Maximum order relation between univariate functional data

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Description

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.

Usage

1

Arguments

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.

Details

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.

Value

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

References

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.

See Also

maxima, minima, fData, area_ordered

Examples

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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 )

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