@article { ISI:000361373800008,
	title = {Functional Data Model for Genetically Related Individuals With Application to Cow Growth},
	journal = {JOURNAL OF COMPUTATIONAL AND GRAPHICAL STATISTICS},
	volume = {24},
	number = {3},
	year = {2015},
	month = {JUL 3},
	pages = {756-770},
	publisher = {AMER STATISTICAL ASSOC},
	type = {Article},
	address = {732 N WASHINGTON ST, ALEXANDRIA, VA 22314-1943 USA},
	abstract = {We propose a new version of functional data model for analyzing familial related individuals, where the within-subject correlation depends smoothly on a covariate such as age and the between-subject correlation follows family-wise genetic association. Our motivating example concerns measurements of weight as a function of age in sibling cows from independent families. Observations are sparsely sampled from trajectories of a phenotype contaminated with measurement error, where the phenotypic trajectory consists of a genetic component and an environmental component. By combining information across individuals, the genetic and environmental covariances are estimated via smoothing techniques. We study the genetic and environmental effects using principal component analysis, taking into account the genetic correlation to enhance the subject-level signal extraction. We show via the real data and simulations that incorporating the correlation structure improves predictions of individual phenotypic trajectories.},
	keywords = {Functional principal components, Genetic relationship, Smoothing, Sparse functional data},
	issn = {1061-8600},
	doi = {10.1080/10618600.2014.948180},
	author = {Lei, Edwin and Yao, Fang and Heckman, Nancy and Meyer, Karin}
}
@article { ISI:000246559600002,
	title = {Seasonal confounding and residual correlation in analyses of health effects of air pollution},
	journal = {ENVIRONMETRICS},
	volume = {18},
	number = {4},
	year = {2007},
	month = {JUN},
	pages = {375-394},
	publisher = {JOHN WILEY \& SONS LTD},
	type = {Article},
	address = {THE ATRIUM, SOUTHERN GATE, CHICHESTER PO19 8SQ, W SUSSEX, ENGLAND},
	abstract = {To investigate the health effects of air pollution via a partially linear model, one must choose an appropriate amount of smoothing for accurate estimation of the linear pollution effects. This choice is complicated by the dependencies between the various covariates and by the potential residual correlation. Most existing approaches to making this choice are inadequate, as they neither target accurate estimation of the linear pollutant effects nor handle residual correlation. In this paper, we illustrate two new adaptive and objective methods for determining an appropriate amount of smoothing. We construct valid confidence intervals for the linear pollutant effects, intervals that account for residual correlation. We use our inferential methods to investigate the same-day effects of PM10 on daily mortality in two data sets for the period 1994 to 1996: one collected in Mexico City, an urban area with high levels of air pollution, and the other collected in Vancouver, British Columbia, an urban area with low levels of air pollution. For Mexico City, our methodology does not detect a PM10 effect. In contrast, for Vancouver, a PM10 effect corresponding to an expected 2.4\% increase (95\% confidence interval ranging from 0.0\% to 4.7\%) in daily mortality for every 10 mu g/m(3) increase in PM10 is identified. Copyright (c) 2006 John Wiley \& Sons, Ltd.},
	keywords = {air pollution, bandwidth selection, generalized additive model, mortality, partially linear model, particulate matter, residual correlation, seasonal confounding, Smoothing},
	issn = {1180-4009},
	doi = {10.1002/env.814},
	author = {Ghement, Isabella R. and Heckman, Nancy E. and Petkau, A. John}
}
@article { ISI:000173007800007,
	title = {CriSP: A tool for bump hunting},
	journal = {JOURNAL OF COMPUTATIONAL AND GRAPHICAL STATISTICS},
	volume = {10},
	number = {4},
	year = {2001},
	month = {DEC},
	pages = {713-729},
	publisher = {AMER STATISTICAL ASSOC},
	type = {Article},
	address = {1429 DUKE ST, ALEXANDRIA, VA 22314 USA},
	abstract = {We propose a test of multimodality of regression functions and their derivatives. The test statistic is a critical smoothing parameter (CriSP), giving the minimum amount of smoothing necessary to force the regression function to satisfy the null hypothesis. The p values are computed via bootstrapping. Our idea is motivated by Silverman{\textquoteright}s test concerning the number of modes in the density function. Simulation studies indicate that the test works well, even when testing for bumps in the derivative. We apply CriSP to children{\textquoteright}s growth data, to study the number of spurts of growth.},
	keywords = {bootstrap, critical smoothing parameter, growth data, multimodality testing, Smoothing},
	issn = {1061-8600},
	doi = {10.1198/106186001317243412},
	author = {Harezlak, J and Heckman, NE}
}
