segreg.bootstrap.boot_resample

boot_resample(indep, dep, fitted_values=None, resid=None, resample_cases=False)[source]

A single boot resampling for a regression model.

If resample_cases is False (the default), then both fitted_values and resid must be set. In this case, it is assumed that there is some (fitted) model of the form:

\[y = f(x) + \epsilon\]

and the fitted_values are \(\{f(x_i)\}\), where indep = \(\{x_1, x_2, \dots, x_n\}\). If resid = \(\{\epsilon_1, \epsilon_2, \dots, \epsilon_n\}\), then this function takes a random sample with replacement from resid, \(\{\epsilon_1^*, \epsilon_2^*, \dots, \epsilon_n^*\}\), and returns

\[\{f(x_i) + \epsilon_i^*\}\]

as the resampled dependent values.

Parameters

  • indep (array-like) – The independent data. Also called predictor, explanatory variable, regressor, or exogenous variable.

  • dep (array-like) – The dependent data. Also called response, regressand, or endogenous variable.

  • fitted_values (array-like of shape (len(indep),)) – The returned dependent data will be these values plus bootstrap residuals (random draws with replacement from resid).

  • resid (array-like of shape (len(indep),)) – Residuals from which to draw a bootstrap resample (random sample with replacement).

  • resample_cases (boolean, default False) – If True, the bootstrap will resample pairs with replacement from (indep, dep). See Section 6.2.4 in Davison and Hinkley, “Bootstrap Methods and their Application”.

Returns

  • indep_resample (numpy array) – When resample_cases is False (the default), the returned array is the input indep. That is, a copy is not made.

  • dep_resample (numpy array)