# MCS: Multivariate conditional Spearman's rho In texmex: Threshold exceedences and multivariate extremes

## Description

Compute multivariate conditional Spearman's rho over a range of quantiles.

## Usage

 ``` 1 2 3 4 5 6 7 8 9 10``` ```MCS(X, p = seq(0.1, 0.9, by = 0.1)) bootMCS(X, p = seq(0.1, 0.9, by = 0.1), R = 100, trace = 10) ## S3 method for class 'MCS' plot(x, xlab="p", ylab="MCS", ...) ## S3 method for class 'bootMCS' summary(object, alpha=0.05, ...) ## S3 method for class 'bootMCS' plot(x, xlab="p", ylab="MCS", alpha=0.05, ylim, ...) ```

## Arguments

 `X` A matrix of numeric variables. `p` The quantiles at which to evaluate. `R` The number of bootstrap samples to run. Defaults to `R = 100`. `trace` How often to inform the user of progress. Defaults to `trace = 10`. `x, object` An object of class `MCS` or `bootMCS`. `xlab, ylab` Axis labels. `alpha` A (1 - alpha)% pointwise confidence interval will be produced. Defaults to `alpha = 0.05`. `ylim` Plotting limits for bootstrap plot. `...` Optional arguments to be passed into methods.

## Details

The method is described in detail by Schmid and Schmidt (2007). The main code was written by Yiannis Papastathopoulos, wrappers written by Harry Southworth.

When the result of a call to `bootMCS` is plotted, simple quantile bootstrap confidence intervals are displayed.

## Value

MCS returns an object of class `MCS`. There are plot and summary methods available for this class.

 `MCS ` The estimated correlations. `p ` The quantiles at which the correlations were evaluated at `call` The function call used.

bootMCS returns an object of class `bootMCS`. There are plot and summary methods available for this class.

 `replicates` Bootstrap replicates. `p ` The quantiles at which the correlations were evaluated at `R` Number of bootstrap samples. `call` The function call used.

## Author(s)

Yiannis Papastathopoulos, Harry Southworth

## References

F. Schmid and R. Schmidt, Multivariate conditional versions of Spearman's rho and related measures of tail dependence, Journal of Multivariate Analysis, 98, 1123 – 1140, 2007

`chi`
 ```1 2 3 4 5 6``` ```D <- liver[liver\$dose == "D",] plot(D) # Following lines commented out to keep CRAN robots happy #Dmcs <- bootMCS(D[, 5:6]) #Dmcs #plot(Dmcs) ```