March 31st 2016
Faculty of Economic and Business Sciences | Seminar 8
Robust inference procedures in functional data analysis
2016/03/31 – 12:00 h | Graciela Boente – Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires and CONICET, Argentina
Abstract
Functional data analysis provides modern analytical tools for data that are recoded as images or as a continuous phenomenon over a period of time. Because of the intrinsic nature of these data, they can be viewed as realizations of random functions often assumed to be in L2(I), with I a real interval or a finite dimensional Euclidean set.
In particular, functional principal components and functional canonical correlation are statistical procedures developed to reduce the dimensionality retaining as much information as possible with respect to the measure of interest. To be more precise, the first q functional principal components provide the best q-dimensional approximation to random elements in Hilbert spaces, while functional canonical correlation is a tool to quantify correlations between pairs of observed random curves for which a sample is available.
We will discuss some approaches leading to obtain estimators of the principal directions or the canonical functions less sensitive to atypical observations. In particular, the robust procedures developed to estimate the principal directions can be used to construct diagnostic measures. If possible, we will also discuss methods to define robust estimators under a semi-linear partly linear model.
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Method of Maximum combination for simultaneous inferences
2016/03/31 – 13:00 h | María Álvarez – EUETI, University of Vigo
Abstract
In statistics one frequently needs to carry out simultaneous inferences on a linear combination of various unknown parameters. These combinations often arise to explain the causes of significance of the homogeneity test for all the parameters. When there are many combinations (or when there is only one, but which was chosen “a posteriori”, that is, after seeing the data), the traditional method for realizing the inferences is that of Scheffé, which in essence only allows one to determine the theoretical distribution on which the said inferences should be based.
This work proposes an alternative methodology based on the maximization of the contrast statistic in the coefficient of the combination. This new method, compatible with Scheffé’s method, in addition yields the statistic which should be used for the global test, as well as the combination of maximum significance. The method is illustrated in the cases of K means of normal distributions and K binomial proportions (independent samples). In the second case, the method allows a homogeneity test that is more powerful than Pearson’s classic chi-squared test to be obtained.
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