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Title:

Theory for penalised spline regression

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Penalised spline regression is a popular new approach to smoothing, but its theoretical properties are not yet well understood. In this paper, mean squared error expressions and consistency results are derived by using a white-noise model representation for the estimator. The effect of the penalty on the bias and variance of the estimator is dis...

Penalised spline regression is a popular new approach to smoothing, but its theoretical properties are not yet well understood. In this paper, mean squared error expressions and consistency results are derived by using a white-noise model representation for the estimator. The effect of the penalty on the bias and variance of the estimator is discussed, both for general splines and for the case of polynomial splines. The penalised spline regression estimator is shown to achieve the optimal nonparametric convergence rateestablished by Stone (1982). Copyright 2005, Oxford University Press. Minimize

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Title:

On asymptotic normality and variance estimation for nondifferentiable survey estimators

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Survey estimators of population quantities such as distribution functions and quantiles contain nondifferentiable functions of estimated quantities. The theoretical properties of such estimators are substantially more complicated to derive than those of differentiable estimators. In this article, we provide a unified framework for obtaining the ...

Survey estimators of population quantities such as distribution functions and quantiles contain nondifferentiable functions of estimated quantities. The theoretical properties of such estimators are substantially more complicated to derive than those of differentiable estimators. In this article, we provide a unified framework for obtaining the asymptotic design-based properties of two common types of nondifferentiable estimators. Estimators of the first type have an explicit expression, while those of the second are defined only as the solution to estimating equations. We propose both analytical and replication-based design-consistent variance estimators for both cases, based on kernel regression. The practical behaviour of the variance estimators is demonstrated in a simulation experiment. Copyright 2011, Oxford University Press. Minimize

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article

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Title:

Model-assisted estimation for complex surveys using penalised splines

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Estimation of finite population totals in the presence of auxiliary information is considered. A class of estimators based on penalised spline regression is proposed. These estimators are weighted linear combinations of sample observations, with weights calibrated to known control totals. They allow straightforward extensions to multiple auxilia...

Estimation of finite population totals in the presence of auxiliary information is considered. A class of estimators based on penalised spline regression is proposed. These estimators are weighted linear combinations of sample observations, with weights calibrated to known control totals. They allow straightforward extensions to multiple auxiliary variables and to complex designs. Under standard design conditions, the estimators are design consistent and asymptotically normal, and they admit consistent variance estimation using familiar design-based methods. Data-driven penalty selection is considered in the context of unequal probability sampling designs. Simulation experiments show that the estimators are more efficient than parametric regression estimators when the parametric model is incorrectly specified, while being approximately as efficient when the parametric specification is correct. An example using Forest Health Monitoring survey data from the U.S. Forest Service demonstrates the applicability of the methodology in the context of a two-phase survey with multiple auxiliary variables. Copyright 2005, Oxford University Press. Minimize

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Title:

Penalized Splines

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Estimation of finite population totals in the presence of auxiliary information is con-sidered. A class of estimators based on penalized spline regression is proposed. These estimators are weighted linear combinations of sample observations, with weights cali-brated to known control totals. Further, they allow straightforward extensions to mul-t...

Estimation of finite population totals in the presence of auxiliary information is con-sidered. A class of estimators based on penalized spline regression is proposed. These estimators are weighted linear combinations of sample observations, with weights cali-brated to known control totals. Further, they allow straightforward extensions to mul-tiple auxiliary variables and to complex designs. Under standard design conditions, the estimators are design consistent and asymptotically normal, and they admit consistent variance estimation using familiar design-based methods. Data-driven penalty selection Minimize

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The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2008-08-15

Source:

http://www.econ.kuleuven.be/public/ndbaf45/papers/pspline_model-assisted.pdf

http://www.econ.kuleuven.be/public/ndbaf45/papers/pspline_model-assisted.pdf Minimize

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text

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en

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Metadata may be used without restrictions as long as the oai identifier remains attached to it.

Metadata may be used without restrictions as long as the oai identifier remains attached to it. Minimize

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Title:

Model Averaging in Survey Estimation

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Model averaging is a widely used method as it ac-counts for uncertainties in model selection. However, its applications in survey estimation are much to be explored. We investigate a model-averaging (MA) regression estimator for the population total, for the case of a nonparametric regression model. Different ways to obtain this estimator are ex...

Model averaging is a widely used method as it ac-counts for uncertainties in model selection. However, its applications in survey estimation are much to be explored. We investigate a model-averaging (MA) regression estimator for the population total, for the case of a nonparametric regression model. Different ways to obtain this estimator are explored through simulation studies. KEY WORDS: Local polynomial regression, cross-validation, regression estimation. Minimize

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The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2015-01-13

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http://www.amstat.org/sections/srms/proceedings/y2006/Files/JSM2006-000651.pdf

http://www.amstat.org/sections/srms/proceedings/y2006/Files/JSM2006-000651.pdf Minimize

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text

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en

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−1∑

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Metadata may be used without restrictions as long as the oai identifier remains attached to it.

Metadata may be used without restrictions as long as the oai identifier remains attached to it. Minimize

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Title:

Local Polynomial Regression Estimators in Survey Sampling

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This paper describes theoretical properties of a new type of model-assisted nonparametric regression estimator for the finite population total, based on local poly- LOCAL POLYNOMIAL REGRESSION ESTIMATORS 3 nomial smoothing. Local polynomial regression is a generalization of kernel regression. Cleveland (1979) and Cleveland and Devlin (1988) show...

This paper describes theoretical properties of a new type of model-assisted nonparametric regression estimator for the finite population total, based on local poly- LOCAL POLYNOMIAL REGRESSION ESTIMATORS 3 nomial smoothing. Local polynomial regression is a generalization of kernel regression. Cleveland (1979) and Cleveland and Devlin (1988) showed that these techniques are applicable to a wide range of problems. Theoretical work by Fan (1992, 1993) and Ruppert and Wand (1994) showed that it has many desirable theoretical properties, including adaptation to the design of the covariate(s), consistency and asymptotic unbiasedness. Wand and Jones (1995) provide a clear explanation of the asymptotic theory for kernel regression and local polynomial regression. The monograph by Fan and Gijbels (1996) explores a wide range of application areas of local polynomial regression techniques. However, the application of these techniques to model-assisted survey sampling is new. In Section 1.2 we introduce the local polynomial regression estimator and in Section 1.3 we state assumptions used in the theoretical derivations of Section 2, in which our main results are described. Section 2.1 shows that the estimator is a weighted linear combination of study variables in which the weights are calibrated to known control totals. Section 2.2 contains a proof that the estimator is asymptotically design unbiased and design consistent, and Section 2.3 provides an approximation to its mean squared error and a consistent estimator of the mean squared error. Section 2.4 provides su#cient conditions for asymptotic normality of the local polynomial regression estimator and establishes a central limit theorem in the case of simple random sampling. We show that the estimator is robust in the sense o. Minimize

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The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2009-04-14

Source:

http://www.public.iastate.edu/~jopsomer/papers/LPRegest_submit.pdf

http://www.public.iastate.edu/~jopsomer/papers/LPRegest_submit.pdf Minimize

Document Type:

text

Language:

en

DDC:

310 Collections of general statistics *(computed)* ; 519 Probabilities & applied mathematics *(computed)*

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Metadata may be used without restrictions as long as the oai identifier remains attached to it.

Metadata may be used without restrictions as long as the oai identifier remains attached to it. Minimize

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Title:

Local likelihood estimation in Generalized Additive Models

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Generalized additive models are a popular class of multivariate nonparametric regression models, due in large part to the ease of use of the local scoring estimation algorithm. However, the theoretical properties of the local scoring estimator are poorly understood. In this article, we propose a local likelihood estimator for generalized additiv...

Generalized additive models are a popular class of multivariate nonparametric regression models, due in large part to the ease of use of the local scoring estimation algorithm. However, the theoretical properties of the local scoring estimator are poorly understood. In this article, we propose a local likelihood estimator for generalized additive models that is closely related to the local scoring estimator tted by local polynomial regression. We derive the statistical properties of the estimator and show that it achieves the same asymptotic convergence rate as a one-dimensional local polynomial regression estimator. We also propose a wild bootstrap estimator for calculating pointwise condence intervals for the additive component functions. The practical behavior of the proposed estimator is illustrated through simulation experiments and an example. Keywords: backtting, bootstrapping, generalized additive models, local likelihood, local polynomial regression, local scoring, wild bo. Minimize

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The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2009-04-14

Source:

http://www.public.iastate.edu/~jopsomer/papers/Loclik_GAM.ps

http://www.public.iastate.edu/~jopsomer/papers/Loclik_GAM.ps Minimize

Document Type:

text

Language:

en

Subjects:

backtting ; bootstrapping ; generalized additive models ; local likelihood ; local polynomial regression ; local scoring ; wild bootstrap. 1

backtting ; bootstrapping ; generalized additive models ; local likelihood ; local polynomial regression ; local scoring ; wild bootstrap. 1 Minimize

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310 Collections of general statistics *(computed)*

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Running title: Weighted Generalized Additive Models.

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This article describes the asymptotic properties of local polynomial regression estimators for univariate and additive models when observation weights are included. Such weighted additive models are a crucial component of local scoring, the widely used estimation algorithm for generalized additive models described in Hastie and Tibshirani (1990)...

This article describes the asymptotic properties of local polynomial regression estimators for univariate and additive models when observation weights are included. Such weighted additive models are a crucial component of local scoring, the widely used estimation algorithm for generalized additive models described in Hastie and Tibshirani (1990). The statistical properties of the univariate local polynomial estimator are shown to be asymptotically unaffected by the weights. In contrast, the weights inflate the asymptotic variance of the additive model estimators. The implications of these findings for the local scoring estimators are discussed. Additive models and generalized additive models are popular multivariate nonparametric regression techniques, widely used by statisticians and other scientists. While a number of different fitting methods are available for these models, the most popular one is backfitting, an iterative algorithm proposed by Friedman and Stuetzle (1981). Minimize

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The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2013-08-12

Source:

http://www.stat.colostate.edu/~jopsomer/papers/Local_scoring.pdf

http://www.stat.colostate.edu/~jopsomer/papers/Local_scoring.pdf Minimize

Document Type:

text

Language:

en

DDC:

310 Collections of general statistics *(computed)*

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Title:

Bootstrapping for Penalized Spline Regression

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We describe and contrast several different bootstrapping procedures for penalized spline smoothers. The bootstrapping procedures considered are variations on existing methods, developed under two different probabilistic frameworks. Under the first framework, penalized spline regression is considered an estimation technique to find an unknown smo...

We describe and contrast several different bootstrapping procedures for penalized spline smoothers. The bootstrapping procedures considered are variations on existing methods, developed under two different probabilistic frameworks. Under the first framework, penalized spline regression is considered an estimation technique to find an unknown smooth function. The smooth function is represented in a high dimensional spline basis, with spline coefficients estimated in a penalized form. Under the second framework, the unknown function is treated as a realization of a set of random spline coefficients, which are then predicted in a linear mixed model. We describe how bootstrapping methods can be implemented under both frameworks, and we show in theory and through simulations and examples that bootstrapping provides valid inference in both cases. We compare the inference obtained under both frameworks, and conclude that the latter generally produces better results than the former. The bootstrapping ideas are extended to hypothesis testing, where parametric components in a model are tested against nonparametric alternatives. Minimize

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The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2009-04-02

Source:

http://www.econ.kuleuven.be/public/ndbaf45/papers/kauermannclaeskensopsomer.pdf

http://www.econ.kuleuven.be/public/ndbaf45/papers/kauermannclaeskensopsomer.pdf Minimize

Document Type:

text

Language:

en

Subjects:

‡ Key words ; Mixed Model ; Nonparametric Regression ; Resampling ; Nonparametric Hypothesis Test

‡ Key words ; Mixed Model ; Nonparametric Regression ; Resampling ; Nonparametric Hypothesis Test Minimize

DDC:

519 Probabilities & applied mathematics *(computed)* ; 310 Collections of general statistics *(computed)*

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Title:

Smoothing Parameter Selection Methods for Nonparametric Regression With . . .

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The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2013-10-14

Source:

http://www.public.iastate.edu/~jopsomer/papers/Spatial_GCV_Biom.pdf

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text

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en

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