Results 1  10
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725
Ideal spatial adaptation by wavelet shrinkage
 Biometrika
, 1994
"... With ideal spatial adaptation, an oracle furnishes information about how best to adapt a spatially variable estimator, whether piecewise constant, piecewise polynomial, variable knot spline, or variable bandwidth kernel, to the unknown function. Estimation with the aid of an oracle o ers dramatic ad ..."
Abstract

Cited by 1269 (5 self)
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With ideal spatial adaptation, an oracle furnishes information about how best to adapt a spatially variable estimator, whether piecewise constant, piecewise polynomial, variable knot spline, or variable bandwidth kernel, to the unknown function. Estimation with the aid of an oracle o ers dramatic
MULTIVARIATE ARRIVAL RATE ESTIMATION USING SEMIDEFINITE PROGRAMMING
"... An efficient method for the smooth estimation of the arrival rate of nonhomogeneous, multidimensional Poisson processes from inexact arrivals is presented. The method provides a piecewise polynomial spline estimator. It is easily parallelized, and it exploits the sparsity of the neighborhood struc ..."
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An efficient method for the smooth estimation of the arrival rate of nonhomogeneous, multidimensional Poisson processes from inexact arrivals is presented. The method provides a piecewise polynomial spline estimator. It is easily parallelized, and it exploits the sparsity of the neighborhood
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 ..."
Abstract

Cited by 221 (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
Sampling signals with finite rate of innovation
 IEEE Transactions on Signal Processing
, 2002
"... Abstract—Consider classes of signals that have a finite number of degrees of freedom per unit of time and call this number the rate of innovation. Examples of signals with a finite rate of innovation include streams of Diracs (e.g., the Poisson process), nonuniform splines, and piecewise polynomials ..."
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Cited by 350 (67 self)
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“bandlimited and sinc kernel ” case. In particular, we show how to sample and reconstruct periodic and finitelength streams of Diracs, nonuniform splines, and piecewise polynomials using sinc and Gaussian kernels. For infinitelength signals with finite local rate of innovation, we show local sampling
Piecewisepolynomial regression trees
 Statistica Sinica
, 1994
"... A nonparametric function 1 estimation method called SUPPORT (“Smoothed and Unsmoothed PiecewisePolynomial Regression Trees”) is described. The estimate is typically made up of several pieces, each piece being obtained by fitting a polynomial regression to the observations in a subregion of the data ..."
Abstract

Cited by 51 (8 self)
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A nonparametric function 1 estimation method called SUPPORT (“Smoothed and Unsmoothed PiecewisePolynomial Regression Trees”) is described. The estimate is typically made up of several pieces, each piece being obtained by fitting a polynomial regression to the observations in a subregion
Splines and Piecewise Interpolation
"... • Understanding that splines minimize oscillations by fitting lowerorder polynomials to data in a piecewise fashion • Knowing how to develop code to perform table lookup • Recognizing why cubic polynomials are preferable to quadratic and higherorder splines • Understanding the conditions that unde ..."
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• Understanding that splines minimize oscillations by fitting lowerorder polynomials to data in a piecewise fashion • Knowing how to develop code to perform table lookup • Recognizing why cubic polynomials are preferable to quadratic and higherorder splines • Understanding the conditions
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 ..."
Abstract

Cited by 23 (8 self)
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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
Piecewise Polynomial Functions . . .
, 2006
"... Splines are piecewise polynomial functions of a given order of smoothness r on a triangulated region ∆ (or polyhedrally subdivided region �) of R d. The set of splines of degree at most k forms a vector space C r k (∆). Moreover, a nice way to study C r k (∆) is to embed ∆ in Rd+1, and form the co ..."
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Splines are piecewise polynomial functions of a given order of smoothness r on a triangulated region ∆ (or polyhedrally subdivided region �) of R d. The set of splines of degree at most k forms a vector space C r k (∆). Moreover, a nice way to study C r k (∆) is to embed ∆ in Rd+1, and form
Piecewise polynomials on polyhedral complexes
 ADVANCES IN APPLIED MATHEMATICS
, 2009
"... For a ddimensional polyhedral complex P, the dimension of the space of piecewise polynomial functions (splines) on P of smoothness r and degree k is given, for k sufficiently large, by a polynomial f(P,r,k) of degree d. When d = 2 and P is simplicial, in [1] Alfeld and Schumaker give a formula fo ..."
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Cited by 7 (3 self)
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For a ddimensional polyhedral complex P, the dimension of the space of piecewise polynomial functions (splines) on P of smoothness r and degree k is given, for k sufficiently large, by a polynomial f(P,r,k) of degree d. When d = 2 and P is simplicial, in [1] Alfeld and Schumaker give a formula
PIECEWISE QUADRATIC TRIGONOMETRIC POLYNOMIAL CURVES
"... Abstract. Analogous to the quadratic Bspline curve, a piecewise quadratic trigonometric polynomial curve is presented in this paper. The quadratic trigonometric polynomial curve has C 2 continuity, while the quadratic Bspline curve has C 1 continuity. The quadratic trigonometric polynomial curve i ..."
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Cited by 9 (2 self)
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Abstract. Analogous to the quadratic Bspline curve, a piecewise quadratic trigonometric polynomial curve is presented in this paper. The quadratic trigonometric polynomial curve has C 2 continuity, while the quadratic Bspline curve has C 1 continuity. The quadratic trigonometric polynomial curve
Results 1  10
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725