trend (version 0.0.1)

partial.mk.test: Partial Mann-Kendall Test

Description

Performs a partial Mann-Kendall test

Usage

partial.mk.test(x, z)

Arguments

x

a "vector" or "ts" object that contains the variable, which is tested for trend (i.e. correlated with time)

z

a "vector" or "ts" object that contains the variable, which effect on "x" is partialled out

Value

• An object of class "htest"
• method
  a character string indicating the chosen test
• data.name
  a character string giving the name(s) of the data
• statistic
  the value of the test statistic
• estimate
  the Mann-Kendall score S and the variance varS
• alternative
  a character string describing the alternative hypothesis
• p.value
  the p-value of the test

Warning

Current Version is for complete observations only. The "method=='Partial'" is in testing mode.

Details

According to Libiseller and Grimvall (2002), the expected value for the Mann-Kendall Score of variable "a" that is correlated with the covariate "b" is: $E = S_b * \sigma_{ab} / \sigma_{bb}$ Furthermore, the expected variance of "a" is: $Var = \sigma_{aa} - \sigma_{ab} / \sigma_{bb} * \sigma_{ba}$ Finally, the Z-Quantile is defined as: $Z = (S_a - E) / \sqrt(Var)$

References

Libiseller, C. and Grimvall, A., (2002). Performance of partial Mann-Kendall tests for trend detection in the presence of covariates. Environmetrics 13, 71-84, http://dx.doi.org/10.1002/env.507.

See Also

partial.cor.trend.test, summary.trend.test

Examples

data(maxau)
s <- maxau[,"s"]; Q <- maxau[,"Q"]
partial.mk.test(s,Q)