Bayesian Methods for Wavelet Series in Single-Index Models

Park, Chun Gun; Vannucci, Marina; Hart, Jeffrey D.

doi:10.1198/106186005x79007

Cited by 10 publications

(12 citation statements)

References 27 publications

(30 reference statements)

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“…Most applications of univariate wavelets focus on developing heuristics or methods for denoising a signal by removing certain higher-resolution terms from this series (see, for example, Park et al, 2005). The purpose of the application presented here, though, is to investigate the importance of high-resolution features; hence, there will be little focus in thresholding.…”

Section: The Data Blending Methodsmentioning

confidence: 99%

A wavelet-based approach to blending observations with deterministic computer models to resolve the intraurban air pollution field

Crooks

Isakov

2013

Journal of the Air & Waste Management Association

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Recent interest in near-road exposure to air pollutants and related health and environmental justice issues has highlighted the importance of improving the accuracy of intraurban ambient concentration estimates. Unfortunately, except in rare cases, no single source of information can accurately estimate the concentration at the desired spatial and temporal resolution over the full time period of epidemiological interest. However, it is possible to blend information from several sources so as to exploit the strengths and offset the weaknesses of each. Specifically, we are interested in combining data from ambient monitors with output from deterministic air pollution computer models. Monitor networks are sparse in both space and time, are costly to maintain, and are usually designed expressly to avoid detecting local-scale features. We use two types of computer models to compensate for these drawbacks. The first, a grid-based regional photochemical model, Community Multiscale Air Quality (CMAQ), covers large areas at high time resolution but cannot resolve features smaller than a grid cell, usually 4, 12, or 36 km across. The second, a plume dispersion model, AMS/EPA Regulatory Model (AERMOD), can resolve these features but cannot track long-distance transport or chemical reactions. We present a new Bayesian method that combines these three sources of information to resolve the intraurban pollution field. This method represents the true latent field using a two-dimensional wavelet basis, which allows direct, efficient incorporation of data at multiple levels of resolution. It furthermore allows a priori selection of the relative importance of each data source. We test its predictive accuracy and precision in a realistic urban-scale simulation. Finally, in the context of two air pollution health studies in Atlanta, Georgia, we use our model to estimate the daily mean concentrations of oxides of nitrogen (NO x ), particulate matter with an aerodynamic diameter 2.5 m (PM 2.5 ), and carbon monoxide (CO) at a mixture of census block group and zip code centroids for the years 2001-2002. Implications: This paper describes a novel method of blending regional and local model results with observations to produce accurate air pollutant concentrations at the desired spatial and temporal resolution over urban areas to support environmental epidemiological studies.

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Section: The Data Blending Methodsmentioning

confidence: 99%

A wavelet-based approach to blending observations with deterministic computer models to resolve the intraurban air pollution field

Crooks

Isakov

2013

Journal of the Air & Waste Management Association

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“…After we apply primary selection and basis selection, we estimate wavelet coefficients using Park et al (2005).…”

Section: Estimation Of Wavelet Coefficientsmentioning

confidence: 99%

Efficient resolution and basis functions selection in wavelet regression

Park

Kim

2015

Comput Stat

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In this paper we propose an efficient method to determine a primary resolution and wavelet basis functions in wavelet regression. Most wavelet shrinkage methods focus on thresholding the wavelet coefficients, given a primary resolution which is usually determined by the sample size. However, both a primary resolution and the basis functions are affected by the shape of an unknown function rather than the sample size. Unlike existing methods, our method takes the shape of the unknown function into account because a proper resolution can be much affected by the shape of it rather than the sample size. Our approach to determine a primary resolution and wavelet basis functions is developed under Bayesian framework using the posterior model probability. We demonstrate the advantage of our approach using a simulation study and a real data application.

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“…See Ichimura [21], Hardle et al [13], Horowitz and Hardle [19], Carroll et al [4], Xia et al [46], Naik and Tsai [31][32][33], Hardle et al [14], Climov et al [6], Daniela et al [7], Huh and Park [20], Simonoff and Tsai [36], Delecroix et al. [8], Delecroix et al [9], Antoniadis et al [1], Yu and Ruppert [50,51], Park et al [34], Stute and Zhu [40], Liang and Wang [26], Zhu and Xue [53], Xue and Zhu [48], Lambert and Peyre [24], Xia and Hardle [47], Kong and Xia [22], Yin and Zhu [49], Lin and Kulasekera [27], Zhang [52], Sun et al [41], Wong et al [45] and Bai et al [2].…”

Section: Introductionmentioning

confidence: 99%

Weighted estimation of single index models with right censored responses

Wang

et al. 2011

Sci. China Math.

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In this paper, the unknown link function, the direction parameter, and the heteroscedastic variance in single index models are estimated by the random weight method under the random censorship, respectively. The central limit theory and the convergence rate of the law of the iterated logarithm for the estimator of the direction parameter are derived, respectively. The optimal convergence rates for the estimators of the link function and the heteroscedastic variance are obtained. Simulation results support the theoretical results of the paper. Keywordssingle index models, random censorship, central limit theorem, law of the iterated logarithm, weighted least squares, unknown link function MSC(2000): 62G20, 62N01 Citation: Wang Y H, Li X Y, Wang Q H, et al. Weighted estimation of single index models with right censored responses.

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Bayesian Methods for Wavelet Series in Single-Index Models

Cited by 10 publications

References 27 publications

A wavelet-based approach to blending observations with deterministic computer models to resolve the intraurban air pollution field

A wavelet-based approach to blending observations with deterministic computer models to resolve the intraurban air pollution field

Efficient resolution and basis functions selection in wavelet regression

Weighted estimation of single index models with right censored responses

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