Bootstrapping

Functions

• apop_data * apop_jackknife_cov (apop_data *in, apop_model model)
• apop_data * apop_bootstrap_cov (apop_data *data, apop_model model, gsl_rng *rng, int iterations)

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Function Documentation

apop_data* apop_bootstrap_cov	(	apop_data *	data,
		apop_model	model,
		gsl_rng *	rng,
		int	iterations
	)

Give me a data set and a model, and I'll give you the bootstrapped covariance matrix of the parameter estimates.

Parameters:

	data	The data set. An apop_data set where each row is a single data point. (No default)
	model	An apop_model, whose estimate method will be used here. (No default)
	iterations	How many bootstrap draws should I make? (default: 1,000)
	rng	An RNG that you have initialized, probably with apop_rng_alloc. (Default: see Auto-allocated RNGs)

Returns:

An apop_data set whose matrix element is the estimated covariance matrix of the parameters.

This function uses the Designated initializers syntax for inputs.

apop_data* apop_jackknife_cov	(	apop_data *	in,
		apop_model	model
	)

Give me a data set and a model, and I'll give you the jackknifed covariance matrix of the model parameters.

The basic algorithm for the jackknife (with many details glossed over): create a sequence of data sets, each with exactly one observation removed, and then produce a new set of parameter estimates using that slightly shortened data set. Then, find the covariance matrix of the derived parameters.

Should I use the jackknife or the bootstrap? As a broad rule of thumb, the jackknife works best on models that are closer to linear. The worse a linear approximation does (at the given data), the worse the jackknife approximates the variance.

Sample usage:

apop_data_show(apop_jackknife_cov(your_data, your_model));

Parameters:

	in	The data set. An apop_data set where each row is a single data point.
	model	An apop_model, that will be used internally by apop_estimate.

Returns:

An apop_data set whose matrix element is the estimated covariance matrix of the parameters.