Statistical Computing in Functional Data Analysis: TheRPackagefda.usc
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This paper is devoted to the R package fda.usc which includes some utilities for functional data analysis. This package carries out exploratory and descriptive analysis of functional data analyzing its most important features such as depth measurements or functional outliers detection, among others. The R package fda.usc also includes functions to compute functional regression models, with a scalar response and a functional explanatory data via non-parametric functional regression, basis representation or functional principal components analysis. There are natural extensions such as functional linear models and semi-functional partial linear models, which allow non-functional covariates and factors and make predictions. The functions of this package complement and incorporate the two main references of functional data analysis: The R package fda and the functions implemented by Ferraty and Vieu (2006).Keywords:
R package
Exploratory data analysis
Complement
Functional decomposition
본 연구는 함수적 데이터 분석의 몇 가지 이론에 대해 소개하고 분석 기법을 실제 자료에 적용하는 내용을 다루었다. 함수적 데이터 분석의 이론적 내용으로 기저를 이용해 자료를 함수적 데이터로 표현하는 방법, 그리고 함수적 데이터의 변동성을 조사하는 주성분분석, 선형모형 등에 대해 살펴보았다. 그리고 우리나라 기온 데이터와 강수량 데이터를 대상으로 각각 함수적 데이터 분석 기법을 적용해 보았다. 또한, 기온과 강수량 데이터에 대해 함수적 회귀모형을 적합시켜 두 변수간의 함수관계를 살펴보았다. In this paper we review some methods for analyzing functional data and illustrate real application of functional data analysis. Representing methods for functional data by using basis function, analyzing functional variation by functional principal component analysis and functional linear models are reviewed. For a real application, we use temperature and precipitation data measured in Korea from the January of 1970 to the May of 2004. We apply functional principal component analysis for each data and test the significance of regional division done by using shining hours. We also estimate functional regression model for temperature and precipitation.
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Basis Objects and Operations.- Functional Data Objects and Operations.- Linear Differential Operators and Smoothing.- Functional Registration.- Functional Linear Models.- Functional Generalized Linear Models.- Functional Principal Components.- Canonical Correlation.- Functional Cluster Analysis.- Principal Differential Analysis.
Smoothing
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Basis (linear algebra)
Functional design
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Abstract This article presents exploratory data analytic methodology for visualizing and summarizing data that can be represented as individual-specific curves. We propose a simplified form of functional data analysis. A nonparametric scatterplot smooth is applied to each individual's data, followed by a principal components analysis of the smoothed data. We then display the individual smooth curves in an array organized by principal component scores. The display suggests interpretable summary measures. The methodology is applied to the measurement of proliferative activity, a biomarker for colon cancer risk. We use the summary measures in the analysis of a pilot study clinical trial.
Exploratory data analysis
Exploratory analysis
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This dissertation is concerned with functional data analysis. Functional data consists of a collection of curves or functions defined on an interval. These curves can be obtained by splitting a continuous time record such as temperature into daily or annual curves. Functional data is also obtained when an experimenter records a curve of data from each subject in a sample, e.g., a growth trajectory of an animal or plant. Several examples of different models for functional data are given. We use the method of principle component analysis to obtain the necessary regularization in each model. Functional principal component analysis is summarized as a natural extension of the traditional vector principal component analysis. The first functional model is concerned with inference based on the mean function of a functional time series. We develop and asymptotically justify a testing procedure for the equality of means in two functional samples exhibiting temporal dependence. As a second example, we consider a quadratic functional regression model in which a scalar response depends on a functional predictor. We develop a test of the significance of the nonlinear term in the model. The asymptotic behavior of our testing procedure is established. In the third model, we observe two sequences of curves which are connected via an integral operator. This model includes linear models as well as autoregressive models in Hilbert spaces. We develop a procedure to test the stability of the model. In the fourth model, we propose a functional version of the popular ARCH model. We establish conditions for the existence of a strictly stationary solution, derive weak dependence and moment conditions, show consistency of the estimators, and perform an empirical study demonstrating how our model matches with real data.
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Perceptron
Functional decomposition
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Functional approach
Handwriting
Code (set theory)
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Abstract This article presents exploratory data analytic methodology for visualizing and summarizing data that can be represented as individual-specific curves. We propose a simplified form of functional data analysis. A nonparametric scatterplot smooth is applied to each individual's data, followed by a principal components analysis of the smoothed data. We then display the individual smooth curves in an array organized by principal component scores. The display suggests interpretable summary measures. The methodology is applied to the measurement of proliferative activity, a biomarker for colon cancer risk. We use the summary measures in the analysis of a pilot study clinical trial.
Exploratory data analysis
Exploratory analysis
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This paper is devoted to the R package fda.usc which includes some utilities for functional data analysis. This package carries out exploratory and descriptive analysis of functional data analyzing its most important features such as depth measurements or functional outliers detection, among others. The R package fda.usc also includes functions to compute functional regression models, with a scalar response and a functional explanatory data via non-parametric functional regression, basis representation or functional principal components analysis. There are natural extensions such as functional linear models and semi-functional partial linear models, which allow non-functional covariates and factors and make predictions. The functions of this package complement and incorporate the two main references of functional data analysis: The R package fda and the functions implemented by Ferraty and Vieu (2006).
R package
Exploratory data analysis
Complement
Functional decomposition
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Citations (338)
Since beginning of the nineties the statistical community has been interested
in developing models for functional data. Functional versions for many branches
of statistics have been given. Examples of such methods include exploratory
data analysis, linear models, longitudinal data or multivariate techniques. In
the same way that standard statistical methods have been generalized to be
used with functional data, it is possible to think that geostatistical methods
can be adapted to these type of data. In this work we propose a methodology
to carry out spatial prediction when measured data are curves. Our approach is
based on the functional linear concurrent model theory. The spatial prediction of
an unobserved curve is obtained as a linear combination of observed functions.
We adapt an optimization criterium used in multivariable spatial prediction to
estimate the kriging parameters. We use the Canadian temperature data set
showed in Ramsay and Silverman (2005) to illustrate the proposals.
Exploratory data analysis
Data set
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Functional decomposition is used in conceptual design to divide an overall problem with an unknown solution into smaller problems with known solutions. The procedure for functional decomposition, however, has not been formalized. In a larger effort to understand and develop rules for functional decomposition, this paper develops rules for composition of reverse-engineered functional models. First, the functional basis hierarchy is used in an attempt to compose the functional model of a hair dryer, which does not produce the desired results. Second, a set of rules for composition is presented and applied to the hair dryer functional model. This composed functional model is more similar to the desired decomposition result than the functional model developed by changing hierarchical levels. Ten additional functional models are also composed and the results shown. The findings demonstrate that composition rules can be developed empirically through analysis of functional models.
Functional decomposition
Functional design
Functional requirement
Functional approach
Functional organization
Functional specification
Functional group
Basis (linear algebra)
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