spte_meanest {SpTe2M}

Estimate the spatio-temporal mean function

Description

The function spte_meanest provides a major tool for estimating the spatio-temporal mean function nonparametrically (cf., Yang and Qiu 2018 and 2022).

Usage

spte_meanest(y, st, ht = NULL, hs = NULL, cor = FALSE, stE = NULL)

Arguments

y

A vector of spatio-temporal observations.

st

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

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.

cor

A logical indicator where cor=FALSE implies that the covariance is not taken into account and the local linear kernel smoothing procedure is used for estimating the mean function (cf., Yang and Qiu 2018) and cor=TRUE implies that the covariance is accommodated and the three-step local smoothing approach is used to estimate the mean function (cf., Yang and Qiu 2022). Default is FALSE.

stE

A three-column matrix specifying the spatial locations and times where we want to calculate the estimate of the mean. Default is NULL, and stE=st if stE=NULL.

Value

bandwidth

The bandwidths (ht, hs) used in the estimation procedure.

stE

Same as the one in the arguments.

muhat

The estimated mean values at the spatial locations and times specified by stE.

Author(s)

Kai Yang [e-mail] and Peihua Qiu

References

Yang, K. and Qiu, P. (2018). Spatio-Temporal Incidence Rate Data Analysis by Nonparametric Regression. Statistics in Medicine, 37, 2094-2107.

Yang, K. and Qiu, P. (2022). A Three-Step Local Smoothing Approach for Estimating the Mean and Covariance Functions of Spatio-Temporal Data. Annals of the Institute of Statistical Mathematics, 74, 49-68.

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,]
cov.est <- spte_meanest(y.sub,st.sub)