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Carroll, Raymond J. (39)

Martinez, Josue G. (5)Maity, Arnab (4)Wei, Jiawei (4)Chatterjee, Nilanjan (3)View MoreJournalJournal of the American Statistical Association (11)Biometrics (3)Journal of the Royal Statistical Society: Series B (Statistical Methodology) (3)Electronic Journal of Statistics (2)Journal of Computational and Graphical Statistics (2)View MoreKAUST Grant NumberKUS-CI-016-04 (36)KUS-C1-016-04 (3)PublisherInforma UK Limited (14)Wiley (9)Institute of Mathematical Statistics (7)Elsevier BV (2)International Press of Boston (2)View MoreSubjectMeasurement error (8)Longitudinal data (4)Functional data analysis (3)Model selection (3)Principal components (3)View MoreTypeArticle (38)Book Chapter (1)Year (Issue Date)2015 (2)2014 (2)2013 (7)2012 (4)2011 (7)View MoreItem AvailabilityMetadata Only (37)Open Access (2)

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Testing and Estimating Shape-Constrained Nonparametric Density and Regression in the Presence of Measurement Error

Carroll, Raymond J.; Delaigle, Aurore; Hall, Peter (Journal of the American Statistical Association, Informa UK Limited, 2011-03) [Article]

In many applications we can expect that, or are interested to know if, a density function or a regression curve satisfies some specific shape constraints. For example, when the explanatory variable, X, represents the value taken by a treatment or dosage, the conditional mean of the response, Y , is often anticipated to be a monotone function of X. Indeed, if this regression mean is not monotone (in the appropriate direction) then the medical or commercial value of the treatment is likely to be significantly curtailed, at least for values of X that lie beyond the point at which monotonicity fails. In the case of a density, common shape constraints include log-concavity and unimodality. If we can correctly guess the shape of a curve, then nonparametric estimators can be improved by taking this information into account. Addressing such problems requires a method for testing the hypothesis that the curve of interest satisfies a shape constraint, and, if the conclusion of the test is positive, a technique for estimating the curve subject to the constraint. Nonparametric methodology for solving these problems already exists, but only in cases where the covariates are observed precisely. However in many problems, data can only be observed with measurement errors, and the methods employed in the error-free case typically do not carry over to this error context. In this paper we develop a novel approach to hypothesis testing and function estimation under shape constraints, which is valid in the context of measurement errors. Our method is based on tilting an estimator of the density or the regression mean until it satisfies the shape constraint, and we take as our test statistic the distance through which it is tilted. Bootstrap methods are used to calibrate the test. The constrained curve estimators that we develop are also based on tilting, and in that context our work has points of contact with methodology in the error-free case.

Testing for constant nonparametric effects in general semiparametric regression models with interactions

Wei, Jiawei; Carroll, Raymond J.; Maity, Arnab (Statistics & Probability Letters, Elsevier BV, 2011-07) [Article]

We consider the problem of testing for a constant nonparametric effect in a general semi-parametric regression model when there is the potential for interaction between the parametrically and nonparametrically modeled variables. The work was originally motivated by a unique testing problem in genetic epidemiology (Chatterjee, et al., 2006) that involved a typical generalized linear model but with an additional term reminiscent of the Tukey one-degree-of-freedom formulation, and their interest was in testing for main effects of the genetic variables, while gaining statistical power by allowing for a possible interaction between genes and the environment. Later work (Maity, et al., 2009) involved the possibility of modeling the environmental variable nonparametrically, but they focused on whether there was a parametric main effect for the genetic variables. In this paper, we consider the complementary problem, where the interest is in testing for the main effect of the nonparametrically modeled environmental variable. We derive a generalized likelihood ratio test for this hypothesis, show how to implement it, and provide evidence that our method can improve statistical power when compared to standard partially linear models with main effects only. We use the method for the primary purpose of analyzing data from a case-control study of colorectal adenoma.

Identification and estimation of nonlinear models using two samples with nonclassical measurement errors

Carroll, Raymond J.; Chen, Xiaohong; Hu, Yingyao (Journal of Nonparametric Statistics, Informa UK Limited, 2010-05) [Article]

This paper considers identification and estimation of a general nonlinear Errors-in-Variables (EIV) model using two samples. Both samples consist of a dependent variable, some error-free covariates, and an error-prone covariate, for which the measurement error has unknown distribution and could be arbitrarily correlated with the latent true values; and neither sample contains an accurate measurement of the corresponding true variable. We assume that the regression model of interest - the conditional distribution of the dependent variable given the latent true covariate and the error-free covariates - is the same in both samples, but the distributions of the latent true covariates vary with observed error-free discrete covariates. We first show that the general latent nonlinear model is nonparametrically identified using the two samples when both could have nonclassical errors, without either instrumental variables or independence between the two samples. When the two samples are independent and the nonlinear regression model is parameterized, we propose sieve Quasi Maximum Likelihood Estimation (Q-MLE) for the parameter of interest, and establish its root-n consistency and asymptotic normality under possible misspecification, and its semiparametric efficiency under correct specification, with easily estimated standard errors. A Monte Carlo simulation and a data application are presented to show the power of the approach.

Estimating the Distribution of Dietary Consumption Patterns

Carroll, Raymond J. (Statistical Science, Institute of Mathematical Statistics, 2014-02) [Article]

In the United States the preferred method of obtaining dietary intake data is the 24-hour dietary recall, yet the measure of most interest is usual or long-term average daily intake, which is impossible to measure. Thus, usual dietary intake is assessed with considerable measurement error. We were interested in estimating the population distribution of the Healthy Eating Index-2005 (HEI-2005), a multi-component dietary quality index involving ratios of interrelated dietary components to energy, among children aged 2-8 in the United States, using a national survey and incorporating survey weights. We developed a highly nonlinear, multivariate zero-inflated data model with measurement error to address this question. Standard nonlinear mixed model software such as SAS NLMIXED cannot handle this problem. We found that taking a Bayesian approach, and using MCMC, resolved the computational issues and doing so enabled us to provide a realistic distribution estimate for the HEI-2005 total score. While our computation and thinking in solving this problem was Bayesian, we relied on the well-known close relationship between Bayesian posterior means and maximum likelihood, the latter not computationally feasible, and thus were able to develop standard errors using balanced repeated replication, a survey-sampling approach.

A Study of Mexican Free-Tailed Bat Chirp Syllables: Bayesian Functional Mixed Models for Nonstationary Acoustic Time Series

Martinez, Josue G.; Bohn, Kirsten M.; Carroll, Raymond J.; Morris, Jeffrey S. (Journal of the American Statistical Association, Informa UK Limited, 2013-06) [Article]

We describe a new approach to analyze chirp syllables of free-tailed bats from two regions of Texas in which they are predominant: Austin and College Station. Our goal is to characterize any systematic regional differences in the mating chirps and assess whether individual bats have signature chirps. The data are analyzed by modeling spectrograms of the chirps as responses in a Bayesian functional mixed model. Given the variable chirp lengths, we compute the spectrograms on a relative time scale interpretable as the relative chirp position, using a variable window overlap based on chirp length. We use 2D wavelet transforms to capture correlation within the spectrogram in our modeling and obtain adaptive regularization of the estimates and inference for the regions-specific spectrograms. Our model includes random effect spectrograms at the bat level to account for correlation among chirps from the same bat, and to assess relative variability in chirp spectrograms within and between bats. The modeling of spectrograms using functional mixed models is a general approach for the analysis of replicated nonstationary time series, such as our acoustical signals, to relate aspects of the signals to various predictors, while accounting for between-signal structure. This can be done on raw spectrograms when all signals are of the same length, and can be done using spectrograms defined on a relative time scale for signals of variable length in settings where the idea of defining correspondence across signals based on relative position is sensible.

Semiparametric regression during 2003–2007

Ruppert, David; Wand, M.P.; Carroll, Raymond J. (Electronic Journal of Statistics, Institute of Mathematical Statistics, 2009) [Article]

Semiparametric regression is a fusion between parametric regression and nonparametric regression that integrates low-rank penalized splines, mixed model and hierarchical Bayesian methodology – thus allowing more streamlined handling of longitudinal and spatial correlation. We review progress in the field over the five-year period between 2003 and 2007. We find semiparametric regression to be a vibrant field with substantial involvement and activity, continual enhancement and widespread application.

Analysis of Case-Control Association Studies: SNPs, Imputation and Haplotypes

Chatterjee, Nilanjan; Chen, Yi-Hau; Luo, Sheng; Carroll, Raymond J. (Statistical Science, Institute of Mathematical Statistics, 2009-11) [Article]

Although prospective logistic regression is the standard method of analysis for case-control data, it has been recently noted that in genetic epidemiologic studies one can use the "retrospective" likelihood to gain major power by incorporating various population genetics model assumptions such as Hardy-Weinberg-Equilibrium (HWE), gene-gene and gene-environment independence. In this article we review these modern methods and contrast them with the more classical approaches through two types of applications (i) association tests for typed and untyped single nucleotide polymorphisms (SNPs) and (ii) estimation of haplotype effects and haplotype-environment interactions in the presence of haplotype-phase ambiguity. We provide novel insights to existing methods by construction of various score-tests and pseudo-likelihoods. In addition, we describe a novel two-stage method for analysis of untyped SNPs that can use any flexible external algorithm for genotype imputation followed by a powerful association test based on the retrospective likelihood. We illustrate applications of the methods using simulated and real data. © Institute of Mathematical Statistics, 2009.

SIMEX and standard error estimation in semiparametric measurement error models

Apanasovich, Tatiyana V.; Carroll, Raymond J.; Maity, Arnab (Electronic Journal of Statistics, Institute of Mathematical Statistics, 2009) [Article]

A simultaneous confidence band for sparse longitudinal regression

Ma, Shujie; Yang, Lijian; Carroll, Raymond J. (Statistica Sinica, Institute of Statistical Science, 2012-01) [Article]

Functional data analysis has received considerable recent attention and a number of successful applications have been reported. In this paper, asymptotically simultaneous confidence bands are obtained for the mean function of the functional regression model, using piecewise constant spline estimation. Simulation experiments corroborate the asymptotic theory. The confidence band procedure is illustrated by analyzing CD4 cell counts of HIV infected patients.

How to estimate the measurement error variance associated with ancestry proportion estimates

Allison, David B.; Carroll, Raymond J.; Divers, Jasmin; Redden, David T. (Statistics and Its Interface, International Press of Boston, 2011) [Article]

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