|Statistical inference on curves|
Abstract: In this talk we will focus on the problem of testing the null hypothesis that the regression functions of two populations are equal versus one-sided alternatives under a general nonparametric homoscedastic regression model. To protect against atypical observations, the test statistic is based on the residuals obtained by using a robust estimate for the regression function under the null hypothesis. The asymptotic distribution of the test statistic is studied under the null hypothesis and under root-n local alternatives. A Monte Carlo study is performed to compare the finite sample behaviour of the proposed tests with the classical one obtained using local averages. A sensitivity analysis is carried on a real data set.
This is joint work with Graciela Boente (Universidad de Buenos Aires).
Ingrid Van Keilegom - "Estimation in measurement error problems under minimal conditions on the distribution of the signal and the noise".
Abstract: In this presentation I will talk about two research problems related to the identifiability and estimation in measurement error problems. We like to make as little assumptions as possible on the error and on the variable that is subject to measurement error, and especially we do not want to impose the heavy assumption that the variance of the error is known, which is a common assumption in the literature.
Marc Hallin - "Dynamic Principal Components and Optimal Dimension Reduction in Functional Time Series".
Abstract: Dimension reduction techniques are central in the analysis of high-dimensional and functional observations, and time series data are no exception. This talk, is addressing the problem of optimal dimension reduction for functional time series. Such time series arise frequently, e.g., when a continuous time process is segmented into some smaller natural units, such as days, each observation representing one intraday curve. We argue that functional principal component analysis (FPCA), which is a key technique in the field, does not provide an adequate dimension reduction in a time series context. FPCA is a static procedure which ignores the essential serial dependence features of the data, and does not enjoy, in the time series context, the Karhunen-LoÃ¨ve optimality justifying its success in the presence of independent observations. Inspired by Brillinger's theory of dynamic principal components, we propose a dynamic version of FPCA which is based on a frequency domain approach, and show that it provides the expected optimal dimension reduction. By means of a simulation study and an empirical illustration, we show the considerable improvement our method entails when compared to the usual (static) FPCA procedure.