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Activity Number: 133 - Statistical Methods for Functional Data
Type: Contributed
Date/Time: Monday, July 29, 2019 : 8:30 AM to 10:20 AM
Sponsor: Section on Nonparametric Statistics
Abstract #307270
Title: Rank Dynamics for Functional Data
Author(s): Yaqing Chen* and Matthew Dawson and Hans Mueller
Companies: University of California, Davis and University of California, Davis and UC Davis
Keywords: Decomposition of rank derivatives; Functional data analysis; House price dynamics; Major League Baseball; Z\"urich Longitudinal Growth Study

We study the dynamic behavior of cross-sectional ranks over time for functional data and show that the ranks of the observed curves at each time point and their evolution over time can yield valuable insights into the time-dynamics of functional data. This approach is of particular interest in sports statistics in addition to other areas where functional data arise. For the analysis of the dynamics of ranks, we obtain estimates of the cross-sectional ranks of functional data and introduce several statistics of interest for ranked functional data. To quantify the evolution of ranks over time, we develop a model for rank derivatives, in which we decompose rank dynamics into two components, where one component corresponds to population changes and the other to individual changes. We establish the joint asymptotic normality for suitable estimates of these two components. These approaches are illustrated with simulations and three longitudinal data sets: Growth curves obtained from the Z\"urich Longitudinal Growth Study, monthly house price data in the U.S. from 1980 to 2015, and Major League Baseball offensive data for the 2017 season.

Authors who are presenting talks have a * after their name.

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