frun: Runs and local extremes
In ftnonpar: Features and Strings for Nonparametric Regression

Description Usage Arguments Value Note Author(s) References See Also

Calculation of bounds for functions such that the residuals satisfy a run criterion

1	frun(y, ..., alpha = 0.5, r = 0, mr = 0)

`y`	the data
`...`	an optional argument which specifies the approximate positions of the local extreme values. These should be consisten with the run length otherwise the result will be nonsensical. Should you wish to use this option then you should first run the macro without it. The item xb of the output list gives the acceptable limits of the local extreme values. You can then specify the positions within these limits.
`alpha`	Quantile determining the acceptable run length.
`r`	Acceptable run length: Overrides alpha if not 0
`mr`	mr=0 minimizes the run length consistent with the number of local extreme values found for the specified run length. mr=1 disables the option.

`l1`	lower bounds
`u1`	upper bounds
`l2`	lower bound with specified extremes: the default choices for the positions of the local extreme values are the mid-points of the intervals specified by xb above.
`u2`	upper bound with specified extremes
`f`	function between l2 and u2 satisfying run condition
`xb`	bounds for location of extremes: the position of the ith extreme value lies between xb[2i-1] and xb[2i]
`nx`	number of extremes
`r`	run length: may differ from specified if mr=1

IN GENERAL THE MEAN OF THE BOUNDS l2 AND u2 (l2+u2)/2 GIVES A BETTER REGRESSION FUNCTION THAN f. HOWEVER THIS FUNCTION IS INFINITE AT THE TWO ENDPOINTS AND AT LOCAL EXTREME VALUES. IN THESE INTERVALS IT CAN BE REPLACED BY ANY VALUES WHICH DO NOT ALTER THE NUMBER OF LOCAL EXTREME VALUES. THE MEDIAN OF THE y-VALUES IN THESE INTERVALS IS A REASONABLE CHOICE.

Laurie Davies Laurie.Davies@uni-essen.de

Davies, P. L. (1995) Data features. Statistica Neerlandica 49,185-245.

Davies, P. L. and Kovac, A. (2001) Local Extremes, Runs, Strings and Multiresolution (with discussion) Annals of Statistics. 29. p1-65

mintvmon,pmreg,l1pmreg

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