomial Splines and Their Tensor Products in Extended Linear Modeling
 Ann. Statist
, 1997
"... ANOVA type models are considered for a regression function or for the logarithm of a probability function, conditional probability function, density function, conditional density function, hazard function, conditional hazard function, or spectral density function. Polynomial splines are used to m ..."
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Cited by 217 (16 self)
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ANOVA type models are considered for a regression function or for the logarithm of a probability function, conditional probability function, density function, conditional density function, hazard function, conditional hazard function, or spectral density function. Polynomial splines are used
Polynomial Spline Signal Processing Algorithms
 Proc. ICASSP III
, 1992
"... We describe new digital filtering algorithms for the processing and representation of signals using polynomial splines. We fast consider the classical polynomial spline interpolation problem and show that it can be solved efficiently by recursire digital filtering. This result also yields a simple p ..."
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Cited by 2 (0 self)
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We describe new digital filtering algorithms for the processing and representation of signals using polynomial splines. We fast consider the classical polynomial spline interpolation problem and show that it can be solved efficiently by recursire digital filtering. This result also yields a simple
Additive coefficient modelling via polynomial spline
 Statistica Sinica
, 2006
"... Abstract: A flexible nonparametric regression model is considered in which the response depends linearly on some covariates, with regression coefficients as additive functions of other covariates. Polynomial spline estimators are proposed for the unknown coefficient functions, with optimal univari ..."
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Cited by 17 (7 self)
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Abstract: A flexible nonparametric regression model is considered in which the response depends linearly on some covariates, with regression coefficients as additive functions of other covariates. Polynomial spline estimators are proposed for the unknown coefficient functions, with optimal
On Stable Local Bases for Bivariate Polynomial Spline Spaces
 Constr. Approx
, 1999
"... . Stable locally supported bases are constructed for the spaces S r d (4) of polynomial splines of degree d 3r + 2 and smoothness r defined on triangulations 4, as well as for various superspline subspaces. In addition, we show that for r 1, it is impossible to construct bases which are simulta ..."
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Cited by 16 (10 self)
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. Stable locally supported bases are constructed for the spaces S r d (4) of polynomial splines of degree d 3r + 2 and smoothness r defined on triangulations 4, as well as for various superspline subspaces. In addition, we show that for r 1, it is impossible to construct bases which
Free knot polynomial spline confidence intervals
 Journal of the Royal Statistical Society Series B
, 2003
"... We construct approximate confidence intervals for a nonparametric regression function. The construction uses polynomial splines with free knot locations. The number of knots is determined by the GCV criteria. The estimates of knot locations and coefficients are obtained through a nonlinear least sq ..."
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Cited by 1 (1 self)
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We construct approximate confidence intervals for a nonparametric regression function. The construction uses polynomial splines with free knot locations. The number of knots is determined by the GCV criteria. The estimates of knot locations and coefficients are obtained through a nonlinear least
Polynomial spline confidence bands for regression curves
, 2007
"... Abstract: Asymptotically exact and conservative confidence bands are obtained for a nonparametric regression function, using piecewise constant and piecewise linear spline estimation, respectively. Compared to the pointwise confidence interval of Huang (2003), the confidence bands are inflated by a ..."
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Cited by 23 (8 self)
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factor proportional to {log (n)} 1/2, with the same width order as the NadarayaWatson bands of HÃ¤rdle (1989), and the local polynomial bands of Xia (1998) and Claeskens and Van Keilegom (2003). Simulation experiments corroborate the asymptotic theory. The linear spline band has been used to identify
Error Bounds for Minimal Energy Bivariate Polynomial Splines
 Numer. Math
, 2001
"... We derive error bounds for bivariate spline interpolants which are calculated by minimizing certain natural energy norms. x1. ..."
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Cited by 14 (13 self)
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We derive error bounds for bivariate spline interpolants which are calculated by minimizing certain natural energy norms. x1.
Results 1  10
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38,562