mintvmon: Minimization of total variation

In ftnonpar: Features and Strings for Nonparametric Regression

Description

Finds a function vector which minimizes the total variation of the function or a derivative under multiresolution constraints and monotonicity and convexity constraints.

Usage

mintvmon(y, sigma = -1, DYADIC = TRUE, thresh = -1, method = 2, MONCONST = TRUE, CONVCONST = FALSE)

Arguments

y	observed values (ordered by value of independent variable).
sigma	if set to a positive value the standard deviation is set to sigma and not estimated from the data
DYADIC	logical, if T (default) the multiresolution constraints are only verifeid on intervals with dyadic endpoints
thresh	if set to a positive value other thresholds for the multiresolution criterion than the default sqrt(2*log(n))*sigma can be used.
method	Number of derivative the total variation of which is minimzed. Possible values are 0,1,2. Higher values lead to numerical inconsistencies.
MONCONST	logical, if T (default) additional monotonicty constraints are gathered from minimzing the total variation of f. Makes only sense, if method is 1 or 2.
CONVCONST	logical, if T (default) additional convexity constraints are gathered from minimzing the total variation of f'. Makes only sense, if method is 2.

Value

A list with components

y	The approximation of the given data
derivsign	Vector of 1 and -1, monotonicty constraints used if MONCONST was true
secsign	Vector of 1 and -1, convexity constraints used if CONVCONST was true
jact	Left endpoints of active multiresolution constraints for the final approximation
kact	Right endpoints of active multiresolution constraints for the final approximation
signact	Vector of 1 and -1, gives for each active multiresolution constraints, if the residuals on that interval attain upper or lower bound
pl	Left endpoint of piecewise constant intervals of the derivative of f being minmized
pr	Right endpoint of piecewise constant intervals of the derivative of f being minmized

Author(s)

Arne Kovac

References

Kovac, A. (2003) Minimizing Total Variation under Multiresolution Conditions

See Also

pmreg

Examples

data(djdata)
djdoppler.tv0 <- mintvmon(djdoppler,method=0)
djdoppler.tv1 <- mintvmon(djdoppler,method=1)
djdoppler.tv2 <- mintvmon(djdoppler)
par(mfrow=c(2,2))
plot(djdoppler,col="lightgrey")
plot(djdoppler,col="lightgrey")
lines(djdoppler.tv0$y,col="blue")
plot(djdoppler,col="lightgrey")
lines(djdoppler.tv1$y,col="green")
plot(djdoppler,col="lightgrey")
lines(djdoppler.tv2$y,col="red")

ftnonpar documentation built on May 2, 2019, 3:04 a.m.