Modified Hypograph Index of univariate functional dataset

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Description

This function computes the Modified Hypograph Index (MEI) of elements of a univariate functional dataste.

Usage

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MHI(Data)

## S3 method for class 'fData'
MHI(Data)

## Default S3 method:
MHI(Data)

Arguments

Data

either an fData object or a matrix-like dataset of functional data (e.g. fData$values), with observations as rows and measurements over grid points as columns.

Details

Given a univariate functional dataset, X_1(t), X_2(t), …, X_N(t), defined over a compact interval I=[a,b], this function computes the MHI, i.e.:

MHI( X(t) ) = \frac{1}{N} ∑_{i=1}^N \tilde{λ}( X(t) ≥q X_i(t) ),

where \tilde{λ}(\cdot) is the normalised Lebesgue measure over I=[a,b], that is \tilde{λ(A)} = λ( A ) / ( b - a ).

Value

The function returns a vector containing the values of MHI for each element of the functional dataset provided in Data.

References

Lopez-Pintado, S. and Romo, J. (2012). A half-region depth for functional data, Computational Statistics and Data Analysis, 55, 1679-1695.

Arribas-Gil, A., and Romo, J. (2014). Shape outlier detection and visualization for functional data: the outliergram, Biostatistics, 15(4), 603-619.

See Also

HI, MEI, EI, fData

Examples

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N = 20
P = 1e2

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

C = exp_cov_function( grid, alpha = 0.2, beta = 0.3 )

Data = generate_gauss_fdata( N,
                             centerline = sin( 2 * pi * grid ),
                             C )
fD = fData( grid, Data )

MHI( fD )

MHI( Data )

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