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SPLINE ESTIMATION OF SINGLEINDEX MODELS
"... Abstract: For the past two decades, the singleindex model, a special case of projection pursuit regression, has proven to be an efficient way of coping with the highdimensional problem in nonparametric regression. In this paper, based on a weakly dependent sample, we investigate a robust singlein ..."
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Cited by 3 (1 self)
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index model, where the singleindex is identified by the best approximation to the multivariate prediction function of the response variable, regardless of whether the prediction function is a genuine singleindex function. A polynomial spline estimator is proposed for the singleindex coefficients
POLYNOMIAL AND SPLINE ESTIMATORS OF THE DISTRIBUTION FUNCTION WITH PRESCRIBED ACCURACY
"... Abstract. Dvoretzky–Kiefer–Wolfowitz type inequalities for some polynomial and spline estimators of distribution functions are constructed. Moreover, hints on the corresponding algorithms are given as well. 1. Introduction. The ..."
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Abstract. Dvoretzky–Kiefer–Wolfowitz type inequalities for some polynomial and spline estimators of distribution functions are constructed. Moreover, hints on the corresponding algorithms are given as well. 1. Introduction. The
A jumpdetecting procedure based on spline estimation
 J. Nonparametric Statist
, 2011
"... In a randomdesign nonparametric regression model, procedures for detecting jumps in the regression function via constant and linear spline estimation method are proposed based on the maximal differences of the spline estimators among neighbouring knots, the limiting distributions of which are obtai ..."
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Cited by 4 (3 self)
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In a randomdesign nonparametric regression model, procedures for detecting jumps in the regression function via constant and linear spline estimation method are proposed based on the maximal differences of the spline estimators among neighbouring knots, the limiting distributions of which
Smoothing spline estimation of variance functions
 Journal of Computational and Graphical Statistics
, 2006
"... This article considers spline smoothing of variance functions. We focus on selection of smoothing parameters and develop three direct datadriven methods: unbiased risk (UBR), generalized approximate cross validation (GACV) and generalized maximum likelihood (GML). In addition to guaranteed converge ..."
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Cited by 3 (0 self)
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This article considers spline smoothing of variance functions. We focus on selection of smoothing parameters and develop three direct datadriven methods: unbiased risk (UBR), generalized approximate cross validation (GACV) and generalized maximum likelihood (GML). In addition to guaranteed
LOCAL AND GLOBAL ASYMPTOTIC INFERENCES FOR THE SMOOTHING SPLINE ESTIMATE
, 2012
"... This article presents the first comprehensive studies on the local and global inferences for the smoothing spline estimate in a unified asymptotic framework. The novel functional Bahadur representation is developed as the theoretical foundation of this article, and is also of independent interest. B ..."
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Cited by 3 (3 self)
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This article presents the first comprehensive studies on the local and global inferences for the smoothing spline estimate in a unified asymptotic framework. The novel functional Bahadur representation is developed as the theoretical foundation of this article, and is also of independent interest
Smoothing Splines Estimators in Functional Linear Regression with ErrorsinVariables
, 2006
"... This work deals with a generalization of the Total Least Squares method in the context of the functional linear model. We first propose a smoothing splines estimator of the functional coefficient of the model without noise in the covariates and we obtain an asymptotic result for this estimator. Then ..."
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Cited by 69 (3 self)
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This work deals with a generalization of the Total Least Squares method in the context of the functional linear model. We first propose a smoothing splines estimator of the functional coefficient of the model without noise in the covariates and we obtain an asymptotic result for this estimator
On the Approximation of Maximum Deviation Spline Estimation of the Probability Density Gaussian Process
"... In the paper, the deviation of the spline estimator for the unknown probability density is approximated with the Gauss process. It is also found zeros for the infimum of variance of the derivation from the approximating process. ..."
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In the paper, the deviation of the spline estimator for the unknown probability density is approximated with the Gauss process. It is also found zeros for the infimum of variance of the derivation from the approximating process.
Spline Estimators for the Functional Linear Model: Consistency, Application and Splus Implementation
"... The functional linear model is a regression model in which the explanatory variable is a continuous time process observed in a closed interval of R: Hence, the "vector of parameters" to be estimated belongs to the infinite dimensional space of Rvalued operators defined on a space of fu ..."
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Cited by 107 (9 self)
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of functions. We propose here two estimators of the functional parameter of such a model by means of spline functions. These estimators take into account the dimensionality problem and we prove their consistency. The first one relies on a truncated functional principal components analysis and the second
A Note on Spline Estimator of Unknown Probability Density Function
 Open M. S. Muminov, K. S. Soatov Journal of Statistics
, 2011
"... In the present paper as estimation of unknown pdf derivative of a spline function is suggested. It is studied its some statistical properties which are used to approximate maximal deviation of the spline estimation from pdf with maximum of nonstationary gaussian process. ..."
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Cited by 1 (1 self)
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In the present paper as estimation of unknown pdf derivative of a spline function is suggested. It is studied its some statistical properties which are used to approximate maximal deviation of the spline estimation from pdf with maximum of nonstationary gaussian process.
Flexible smoothing with Bsplines and penalties
 STATISTICAL SCIENCE
, 1996
"... Bsplines are attractive for nonparametric modelling, but choosing the optimal number and positions of knots is a complex task. Equidistant knots can be used, but their small and discrete number allows only limited control over smoothness and fit. We propose to use a relatively large number of knots ..."
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Cited by 396 (6 self)
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Bsplines are attractive for nonparametric modelling, but choosing the optimal number and positions of knots is a complex task. Equidistant knots can be used, but their small and discrete number allows only limited control over smoothness and fit. We propose to use a relatively large number
Results 1  10
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83,514