Rotation Sampling for Functional Data

Details Rotation Sampling for Functional Data Rotation Sampling for Functional Data

2012-04-19

arxiv.org/abs/1204.4494v2

Statistics

Methodology

Scientific paper

Survey sampling methods provide cost-effective solutions for monitoring global parameters in large populations. Although time-varying samples are known to outperform fixed panels in various instances of discrete-time repeated surveys, they have not yet been examined in the continuous-time setup of sensor networks. In this paper we devise sampling designs for functional data (that is, continuous signals) based on rotation sampling and stratification. We propose to periodically replace the sample according to a Markov chain, which allows for spatial and temporal adaptation to the network. Considering the Horvitz-Thompson estimator of the mean temporal signal, we show that the variance of the Integrated Squared Error (ISE) can be dramatically reduced by increasing the frequency or intensity of sample replacements. Further, the average ISE can be decreased by suitably allocating the sample across strata at replacement times. An application to simulated electricity consumption data illustrates the good performances of our sampling designs relative to fixed panels.

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