bede {inflection} | R Documentation |
Bisection Extremum Distance Estimator Method
Description
It iterates in a way similar to the well known bisection method in root finding, with the only exception that
our intervals contain the inflection point now and the rule for choosing them follows definitions
and Lemmas of [1], [2].
Usage
bede(x, y, index)
Arguments
x |
The numeric vector of x-abscissas, must be of length at least 4. |
y |
The numeric vector of the noisy or not y-ordinates, must be of length at least 4. |
index |
If data is convex/concave then index=0 |
Details
It is the fastest solution for very large data sets, over one million rows.
Value
It returns a list of two elements:
iplast |
the last EDE estimation that was found |
iters |
a matrix with 4 columns ("n", "a", "b", "EDE") that give the number of x-y pairs used at each iteration, the [a,b] range where we searched and the EDE estimated inflection point. |
Author(s)
Demetris T. Christopoulos
References
[1]Demetris T. Christopoulos (2014). Developing methods for identifying the inflection point of a convex/concave curve. arXiv:1206.5478v2 [math.NA]. https://arxiv.org/pdf/1206.5478v2.pdf
[2]Demetris T. Christopoulos (2016). On the efficient identification of an inflection point.International Journal of Mathematics and Scientific Computing, (ISSN: 2231-5330), vol. 6(1). https://veltech.edu.in/wp-content/uploads/2016/04/Paper-04-2016.pdf
See Also
See also the simple version ede
, edeci
and iterations plot using findipiterplot
.
Examples
#
#Fisher-pry model with heavy noise, unequal spaces
#and 1 million cases:
N=10^6+1;
set.seed(2017-05-11);x=sort(runif(N,0,10));y=5+5*tanh(x-5)+runif(N,-1,1);
#
ptm <- proc.time()
tede=ede(x,y,0);tede;proc.time() - ptm
# j1 j2 chi
# EDE 351061 648080 4.997139
# user system elapsed
# 0.02 0.02 0.05
#