@article {9349,
	title = {Switching nonparametric regression models for multi-curve data},
	journal = {Canadian Journal of Statistics},
	volume = {45},
	year = {2017},
	pages = {442{\textendash}460},
	keywords = {EM algorithm, Functional data analysis, latent variables, machine learning, MSC 2010: Primary 62G08, nonparametric regression, power usage, secondary 62G05, switching nonparametric regression model},
	issn = {1708-945X},
	doi = {10.1002/cjs.11331},
	url = {http://dx.doi.org/10.1002/cjs.11331},
	author = {de Souza, Camila P. E. and Heckman, Nancy E. and Xu, Fan}
}
@article { ISI:000365144600020,
	title = {S-Estimators for Functional Principal Component Analysis},
	journal = {JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION},
	volume = {110},
	number = {511},
	year = {2015},
	month = {SEP},
	pages = {1100-1111},
	publisher = {AMER STATISTICAL ASSOC},
	type = {Article},
	address = {732 N WASHINGTON ST, ALEXANDRIA, VA 22314-1943 USA},
	abstract = {<p>Principal component analysis is a widely used technique that provides an optimal lower-dimensional approximation to multivariate or functional datasets. These approximations can be very useful in identifying potential outliers among high-dimensional or functional observations. In this article, we propose a new class of estimators for principal components based on robust scale estimators. For a fixed dimension q, we robustly estimate the q-dimensional linear space that provides the best prediction for the data, in the sense of minimizing the sum of robust scale estimators of the coordinates of the residuals. We also study an extension to the infinite-dimensional case. Our method is consistent for elliptical random vectors, and is Fisher consistent for elliptically distributed random elements on arbitrary Hilbert spaces. Numerical experiments show that our proposal is highly competitive when compared with other methods. We illustrate our approach on a real dataset, where the robust estimator discovers atypical observations that would have been missed otherwise. Supplementary materials for this article are available online.</p>
},
	keywords = {Functional data analysis, Robust estimation, Sparse data},
	issn = {0162-1459},
	doi = {10.1080/01621459.2014.946991},
	author = {Boente, Graciela and Salibian-Barrera, Mat{\'\i}as}
}
@article { ISI:000332125300001,
	title = {Modeling regional impacts of climate teleconnections using functional data analysis},
	journal = {ENVIRONMENTAL AND ECOLOGICAL STATISTICS},
	volume = {21},
	number = {1},
	year = {2014},
	month = {MAR},
	pages = {1-26},
	publisher = {SPRINGER},
	type = {Article},
	address = {VAN GODEWIJCKSTRAAT 30, 3311 GZ DORDRECHT, NETHERLANDS},
	abstract = {Teleconnections are quasi-periodic changes in atmospheric circulation that oscillate over long periods of time and impact climate over large regions. These patterns are often linked to long-term variations in climate and extreme weather events and may explain regional differences in climate vulnerability. We apply methods of functional data analysis to examine regional impacts of teleconnections on climate in British Columbia, Canada, between 1951 and 2000. We focus on monthly mean temperature as an overall determinant of crop growth and apply functional principal components analysis (FPCA) to study variations in the impacts of four major teleconnection indices affecting the Northern Hemisphere (the Southern Oscillation Index, the Pacific North American (PNA), Pacific Decadal Oscillation, and the North American Oscillation indices). Two challenges we consider are that the impacts of teleconnections cannot be observed directly and that fine scale data required to study regional variations may come from different sources with highly varied records. We first fit thin-plate regression splines to the raw data to construct complete series of pseudo-data at fixed grid points. Regression models incorporating Bayesian P-splines were then fit to the pseudo-data to estimate the impacts of the four teleconnections over time. Finally, FPCA was then applied to study regional variations in these effects. Our analysis identified strong variations in mean temperature associated with the PNA. The resulting spatial patterns also reveal areas of increased/decreased temperature variability that may have higher climate risk or be suitable for expansion of agricultural activity.},
	keywords = {Agriculture, Climate variability, Functional data analysis, Functional principal components analysis, Teleconnections},
	issn = {1352-8505},
	doi = {10.1007/s10651-013-0241-8},
	author = {Bonner, Simon J. and Newlands, Nathaniel K. and Heckman, Nancy E.}
}
@article { ISI:000255532900018,
	title = {Hypothesis testing in comparative and experimental studies of function-valued traits},
	journal = {EVOLUTION},
	volume = {62},
	number = {5},
	year = {2008},
	month = {MAY},
	pages = {1229-1242},
	publisher = {BLACKWELL PUBLISHING},
	type = {Article},
	address = {9600 GARSINGTON RD, OXFORD OX4 2DQ, OXON, ENGLAND},
	abstract = {Many traits of evolutionary interest, when placed in their developmental, physiological, or environmental contexts, are function-valued. For instance, gene expression during development is typically a function of the age of an organism and physiological processes are often a function of environment. In comparative and experimental studies, a fundamental question is whether the function-valued trait of one group is different from another. To address this question, evolutionary biologists have several statistical methods available. These methods can be classified into one of two types: multivariate and functional. Multivariate methods, including univariate repeated-measures analysis of variance (ANOVA), treat each trait as a finite list of data. Functional methods, such as repeated-measures regression, view the data as a sample of points drawn from an underlying function. A key difference between multivariate and functional methods is that functional methods retain information about the ordering and spacing of a set of data values, information that is discarded by multivariate methods. In this study, we evaluated the importance of that discarded information in statistical analyses of function-valued traits. Our results indicate that functional methods tend to have substantially greater statistical power than multivariate approaches to detect differences in a function-valued trait between groups.},
	keywords = {Functional data analysis, multivariate analysis, phenotype, power, repeated-measures ANOVA, repeated-measures regression},
	issn = {0014-3820},
	doi = {10.1111/j.1558-5646.2008.00340.x},
	author = {Griswold, Cortland K. and Gomulkiewicz, Richard and Heckman, Nancy}
}
@article { ISI:000174685600010,
	title = {Estimating and depicting the structure of a distribution of random functions},
	journal = {BIOMETRIKA},
	volume = {89},
	number = {1},
	year = {2002},
	month = {MAR},
	pages = {145-158},
	publisher = {BIOMETRIKA TRUST},
	type = {Article},
	address = {UNIV COLLEGE LONDON GOWER ST-BIOMETRIKA OFFICE, LONDON WC1E 6BT, ENGLAND},
	abstract = {We suggest a nonparametric approach to making inference about the structure of distributions in a potentially infinite-dimensional space, for example a function space, and displaying information about that structure. It is suggested that the simplest way of presenting the structure is through modes and density ascent lines, the latter being the projections into the sample space of the curves of steepest ascent up the surface of a functional-data density. Modes are always points in the sample space, and ascent lines are always one-parameter structures, even when the sample space is determined by an infinite number of parameters. They are therefore relatively easily depicted. Our methodology is based on a functional form of an iterative data-sharpening algorithm.},
	keywords = {bandwidth, cluster analysis, Functional data analysis, Gaussian process, generalised Fourier expansion, Karhunen-Loeve expansion, kernel methods, line of steepest ascent, mode, nonparametric density estimation, tree diagram},
	issn = {0006-3444},
	doi = {10.1093/biomet/89.1.145},
	author = {Hall, P and Heckman, NE}
}
