ftnonpar (version 0.1-88)

mintvmon: Minimization of total variation

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

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")