Covariances Class

Covariances Class

Computes the sample variance-covariance or correlation matrix.

Inheritance Hierarchy

SystemObject
Imsl.StatCovariances

Namespace: Imsl.Stat
Assembly: ImslCS (in ImslCS.dll) Version: 6.5.2.0

Syntax

C++

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[SerializableAttribute]
public class Covariances

<SerializableAttribute>
Public Class Covariances

[SerializableAttribute]
public ref class Covariances

[<SerializableAttribute>]
type Covariances =  class end

The Covariances type exposes the following members.

Constructors

	Name	Description
	Covariances	Constructor for Covariances.

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Methods

	Name	Description
	Compute	Computes the matrix.
	Equals	Determines whether the specified object is equal to the current object. (Inherited from Object.)
	Finalize	Allows an object to try to free resources and perform other cleanup operations before it is reclaimed by garbage collection. (Inherited from Object.)
	GetHashCode	Serves as a hash function for a particular type. (Inherited from Object.)
	GetIncidenceMatrix	Returns the incidence matrix. Note that the Compute method must be invoked first before invoking this method. Otherwise, the method throws a NullReferenceException exception.
	GetMeans	Returns the means of the variables in x.
	GetType	Gets the Type of the current instance. (Inherited from Object.)
	MemberwiseClone	Creates a shallow copy of the current Object. (Inherited from Object.)
	SetFrequencies	The frequency for each observation.
	SetWeights	Sets the weight for each observation.
	ToString	Returns a string that represents the current object. (Inherited from Object.)

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Properties

	Name	Description
	MissingValueMethod	Sets the method used to exclude missing values in x from the computations.
	NumberOfProcessors	Perform the parallel calculations with the maximum possible number of processors set to NumberOfProcessors.
	NumRowMissing	Returns the total number of observations that contain any missing values (Double.NaN). Note that the Compute method must be invoked first before invoking this method. Otherwise, the return value is 0.
	Observations	Returns the sum of the frequencies. Note that the Compute method must be invoked first before invoking this method. Otherwise, the return value is 0.
	SumOfWeights	Returns the sum of the weights of all observations. Note that the Compute method must be invoked first before invoking this method. Otherwise, the return value is 0.

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Remarks

Class Covariances computes estimates of correlations, covariances, or sums of squares and crossproducts for a data matrix x. Weights and frequencies are allowed but not required.

The means, (corrected) sums of squares, and (corrected) sums of crossproducts are computed using the method of provisional means. Let $x_{ki}$ denote the mean based on i observations for the k-th variable, denote the frequency of the i-th observation, denote the weight of the i-th observations, and $c_{jki}$ denote the sum of crossproducts (or sum of squares if j = k) based on i observations. Then the method of provisional means finds new means and sums of crossproducts as shown in the example below.

The means and crossproducts are initialized as follows:

$x_{k0} = 0.0\,\,\,\,\,for\,\,k = 1,\, \ldots ,\,p$

$c_{jk0} = 0.0\,\,\,for\,\,j,\,k = 1,\, \ldots ,\,p$

where p denotes the number of variables. Letting $x_{k,i+1}$ denote the k-th variable of observation i + 1, each new observation leads to the following updates for $x_{ki}$ and $c_{jki}$ using the update constant $r_{i+1}$ :

$r_{i + 1} = \frac{{f_{i + 1} w_{i + 1} }}{{\sum\limits_{l = 1}^{i + 1} {f_l w_l } }}$

$\bar x_{k,\;i + 1} = \bar x_{ki} + \left( {x_{k,\;i + 1} - \bar x_{ki} } \right)r_{i + 1}$

$c_{jk,\;i + 1} = c_{jki} + f_{i + 1} w_{i + 1} \left( {x_{j,\;i + 1} - \bar x_{ji} } \right)\left( {x_{k,\;i + 1} - \bar x_{ki} } \right)\left( {1 - r_{i + 1} } \right)$

The default value for weights and frequencies is 1. Means and variances are computed based on the valid data for each variable or, if required, based on all the valid data for each pair of variables.

Reference

Imsl.Stat Namespace

Other Resources

Example