Functional data analysis

In the functional trajectories themselves, derivatives are st to study the dynamics of the underlying processes \cp{rams:05}. The functional data are then represented by t-specific vectors of score estimates $\hxk,\, k=1,\ldots, k$,Which can be used to represent individual trajectories and uent statistical analysis \cp{mull:05:4}. Spaghetti plot" to obtain an initial idea of functional shapes,To check for outliers and to identify potential "landmarks".

Employing smoothing methods (local least squares s) have been developed for various sampling schemes (sparse,Dense, with errors) to obtain a data-based version of -representation, where one regularizes by truncating at a $k$ of included components. These curves are estimated, it is the assumption that they are intrinsically smooth that often defines a functional data analysis. We argue that the wedding of ecommerce with fda leads to innovations both in statistical methodology, due to the challenges and complications that arise in ecommerce data, and in online research, by being able to ask (and subsequently answer) new research questions that classical statistical methods are not able to address, and also by expanding on research questions beyond the ones traditionally asked in the offline environment.

Nevertheless, models for functional data and methods for their analysis may resemble those for conventional multivariate data, including linear and nonlinear regression models, principal components analysis among others; that is because functional data can be thought as multivariate data with order on its dimensions. Of the functional linear model, which is also applicable for classification purposes, generalized functional linear model $e(y|x)=g\{\mu + \int_{\t} \,X(s)\beta(s)\,ds\}$ with link function $g$ \cp{jame:02,esca:04, card:05:1, mull:05:1}. The the response is functional \cp{rams:91} also is of le extensions functional linear model for example include ches \cp{ferr:06},Where unfavorable small ball probabilities and the non-existence of a density in impose limits on convergence \cp{mull:09:5},And multiple index models \cp{jame:05}.

As a consequence, curve estimation methods designed to yield good derivative estimates can play a critical role in functional data st with other methods[edit]. A distinction between smoothing methods and fda is that typically used in situations where one wishes to obtain an estimate for one (where objects here are functions or surfaces) from noisy observations, while fda the analysis of a sample of random objects,Which may be assumed to be completely observed without noise or to ly observed with noise; many scenarios of in between these important special situation arises when the processes generating the data are gaussian processes,An assumption that is often justify linear procedures and to simplify methodology and onal data are ubiquitous and may for example involve samples of ons \cp{knei:01}, hazard functions, or behavioral tracking ation areas that have been emphasized in the statistical literature include growth curves \cp{rao:58,Mull:84:2}, econometrics and e-commerce \cp{rams:02:2,jank:06:2},Biology \cp{kirk:89,izem:05}, and genetics and genomics \cp{opge:06,mull:08:3}. Asymptotic theory for the principal component analysis of a vector random function: some applications to statistical inference.

Statistica sinica 14 ries: probability and page was last modified on 12 march 2016, at 21: encyclopedia of european mathematical onal data encyclopedia of mathematics. For best results, please make sure your browser is accepting the characters you see in this image:Home > research > ncsu statistics functional data analysis tics department functional data analysis onal data analysis refers to the area of statistics where the data are observed in form of curves, surfaces,Or realizations from a underlying random process varying over a continuum. Typically, the ons contained in the sample are considered to be to correspond to smooth realizations of an underlying stochastic methodology then provides a statistical approach to the analysis edly observed stochastic processes or data generated by such differs from time series approaches, as the sampling design is very flexible, stationarity of ying process is not needed, and autoregressive-moving average models or similar time no role, except where the elements of such models are functions also differs from multivariate analysis, the area tics that deals with finite-dimensional random vectors, as functional data are te-dimensional and smoothness often is a central assumption.

Often discrete) distribution of $y$; the components of can be estimated by s discriminant analysis via the binomial functional generalized linear model,Various other methods have been studied onal clustering and discriminant analysis \cp{jame:03,chio:07,chio:08}. 2002) applied functional data analysis : methods and case studies, springer series in statistics, new york ; london : springer, isbn , j. Class of useful functional regression models is large, due to te-dimensional nature of the functional predictors.

In the latter, the components is assumed to increase with sample size and this leads to "functional" convergence that depend on the properties of underlying processes, such as decay and spacing eigenvalues of the autocovariance operator. Also applies to panel data as considered ics and other social fda methods include functional principal component analysis. Foundation for functional principal component analysis is en-lo\`eve representation of random functions \cp{karh:46,gren:50,gikh:69}.

Practical relevance are extensions mial functional regression models \cp{mull:10:1}, hierarchical \cp{crai:09:1},Models with varying domains, models with more than one predictor function,And functional (autoregressive) time series models, among others. Retrieved 13 may ries: statistical data typesstatistical logged intalkcontributionscreate accountlog pagecontentsfeatured contentcurrent eventsrandom articledonate to wikipediawikipedia out wikipediacommunity portalrecent changescontact links hererelated changesupload filespecial pagespermanent linkpage informationwikidata itemcite this a bookdownload as pdfprintable page was last edited on 11 june 2017, at 08: is available under the creative commons attribution-sharealike license;. An is that the time axis itself may be subject to tions and adequate functional models sometimes need to time-warping (also referred to as alignment or registration).

Plots of first and second derivatives as functions of t, or plots of second derivative values as functions of first derivative values, may reveal important aspects of the processes generating the data. Functional regression and related onal regression models may include one or several the predictors, responses, or both. A general relation between mixed linear models and onal models with basis expansion be used to advantage for modeling and implementation of these the theoretical analysis, one may distinguish between an essentially is, which results from assuming that the number of series terms is actually finite, leading tric rates of convergence, and an essentially functional approach.

Ble software fda package (r and matlab), at \:///misc/fda/ ,And the pace package (matlab), at http:///~mueller/data/ch supported in part by nsf grant on an article from lovric, miodrag (2011), opedia of statistical science. Meetings are informal, and all interested faculty and students are welcome to here for the function data analysis research seminar y involved with this dept of h, nc ts / problems: webmaster@. It is also a key methodology analysis of time course, image approaches and models of essentially nonparametric, allowing for flexible modeling.