max_ordered: Maximum order relation between univariate functional data
In roahd: Robust Analysis of High Dimensional Data

Description Usage Arguments Details Value References See Also Examples

This function implements an order relation between univariate functional data based on the maximum relation, that is to say a pre-order relation obtained by comparing the maxima of two different functional data.

1	max_ordered(fData, gData)

`fData`	the first univariate functional dataset containing elements to be compared, in form of `fData` object.
`gData`	the second univariate functional dataset containing elements to be compared, in form of `fData` object.

Given a univariate functional dataset, X_1(t), X_2(t), …, X_N(t) and another functional dataset Y_1(t), Y_2(t), …, Y_M(t) defined over the same compact interval I=[a,b], the function computes the maxima in both the datasets, and checks whether the first ones are lower or equal than the second ones.

By default the function tries to compare each X_i(t) with the corresponding Y_i(t), thus assuming N=M, but when either N=1 or M=1, the comparison is carried out cycling over the dataset with fewer elements. In all the other cases (N\neq M, and either N \neq 1 or M \neq 1) the function stops.

The function returns a logical vector of length \max(N,M) containing the value of the predicate for all the corresponding elements.

Valencia, D., Romo, J. and Lillo, R. (2015). A Kendall correlation coefficient for functional dependence, Universidad Carlos III de Madrid technical report, http://EconPapers.repec.org/RePEc:cte:wsrepe:ws133228.

maxima, minima, fData, area_ordered

P = 1e2

grid = seq( 0, 1, length.out = P )

Data_1 = matrix( c( 1 * grid,
                    2 *  grid ),
                 nrow = 2, ncol = P, byrow = TRUE )

Data_2 = matrix( 3 * ( 0.5 - abs( grid - 0.5 ) ),
                 nrow = 1, byrow = TRUE )

Data_3 = rbind( Data_1, Data_1 )


fD_1 = fData( grid, Data_1 )
fD_2 = fData( grid, Data_2 )
fD_3 = fData( grid, Data_3 )

max_ordered( fD_1, fD_2 )

max_ordered( fD_2, fD_3 )