Estimation of the mean of functional time series and a two‐sample problem

By Lajos Horv'ath, Piotr Kokoszka, Ron Reeder. 2011

195 citations recorded by the source corpus.

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.

Subfields: Finance, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/1505c949ed4b9b97c6c2be4b16a82abef1f3e90e

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Citations in the corpus

Asymptotic normality of the principal components of functional time series (2013, methodology): “We focused on L4-m-approximability because it has already been used in the functional context, in addition to Hörmann and Kokoszka [17]; see also [12,20].”
Testing stationarity of functional time series (2014, background): “(2.8) It is proven in Horváth et al. (2013) that the series in (2.8) is convergent in L 2 .”
A Two Sample Distribution-Free Test for Functional Data with Application to a Diffusion Tensor Imaging Study of Multiple Sclerosis (2016, background): “…of two independent samples of curves Ramsay and Silverman (2005) introduced a pointwise t-test, Zhang et al. (2010) presented an L2-norm-based test, Horváth et al. (2013) proposed a test based on the sample means of the curves and Staicu et al. (2014) developed a pseudolikelihood ratio test.”
Testing relevant hypotheses in functional time series via self‐normalization (2018, methodology): “More recently Horváth et al. (2013) suggested tests for a comparison of two mean functions from temporally dependent curves under model-free assumptions and Pomann et al. (2016) compared the distributions of two samples by methods which are based on functional principal component analysis.”