SpTe2M (version 1.0.3)

spte_decor: Decorrelate the spatio-temporal data

Description

The function spte_decor uses the estimated spatio-temporal mean and covariance to decorrelate the observed spatio-temporal data. After data decorrelation, each decorrelated observation should have asymptotic mean of 0 and asymptotic variance of 1, and the decorrelated data should be asymptotically uncorrelated with each other.

Usage

spte_decor(y, st, y0, st0, T = 1, ht = NULL, hs = NULL, gt = NULL, gs = NULL)

Value

st

Same as the one in the arguments.

std.res

The decorrelated data.

Arguments

y

A vector of \(N\) spatio-temporal observations to decorrelate.

st

A three-column matrix specifying the spatial locations and observation times of the observations to decorrelate.

y0

A vector of \(N_0\) in-control (IC) spatio-temporal observations from which the IC spatio-temporal mean and covariance functions can be estimated via spte_meanest and spte_covest.

st0

A three-column matrix specifying the spatial locations and times for all the spatio-temporal observations in y0.

T

The period of the spatio-temporal mean and covariance. Default value is 1.

ht

The temporal kernel bandwidth ht; default is NULL, and it will be chosen by the modified cross-validation mod_cv if ht=NULL.

hs

The spatial kernel bandwidth hs; default is NULL, and it will be chosen by the function mod_cv if hs=NULL.

gt

The temporal kernel bandwidth gt; default is NULL, and it will be chosen by minimizing the mean squared prediction error via cv_mspe if gt=NULL.

gs

The spatial kernel bandwidth gs; default is NULL, and it will be chosen by the function cv_mspe if gs=NULL.

Author

Kai Yang and Peihua Qiu

References

Yang, K. and Qiu, P. (2020). Online Sequential Monitoring of Spatio-Temporal Disease Incidence Rates. IISE Transactions, 52, 1218-1233.

Examples

library(SpTe2M)
data(sim_dat)
y <- sim_dat$y; st <- sim_dat$st
ids <- 1:500; y.sub <- y[ids]; st.sub <- st[ids,]
decor <- spte_decor(y.sub,st.sub,y0=y.sub,st0=st.sub)