AntonAntonov/QuantileRegression

AntonAntonov`QuantileRegression`

QuantileRegression

QuantileRegression [data,ks_List,probs]
	finds the regression quantiles corresponding to the probabilities probs for a list of data as linear combinations of splines generated over the knots ks. With the signature

QuantileRegression [data,n_Integer,probs]
	n equally spaced knots are generated. The order of the splines is specified with the option InterpolationOrder .

Details and Options



Examples

(18)

Basic Examples

(1)

Make a random signal:

In[1]:=

SeedRandom[23];n=200;randData=Transpose[{Range[n],RandomReal[{0,100.},n]}];

Compute Quantile Regression with

knots for the probabilities

0.25

and

0.75

In[2]:=

qFuncs=

QuantileRegression

[randData,5,{0.25,0.75}];

Here are the formulas of the obtained regression quantiles:

In[3]:=

Simplify/@Through[qFuncs[x]]

Out[3]=



0.	x>200\|\|x<1
3818.78-70.5999x+0.433163 2 x -0.000875772 3 x	801 5 <x≤200
4099.05-75.8484x+0.465925 2 x -0.000943942 3 x	5x801
84.2683-0.501637x-0.00576232 2 x +0.0000412732 3 x	403 5 <x≤ 602 5
-62.9078+4.97638x-0.0737278 2 x +0.000322355 3 x	204 5 ≤x≤ 403 5
34.9017-2.21549x+0.102544 2 x -0.00111777 3 x	1≤x< 204 5
110.681-1.15976x-0.000296216 2 x +0.0000261401 3 x	True

0.	x>200\|\|x<1
506.187-14.1371x+0.14281 2 x -0.000456464 3 x	403 5 ≤x< 602 5
983.69-15.2439x+0.0846418 2 x -0.000155264 3 x	801 5 <x≤200
59.6756+1.19519x-0.0158668 2 x -0.0000579967 3 x	1≤x< 204 5
-759.529+17.4007x-0.119132 2 x +0.000268735 3 x	602 5 ≤x≤ 801 5
24.2224+3.80204x-0.0797601 2 x +0.000464008 3 x	True



Here is a plot of the original data and the obtained regression quantiles:

In[4]:=

ListLinePlot[{randData,qFuncs〚1〛/@randData〚All,1〛,qFuncs〚2〛/@randData〚All,1〛},PlotLegends{"data",0.25`,0.75`},PlotStyle{Thin,Thick,Thick},PlotTheme"Detailed"]

Out[4]=