在Python中，如何拟合最小分位数b样条回归线？

Question

You can find the minimum quantile regression line fit like this:

import statsmodels.api as sm
import statsmodels.formula.api as smf
from statsmodels.regression.quantile_regression import QuantReg

mod = smf.quantreg('y ~ x', data)
res = mod.fit(q = 0.000001)

But what if you want to find the minimum b-spline regression fit line?

Answer 1

If you want cubic b-splines you can do this:

#!/usr/bin/env python3

import matplotlib.pyplot as plt
import numpy as np
import statsmodels.formula.api as smf


x = np.linspace(0, 2, 100)
y = np.sqrt(x) * np.sin(2 * np.pi * x) + np.random.random_sample(100)

mod = smf.quantreg('y ~ bs(x, df=9)', dict(x=x, y=y))
res = mod.fit(q=0.000001)
print(res.summary())

plt.plot(x, y, '.')
plt.plot(x, res.predict(), 'r')
plt.show()

You will need to play with the degrees of freedom ( df parameter) or specify the knots parameter instead. Depending on your data you may wish to use cr() for natural cubic splines or cc() for cyclic cubic splines. See http://patsy.readthedocs.io/en/latest/spline-regression.html for more details.