theplu::yat::regression::OneDimensionalWeighted Class Reference

Interface Class for One Dimensional fitting in a weighted fashion. More...

#include <yat/regression/OneDimensionalWeighted.h>

Inheritance diagram for theplu::yat::regression::OneDimensionalWeighted:

List of all members.

Public Member Functions

OneDimensionalWeighted (void)

virtual ~OneDimensionalWeighted (void)

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

virtual double predict (const double x) const =0

double prediction_error2 (const double x, const double w=1.0) const

double r2 (void) const

virtual double s2 (double w=1) const =0

virtual double standard_error2 (const double x) const =0

Protected Attributes

statistics::AveragerPairWeighted ap_

double chisq_

Chi-squared.

Detailed Description

Interface Class for One Dimensional fitting in a weighted fashion.

Constructor & Destructor Documentation

theplu::yat::regression::OneDimensionalWeighted::OneDimensionalWeighted ( void )

Default Constructor.

virtual theplu::yat::regression::OneDimensionalWeighted::~OneDimensionalWeighted ( void ) [virtual]

Destructor

Member Function Documentation

virtual void theplu::yat::regression::OneDimensionalWeighted::fit	(	const utility::VectorBase &	x,
		const utility::VectorBase &	y,
		const utility::VectorBase &	w
	)			`[pure virtual]`

This function computes the best-fit given a model (see specific class for details) by minimizing $\sum{w_i(\hat{y_i}-y_i)^2}$ , where $\hat{y}$ is the fitted value. The weight $ w_i $ should be proportional to the inverse of the variance for $ y_i $

Implemented in theplu::yat::regression::LinearWeighted, theplu::yat::regression::NaiveWeighted, and theplu::yat::regression::PolynomialWeighted.

virtual double theplu::yat::regression::OneDimensionalWeighted::predict ( const double x ) const [pure virtual]

Returns:: expected value in x according to the fitted model

Implemented in theplu::yat::regression::LinearWeighted, theplu::yat::regression::NaiveWeighted, and theplu::yat::regression::PolynomialWeighted.

double theplu::yat::regression::OneDimensionalWeighted::prediction_error2	(	const double	x,
		const double	w = `1.0`
	)			const

The prediction error is defined as expected squared deviation a new data point (with weight w) will be from the model value $E((Y|x - \hat{y}(x))^2|w)$ 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 $ .

$E((Y|x - E(Y|x))^2|w) + E((E(Y|x) - \hat{y}(x))^2)$

Returns:: expected prediction error for a new data point in x with weight w.

double theplu::yat::regression::OneDimensionalWeighted::r2 ( void ) const

r2 is defined as $\frac{\sum w_i(y_i-\hat{y}_i)^2}{\sum w_i(y_i-m_y)^2}$ or the fraction of the variance explained by the regression model.

virtual double theplu::yat::regression::OneDimensionalWeighted::s2 ( double w = 1 ) const [pure virtual]

$ s^2 $ is the estimation of variance of residuals or equivalently the conditional variance of Y.

Returns:: Conditional variance of Y

Implemented in theplu::yat::regression::LinearWeighted, theplu::yat::regression::NaiveWeighted, and theplu::yat::regression::PolynomialWeighted.

virtual double theplu::yat::regression::OneDimensionalWeighted::standard_error2 ( const double x ) const [pure virtual]

The standard error is defined as $E((Y|x,w - \hat{y}(x))^2)$

Returns:: error of model value in x

Implemented in theplu::yat::regression::LinearWeighted, theplu::yat::regression::NaiveWeighted, and theplu::yat::regression::PolynomialWeighted.

Member Data Documentation

statistics::AveragerPairWeighted theplu::yat::regression::OneDimensionalWeighted::ap_ [protected]

Averager for pair of x and y

double theplu::yat::regression::OneDimensionalWeighted::chisq_ [protected]

Chi-squared.

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

The documentation for this class was generated from the following file:

yat/regression/OneDimensionalWeighted.h


Public Member Functions
	OneDimensionalWeighted (void)
virtual	~OneDimensionalWeighted (void)
virtual void	fit (const utility::VectorBase &x, const utility::VectorBase &y, const utility::VectorBase &w)=0
virtual double	predict (const double x) const =0
double	prediction_error2 (const double x, const double w=1.0) const
double	r2 (void) const
virtual double	s2 (double w=1) const =0
virtual double	standard_error2 (const double x) const =0
Protected Attributes
statistics::AveragerPairWeighted	ap_
double	chisq_
	Chi-squared.