scpt: Spatio-Temporal Change-Point Test
In scpt: Change Point Test for Spatio-Temporal Functional Data

Description Usage Arguments Details Value

Caries out a change-point test for sequences of functional data observed at different spatial locations. Three tests are carried out and three pvalues are returned.

1 2	spatial_change_test(DATA3, loc, varprop = 0.85, ncores = "all", reps_per_core = 100)

`DATA3`	Data for testing. This should be an 3D array with the first coordinate indicating the temporal location on a curve, the second the spatial location, and the third the repitition number/time series iteration.
`loc`	Two column matrix of spatial locations.
`varprop`	Proportion of temporal variance explained in first two tests (third test uses all explained variance)
`ncores`	Number of cores to be used for monte carlo sampling.
`reps_per_core`	Number of monte carlo samples per core.

Carries out three different change point tests as outlined in Gromenko, Kokoszka, and Reimherr (2015). P-values are generated using Monte-Carlo. The total MC sample size is given by ncores*reps_per_core. Be warned that the code will not try to use more cores than are available, so users should choose the ncores value appropriately. By default, the code will use all available cores. This will cause a computer to be slugish in other tasks and so the user should be careful when using the default.

Data3[i,j,k] indicates an the ith observation at the jth location and on the kth curve. It is important that this order is accurate. The method assumes that the spatio-temporal covariance is separable. Methods such as Constantinou, Kokoszka, and Reimherr (2015) can be used to check this assumption. This allows the spatial and temporal covariances to be estimated separately. The spatial covariance is assumed to be stationary and isotropic. A tapered bsplines estimator is then used to estiamte it nonparametrically. No assumptions are made on the form of the temporal covariance function. It is estimated by pooling appropriately across space.

The testing procedures are all based on integrated CUSUM test statistics. The primary difference between the three is in how they handle the temporal covariance. The first statistic uses FPCA to reduce the dimension of the data and normalizes by the corresponding eigenvalues. The second does the same, but does not normalize by the eigenvalue. The third procedure does not use FPCA and does not normalize by the eigenvalues. It can be thought of as the same as procedure 2, but with all dimensions included. The first procedure should be used with caution as it can be unstable for smaller sample sizes/larger numbers of FPCs.

Returns three values for three change-point tests. The first normalizes each FPC, while the second two do not. The only difference between the second and third is that the third uses all explained variance.

scpt documentation built on May 2, 2019, 5:48 p.m.