Smoothing Spline Estimation of Variance Functions

Liu, Anna; Tong, Tiejun; Wang, Yuedong

doi:10.1198/106186007x204528

Cited by 14 publications

(10 citation statements)

References 32 publications

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“…Yau and Kohn (2003), for example, modeled log{ v ( X )} using flexible mixtures of polynomial and thin-plate splines. Liu, et al (2006) proposed a penalized mixture of smoothing splines, whereas Chan, et al (2006) considered mixtures of locally adaptive radial basis functions.…”

Section: Density Deconvolution Modelsmentioning

confidence: 99%

Bayesian Semiparametric Density Deconvolution in the Presence of Conditionally Heteroscedastic Measurement Errors

Sarkar¹,

Mallick²,

Staudenmayer³

et al. 2014

Journal of Computational and Graphical Statistics

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We consider the problem of estimating the density of a random variable when precise measurements on the variable are not available, but replicated proxies contaminated with measurement error are available for sufficiently many subjects. Under the assumption of additive measurement errors this reduces to a problem of deconvolution of densities. Deconvolution methods often make restrictive and unrealistic assumptions about the density of interest and the distribution of measurement errors, e.g., normality and homoscedasticity and thus independence from the variable of interest. This article relaxes these assumptions and introduces novel Bayesian semiparametric methodology based on Dirichlet process mixture models for robust deconvolution of densities in the presence of conditionally heteroscedastic measurement errors. In particular, the models can adapt to asymmetry, heavy tails and multimodality. In simulation experiments, we show that our methods vastly outperform a recent Bayesian approach based on estimating the densities via mixtures of splines. We apply our methods to data from nutritional epidemiology. Even in the special case when the measurement errors are homoscedastic, our methodology is novel and dominates other methods that have been proposed previously. Additional simulation results, instructions on getting access to the data set and R programs implementing our methods are included as part of online supplemental materials.

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Section: Density Deconvolution Modelsmentioning

confidence: 99%

Bayesian Semiparametric Density Deconvolution in the Presence of Conditionally Heteroscedastic Measurement Errors

Sarkar¹,

Mallick²,

Staudenmayer³

et al. 2014

Journal of Computational and Graphical Statistics

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“…Specifically, at each iteration, we compute the working variable z k =g k + y k exp(−g k ) − 1 and weight w k = 1 where tilde indicates current estimates. Note that, as [Pawitan and O'Sullivan (1994)], we use the Fisher scoring method instead of the Newton-Raphson method employed in Wahba et al (1995), Gu (2002) and Liu, Tong and Wang (2006). Our experience indicates that the Fisher scoring method is more stable in this situation.…”

Section: 2mentioning

confidence: 99%

Nonparametric spectral analysis with applications to seizure characterization using EEG time series

Li¹,

Wang²

2008

Ann. Appl. Stat.

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Understanding the seizure initiation process and its propagation pattern(s) is a critical task in epilepsy research. Characteristics of the pre-seizure electroencephalograms (EEGs) such as oscillating powers and high-frequency activities are believed to be indicative of the seizure onset and spread patterns. In this article, we analyze epileptic EEG time series using nonparametric spectral estimation methods to extract information on seizure-specific power and characteristic frequency [or frequency band(s)]. Because the EEGs may become nonstationary before seizure events, we develop methods for both stationary and local stationary processes. Based on penalized Whittle likelihood, we propose a direct generalized maximum likelihood (GML) and generalized approximate cross-validation (GACV) methods to estimate smoothing parameters in both smoothing spline spectrum estimation of a stationary process and smoothing spline ANOVA time-varying spectrum estimation of a locally stationary process. We also propose permutation methods to test if a locally stationary process is stationary. Extensive simulations indicate that the proposed direct methods, especially the direct GML, are stable and perform better than other existing methods. We apply the proposed methods to the intracranial electroencephalograms (IEEGs) of an epileptic patient to gain insights into the seizure generation process.

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“…However, for generalized smoothing spline models, direct methods are proposed to overcome the convergence problem and improve effectiveness [29,31,16].…”

Section: Indirect Methodsmentioning

confidence: 99%

M-type smoothing spline ANOVA for correlated data

Liu

Staudenmayer

2010

Journal of Multivariate Analysis

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a b s t r a c tThis paper concerns outlier robust non-parametric regression with smoothing splines for data that are possibly correlated. We define a robust smoother as the minimizer of a penalized robustified log likelihood. Our estimation algorithm uses iteratively reweighted least squares to estimate the regression function. We develop two types of robust methods for joint estimation of the smoothing parameters and the correlation parameters: indirect methods and direct methods, terms borrowed from the related generalized smoothing spline literature. The indirect methods choose those parameters by conveniently approximating the distribution of the working data at each iteration as Gaussian. The direct methods estimate those parameters to minimize an estimate of the loss between the truth and the final estimated regression. Indirect methods are computationally more efficient, but our empirical studies suggest that direct methods result in more accurate estimates. Finally, the methods are applied to a data set from a macaque Simian-Human Immunodeficiency Virus (SHIV) challenge study.

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Smoothing Spline Estimation of Variance Functions

Cited by 14 publications

References 32 publications

Bayesian Semiparametric Density Deconvolution in the Presence of Conditionally Heteroscedastic Measurement Errors

Bayesian Semiparametric Density Deconvolution in the Presence of Conditionally Heteroscedastic Measurement Errors

Nonparametric spectral analysis with applications to seizure characterization using EEG time series

M-type smoothing spline ANOVA for correlated data

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