Median polish trend

Description

Direct method to remove trend of spatio - temporal data througth median polish.

Usage

1
removetrendMPst(MPST,eps=0.01, maxiter=10L)

Arguments

MPST

object of class ConstructMPst

eps

real number greater than 0, default 0.01. A tolerance for convergence of median polish.

maxiter

the maximum number of iterations. Default 10.

Details

Robust method introduced for Cressie(1993) and enhanced by Berke(2001) to remove trend of a space - time process with data ≤ft\{y(\mathbf{s}_{abc},t), a=1,...,U; b=1,...,V; c=1,...,W, t=1,...,n \right\}

Y(\mathbf{s}_{abc},t)= μ_{y}(\mathbf{s}_{abc},t) + δ _{abct}

where

μ _{y}(\mathbf{s}_{abc},t)= μ +α _{a} + β _{b} + ξ _{c} + τ _{t}

and δ _{abct} is a fluctuation arising from natural variability and from the measurement process. Additionally, μ is an overall mean, α_{a} is the a-th row effect, β_{b} is the effect b-th column effect, ξ_{c} is the c-th layer effect, τ _{t} is the t-th time effect.

Value

data.frame with the following fields:

ET

indicate the time of a observation

x

spatial coordinates x

y

spatial coordinates y

z

spatial coordinates z

Trend

trend calculated through median polish space - time

Value

observed values

Residual

Residual = Value-Trend

References

Berke, O. (2001). Modified median polish kriging and its application to the wolfcamp - aquifer data. Environmetrics, 12(8):731-748.[link]

Cressie, N. (1993). Statistics for spatial data. Wiley series in probability and statistics.[link]

Examples

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## Not run:
data(Metadb)
x<-matrix(0,1,37)
for(i in 1:37){
 x[,i] <- 2007 + (seq(0, 36)/12)[i]
}
x<-as.Date (as.yearmon(x), frac = 1)
time = as.POSIXct(x, tz = "GMT")

MPST<-ConstructMPst(Metadb[,-c(1:4)],time,pts=Metadb[,2:4],Delta=c(7,6,5))
residuals<-removetrendMPst(MPST,eps=0.01, maxiter=2)
## End(Not run)