[Quantproject-developers] QuantProject/b1_ADT/Econometrics LinearRegression.cs, 1.2, 1.3

[Glauco S. <gla...@us...>]

Update of /cvsroot/quantproject/QuantProject/b1_ADT/Econometrics
In directory vz-cvs-3.sog:/tmp/cvs-serv30293/b1_ADT/Econometrics

Modified Files:
	LinearRegression.cs 
Log Message:
The read only property
public double[] Residuals 
has been added.

The read only property
public double CenteredTotalSumOfSquares
has been added

IMPORTANT: the read only property
public double PredictedResidualsSumOfSquares 
has been added.
It is the PRESS statistic, a statistic based on the leave-one-out technique. This statistic is much more robust than Rsquare, to outliers.

The read only property
public double PredictedCenteredTotalSumOfSquares
has been added.

IMPORTANT: the read only property
public double CenteredPSquare 
has been added.
It is a normalized version of the the PRESS statistics, and it can be used as a fitness alternative the CenteredRSquare: the CenteredPSquare is much more robust with respect to outliers.

Index: LinearRegression.cs
===================================================================
RCS file: /cvsroot/quantproject/QuantProject/b1_ADT/Econometrics/LinearRegression.cs,v
retrieving revision 1.2
retrieving revision 1.3
diff -C2 -d -r1.2 -r1.3
*** LinearRegression.cs	6 Jan 2011 18:31:18 -0000	1.2
--- LinearRegression.cs	30 Apr 2012 23:37:46 -0000	1.3
***************
*** 34,37 ****
--- 34,39 ----
  	public class LinearRegression : ILinearRegression
  	{
+ 		private double[] regressand;
+ 		private double[,] regressors;
  		private double[,] covarianceMatrix;		// (XTransposeX)^-1
  		private double sumOfSquareResiduals;
***************
*** 51,54 ****
--- 53,116 ----
  		}
  		
+ 		#region HatMatrixDiagonal
+ 		private double[] hatMatrixDiagonal;
+ 		
+ 		#region setHatMatrixDiagonal
+ 		
+ 		#region getHatMatrixDiagonal
+ 		
+ 		#region get_i_th_row_of_X_XtransposeX_inverse
+ 		private double get_i_th_row_of_X_XtransposeX_inverse( int i , int j )
+ 		{
+ 			double partialSum = 0;
+ 			for( int q = 0 ; q < this.regressors.GetLength( 1 ) ; q++ )
+ 				partialSum += this.regressors[ i , q ] *
+ 					this.covarianceMatrix[ q , j ];
+ 			return partialSum;
+ 		}
+ 
+ 		private double[] get_i_th_row_of_X_XtransposeX_inverse( int i )
+ 		{
+ 			double[] i_th_row_of_X_XtransposeX_inverse = new double[ this.regressors.GetLength( 1 ) ];
+ 			for( int j = 0 ; j < this.regressors.GetLength( 1 ) ; j++ )
+ 				i_th_row_of_X_XtransposeX_inverse[ j ] =
+ 					this.get_i_th_row_of_X_XtransposeX_inverse( i , j );
+ 			return i_th_row_of_X_XtransposeX_inverse;
+ 		}
+ 		#endregion get_i_th_row_of_X_XtransposeX_inverse
+ 		
+ 		private double getHatMatrixDiagonal( int i )
+ 		{
+ 			double[] i_th_row_of_X_XtransposeX_inverse =
+ 				this.get_i_th_row_of_X_XtransposeX_inverse( i );
+ 			double partialSum = 0;
+ 			for( int j = 0 ; j < this.regressors.GetLength( 1 ) ; j++ )
+ 				partialSum += i_th_row_of_X_XtransposeX_inverse[ j ] *
+ 					this.regressors[ i , j ];
+ 			return partialSum;
+ 		}
+ 		#endregion getHatMatrixDiagonal
+ 		
+ 		private void setHatMatrixDiagonal()
+ 		{
+ 			this.hatMatrixDiagonal = new double[ this.regressand.Length ];
+ 			for( int i = 0 ; i < hatMatrixDiagonal.Length ; i++ )
+ 				this.hatMatrixDiagonal[ i ] = this.getHatMatrixDiagonal( i );
+ 		}
+ 		#endregion setHatMatrixDiagonal
+ 		
+ 		/// <summary>
+ 		/// returns the diagonal of the hat matrix
+ 		/// </summary>
+ 		public double[] HatMatrixDiagonal
+ 		{
+ 			get{
+ 				if ( this.hatMatrixDiagonal == null )
+ 					this.setHatMatrixDiagonal();
+ 				return this.hatMatrixDiagonal;
+ 			}
+ 		}
+ 		#endregion HatMatrixDiagonal
+ 		
  		private double centeredRSquare;
  		
***************
*** 57,62 ****
--- 119,261 ----
  		}
  		
+ 		#region Residuals
+ 		
+ 		private double[] residuals;
+ 		
+ 		#region setResiduals
+ 		
+ 		#region setResidual
+ 		
+ 		private double getPredictedValue( int i )
+ 		{
+ 			double predictedValue = 0;
+ 			for ( int j = 0 ; j < this.EstimatedCoefficients.Length ; j++ )
+ 				predictedValue +=
+ 					this.estimatedCoefficients[ j ] * this.regressors[ i , j ];
+ 			return predictedValue;
+ 		}
+ 		
+ 		private void setResidual( int i )
+ 		{
+ 			double predictedValue = this.getPredictedValue( i );
+ 			this.residuals[ i ] = this.regressand[ i ] - predictedValue;
+ 		}
+ 		#endregion setResidual
+ 		
+ 		private void setResiduals()
+ 		{
+ 			this.residuals = new double[ this.regressand.Length ];
+ 			for( int i = 0 ; i < this.regressand.Length ; i++ )
+ 				this.setResidual( i );
+ 		}
+ 		#endregion setResiduals
+ 		
+ 		public double[] Residuals {
+ 			get {
+ 				if ( this.residuals == null )
+ 					this.setResiduals();
+ 				return this.residuals; }
+ 		}
+ 		#endregion Residuals
+ 
+ 		
+ 		#region CenteredTotalSumOfSquares
+ 		
+ 		#region setCenteredTotalSumOfSquares
+ 		private double getYBar()
+ 		{
+ 			double partialSum = 0;
+ 			for( int i = 0 ; i < this.regressand.Length ; i++ )
+ 				partialSum += this.regressand[ i ];
+ 			
+ 			double yBar = partialSum / this.regressand.Length;
+ 			return yBar;
+ 		}
+ 		private void setCenteredTotalSumOfSquares()
+ 		{
+ 			double partialSum = 0;
+ 			double yBar = this.getYBar();
+ 			for( int i = 0 ; i < this.regressand.Length ; i++ )
+ 				partialSum += Math.Pow( this.regressand[ i ] - yBar , 2 );
+ 			this.centeredTotalSumOfSquares = partialSum;
+ 		}
+ 		#endregion setCenteredTotalSumOfSquares
+ 		
+ 		public double CenteredTotalSumOfSquares
+ 		{
+ 			get
+ 			{
+ 				if ( this.centeredTotalSumOfSquares == double.MinValue )
+ 					this.setCenteredTotalSumOfSquares();
+ 				return this.centeredTotalSumOfSquares;	
+ 			}
+ 		}
+ 		#endregion CenteredTotalSumOfSquares
+ 		
+ 		#region PredictedResidualsSumOfSquares
+ 		
+ 		private double predictedResidualsSumOfSquares;
+ 
+ 		#region setPredictedResidualsSumOfSquares
+ 		private double getExternalResidual( int i )
+ 		{
+ 			double externalResidual = this.Residuals[ i ] / ( 1 - this.HatMatrixDiagonal[ i ] );
+ 			return externalResidual;
+ 		}
+ 		private void setPredictedResidualsSumOfSquares()
+ 		{
+ 			double partialSum = 0;
+ 			for( int i = 0 ; i < this.regressand.Length ; i++ )
+ 				partialSum += Math.Pow( this.getExternalResidual( i ) , 2 );
+ 			this.predictedResidualsSumOfSquares = partialSum;
+ 		}
+ 		#endregion setPredictedResidualsSumOfSquares
+ 		
+ 		/// <summary>
+ 		///  the PRESS statistic, a statistic based on the leave-one-out technique
+ 		/// </summary>
+ 		public double PredictedResidualsSumOfSquares {
+ 			get {
+ 				if ( this.predictedResidualsSumOfSquares == Double.MinValue )
+ 					// the PRESS statistic has not been set yet
+ 					this.setPredictedResidualsSumOfSquares();
+ 				return this.predictedResidualsSumOfSquares; }
+ 		}
+ 		#endregion PredictedResidualsSumOfSquares
+ 		
+ 		
+ 		/// <summary>
+ 		/// similar to the Total Sum of Squares, but each observation is subtracted
+ 		/// the mean of the other observations: in other words, the current observation
+ 		/// does not partecipate to the computationo of the current mean. It has been
+ 		/// proven that the Prodicted Total Sum Of Squares (defined as above) is equal to
+ 		/// the (usual) Centered Total Sum of Squares times (n/(n-1))^2
+ 		/// </summary>
+ 		public double PredictedCenteredTotalSumOfSquares
+ 		{
+ 			get
+ 			{
+ 				double n = Convert.ToDouble( this.regressand.Length );
+ 				double predictedTotalSumOfSquares =
+ 					this.CenteredTotalSumOfSquares * Math.Pow(  n / ( n - 1 ) , 2 );
+ 				return predictedTotalSumOfSquares;
+ 			}
+ 		}
+ 
+ 		/// <summary>
+ 		/// a normalized version of the the PRESS statistics
+ 		/// </summary>
+ 		public double CenteredPSquare {
+ 			get
+ 			{
+ 				double centerdPSquare = 1 - this.PredictedResidualsSumOfSquares /
+ 					this.PredictedCenteredTotalSumOfSquares;
+ 				return centerdPSquare;
+ 			}
+ 		}
+ 		
  		public LinearRegression()
  		{
+ 			this.predictedResidualsSumOfSquares = double.MinValue;
  		}
  		
***************
*** 159,162 ****
--- 358,363 ----
  		{
  			this.runRegression_checkParameters( regressand , regressors );
+ 			this.regressand = regressand;
+ 			this.regressors = regressors;
  			double[,] xTransposeX = this.getXtransposeX( regressors );
  			this.covarianceMatrix = PositiveDefiniteMatrix.GetInverse( xTransposeX );