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Estimation of the mean of functional time series and a two‐sample problem
Author(s) -
Horváth Lajos,
Kokoszka Piotr,
Reeder Ron
Publication year - 2013
Publication title -
journal of the royal statistical society: series b (statistical methodology)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 6.523
H-Index - 137
eISSN - 1467-9868
pISSN - 1369-7412
DOI - 10.1111/j.1467-9868.2012.01032.x
Subject(s) - series (stratigraphy) , mathematics , inference , sample size determination , sample (material) , kernel (algebra) , sample mean and sample covariance , function (biology) , statistics , time series , variance (accounting) , set (abstract data type) , mathematical optimization , computer science , artificial intelligence , discrete mathematics , estimator , paleontology , chemistry , accounting , chromatography , evolutionary biology , business , biology , programming language
Summary. The paper is concerned with inference based on the mean function of a functional time series. We develop a normal approximation for the functional sample mean and then focus on the estimation of the asymptotic variance kernel. Using these results, we develop and asymptotically justify testing procedures for the equality of means in two functional samples exhibiting temporal dependence. Evaluated by means of a simulation study and application to a real data set, these two‐sample procedures enjoy good size and power in finite samples.