partial.mk.test: Partial Mann-Kendall Trend Test

In trend: Non-Parametric Trend Tests and Change-Point Detection

Partial Mann-Kendall Trend Test

Description

Performs a partial Mann-Kendall Trend Test

Usage

partial.mk.test(x, y, alternative = c("two.sided", "greater", "less"))

Arguments

x	a "vector" or "ts" object that contains the variable, which is tested for trend (i.e. correlated with time)
y	a "vector" or "ts" object that contains the variable, which effect on "x" is partialled out
alternative	character, the alternative method; defaults to "two.sided"

Details

According to Libiseller and Grimvall (2002), the test statistic for x with its covariate y is

z = \frac{S_x - r_{xy} S_y}{\left[ \left( 1 - r_{xy}^2 \right) n \left(n - 1 \right) \left(2 n + 5 \right) / 18 \right]^{0.5}}

where the correlation r is calculated as:

r_{xy} = \frac{\sigma_{xy}} {n \left(n - 1\right) \left(2 n + 5 \right) / 18}

The conditional covariance between x and y is

\sigma_{xy} = \frac{1}{3} \left[K + 4 \sum_{j=1}^n R_{jx} R_{jy} - n \left(n + 1 \right) \left(n + 1 \right) \right]

with

K = \sum_{1 \le i < j \le n} \mathrm{sgn} \left\{ \left( x_j - x_i \right) \left( y_j - y_i \right) \right\}

and

R_{jx} = \left\{ n + 1 + \sum_{i=1}^n \mathrm{sgn} \left( x_j - x_i \right) \right\} / 2

Value

A list with 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, the variance varS and the correlation between x and y
alternative	a character string describing the alternative hypothesis
p.value	the p-value of the test
null.value	the null hypothesis

Note

Current Version is for complete observations only. The test statistic is not corrected for ties.

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, \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1002/env.507")}.

See Also

partial.cor.trend.test,

Examples

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

trend documentation built on Oct. 10, 2023, 9:06 a.m.