source: trunk/yat/regression/OneDimensionalWeighted.h @ 729

#ifndef _theplu_yat_regression_onedimensioanlweighted_
#define _theplu_yat_regression_onedimensioanlweighted_

// $Id: OneDimensionalWeighted.h 729 2007-01-05 16:00:15Z peter $

/*
  Copyright (C) The authors contributing to this file.

  This file is part of the yat library, http://lev.thep.lu.se/trac/yat

  The yat library is free software; you can redistribute it and/or
  modify it under the terms of the GNU General Public License as
  published by the Free Software Foundation; either version 2 of the
  License, or (at your option) any later version.

  The yat library is distributed in the hope that it will be useful,
  but WITHOUT ANY WARRANTY; without even the implied warranty of
  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
  General Public License for more details.

  You should have received a copy of the GNU General Public License
  along with this program; if not, write to the Free Software
  Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA
  02111-1307, USA.
*/

#include "yat/statistics/AveragerPairWeighted.h"

#include <ostream>

namespace theplu {
namespace yat {
namespace utility {
  class vector;
}
namespace regression {
  
  ///
  /// Abstract Base Class for One Dimensional fitting in a weighted
  /// fashion.
  ///
  class OneDimensionalWeighted 
  {
  
  public:
    ///
    /// Default Constructor.
    ///
    OneDimensionalWeighted(void);

    ///
    /// Destructor
    ///
    virtual ~OneDimensionalWeighted(void);
         
    /**
       This function computes the best-fit given a model (see
       specific class for details) by minimizing \f$
       \sum{w_i(\hat{y_i}-y_i)^2} \f$, where \f$ \hat{y} \f$ is the
       fitted value. The weight \f$ w_i \f$ should be proportional
       to the inverse of the variance for \f$ y_i \f$
    */
    virtual void fit(const utility::vector& x, const utility::vector& y, 
                     const utility::vector& w)=0;

    ///
    /// @return expected value in @a x according to the fitted model
    ///
    virtual double predict(const double x) const=0;

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

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

       @return expected prediction error for a new data point in @a x
       with weight @a w.
    */
    double prediction_error2(const double x, const double w=1.0) const; 

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

    /**
       \f$ s^2 \f$ is the estimation of variance of residuals or
       equivalently the conditional variance of Y.

       @return Conditional variance of Y
    */
    virtual double s2(double w=1) const=0;

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

       @return error of model value in @a x
    */
    virtual double standard_error2(const double x) const=0;

  protected:
    ///
    /// Averager for pair of x and y
    ///
    statistics::AveragerPairWeighted ap_;

    /**
       @brief Chi-squared
       
       Chi-squared is defined as the \f$ 
       \sum{w_i(\hat{y_i}-y_i)^2} \f$
    */
    double chisq_;

  private:
  };

}}} // of namespaces regression, yat, and theplu

#endif