Interface Class for One Dimensional fitting. More...

#include <yat/regression/OneDimensional.h>

Inheritance diagram for theplu::yat::regression::OneDimensional:

Public Member Functions
	OneDimensional (void)
	The default constructor.

virtual	~OneDimensional (void)
	The destructor.

double	chisq (void) const
	Chi-squared. More...

virtual void	fit (const utility::VectorBase &x, const utility::VectorBase &y)=0

virtual double	predict (const double x) const =0

double	prediction_error2 (const double x) const

std::ostream &	print (std::ostream &os, const double min, double max, const unsigned int n) const
	print output to ostream os More...

double	r2 (void) const

virtual double	s2 (void) const =0

virtual double	standard_error2 (const double x) const =0

Protected Member Functions
double	variance (void) const

Protected Attributes
statistics::AveragerPair	ap_

double	chisq_

Detailed Description

Interface Class for One Dimensional fitting.

See Also: OneDimensionalWeighted.

Member Function Documentation

double theplu::yat::regression::OneDimensional::chisq ( void ) const

Chi-squared.

Chi-squared is defined as the $\sum{(\hat{y_i}-y_i)^2}$

virtual void theplu::yat::regression::OneDimensional::fit	(	const utility::VectorBase &	x,
		const utility::VectorBase &	y
	)

pure virtual

This function computes the best-fit given a model (see specific class for details) by minimizing $\sum{(\hat{y_i}-y_i)^2}$ , where $\hat{y}$ is the fitted value.

Implemented in theplu::yat::regression::Linear, theplu::yat::regression::Polynomial, and theplu::yat::regression::Naive.

virtual double theplu::yat::regression::OneDimensional::predict ( const double x ) const

pure virtual

Returns: expected value in x accrding to the fitted model

Implemented in theplu::yat::regression::Linear, theplu::yat::regression::Polynomial, and theplu::yat::regression::Naive.

double theplu::yat::regression::OneDimensional::prediction_error2 ( const double x ) const

The prediction error is defined as the expected squared deviation a new data point will have from value the model provides: $E(Y|x - \hat{y}(x))^2$ and is typically divided into the conditional variance ( see s2() ) given $ x $ and the squared standard error ( see standard_error2() ) of the model estimation in $ x $ .

Returns: expected squared prediction error for a new data point in x

std::ostream& theplu::yat::regression::OneDimensional::print	(	std::ostream &	os,
		const double	min,
		double	max,
		const unsigned int	n
	)		const

print output to ostream os

Printing estimated model to os in the points defined by min, max, and n. The values printed for each point is the x-value, the estimated y-value, and the estimated standard deviation of a new data poiunt will have from the y-value given the x-value (see prediction_error()).

Parameters

os	Ostream printout is sent to
n	number of points printed
min	smallest x-value for which the model is printed
max	largest x-value for which the model is printed