487 research outputs found
Deconvolution Estimation in Measurement Error Models: The R Package decon
Data from many scientific areas often come with measurement error. Density or distribution function estimation from contaminated data and nonparametric regression with errors in variables are two important topics in measurement error models. In this paper, we present a new software package decon for R, which contains a collection of functions that use the deconvolution kernel methods to deal with the measurement error problems. The functions allow the errors to be either homoscedastic or heteroscedastic. To make the deconvolution estimators computationally more efficient in R, we adapt the fast Fourier transform algorithm for density estimation with error-free data to the deconvolution kernel estimation. We discuss the practical selection of the smoothing parameter in deconvolution methods and illustrate the use of the package through both simulated and real examples.
Kernel density estimation on the torus
Kernel density estimation for multivariate, circular data has been formulated only when the sample space is the sphere, but theory for the torus would also be useful. For data lying on a d-dimensional torus (d >= 1), we discuss kernel estimation of a density, its mixed partial derivatives, and their squared functionals. We introduce a specific class of product kernels whose order is suitably defined in such a way to obtain L-2-risk formulas whose structure can be compared to their Euclidean counterparts. Our kernels are based on circular densities; however, we also discuss smaller bias estimation involving negative kernels which are functions of circular densities. Practical rules for selecting the smoothing degree, based on cross-validation, bootstrap and plug-in ideas are derived. Moreover, we provide specific results on the use of kernels based on the von Mises density. Finally, real-data examples and simulation studies illustrate the findings
Local Multiplicative Bias Correction for Asymmetric Kernel Density Estimators
We consider semiparametric asymmetric kernel density estimators when the unknown density has support on [0, ¥). We provide a unifying framework which contains asymmetric kernel versions of several semiparametric density estimators considered previously in the literature. This framework allows us to use popular parametric models in a nonparametric fashion and yields estimators which are robust to misspecification. We further develop a specification test to determine if a density belongs to a particular parametric family. The proposed estimators outperform rival non- and semiparametric estimators in finite samples and are simple to implement. We provide applications to loss data from a large Swiss health insurer and Brazilian income data.semiparametric density estimation; asymmetric kernel; income distribution; loss distribution; health insurance; specification testing
Nonparametric Estimation of Scalar Diffusion Processes of Interest Rates Using Asymmetric Kernels
This paper proposes a nonparametric regression using asymmetric kernel functions for nonnegative, absolutely regular processes, and specializes this technique to estimating scalar diffusion models of spot interest rate. We illustrate the advantages of asymmetric kernel estimators for bias correction and efficiency gains. The finite-sample properties and the practical relevance of the proposed estimators are evaluated in the context of bond and option pricing. We also present estimation results from empirical analysis of the term structure of U.S. interest rates.Nonparametric regression; Gamma kernel; diffusion estimation; spot interest rate; derivative pricing
Nonparametric confidence bands in deconvolution density estimation
Uniform confidence bands for densities f via nonparametric kernel estimates were first constructed by Bickel and Rosenblatt [Ann. Statist. 1, 1071.1095]. In this paper this is extended to confidence bands in the deconvolution problem g = f for an ordinary smooth error density . Under certain regularity conditions, we obtain asymptotic uniform confidence bands based on the asymptotic distribution of the maximal deviation (LÉ-distance) between a deconvolution kernel estimator . f and f. Further consistency of the simple nonparametric bootstrap is proved. For our theoretical developments the bias is simply corrected by choosing an undersmoothing bandwidth. For practical purposes we propose a new data-driven bandwidth selector based on heuristic arguments, which aims --
Kernel density estimation via diffusion
We present a new adaptive kernel density estimator based on linear diffusion
processes. The proposed estimator builds on existing ideas for adaptive
smoothing by incorporating information from a pilot density estimate. In
addition, we propose a new plug-in bandwidth selection method that is free from
the arbitrary normal reference rules used by existing methods. We present
simulation examples in which the proposed approach outperforms existing methods
in terms of accuracy and reliability.Comment: Published in at http://dx.doi.org/10.1214/10-AOS799 the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org
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