Options Class for g02qg

Syntax

C#
public class g02qgOptions

Visual Basic
Public Class g02qgOptions

Visual C++
public ref class g02qgOptions

F#
type g02qgOptions = class end

Description of the Optional Parameters

For each option, we give a summary line, a description of the optional parameter and details of constraints.

The summary line contains:

the keywords, where the minimum abbreviation of each keyword is underlined (if no characters of an optional qualifier are underlined, the qualifier may be omitted);
a parameter value, where the letters $a$ , $i and r$ denote options that take character, integer and real values respectively;
the default value, where the symbol $ε$ is a generic notation for machine precision (see x02aj).

Keywords and character values are case and white space insensitive.

Band Width Alpha

A multiplier used to construct the parameter

α_{b}

used when calculating the Sheather–Hall bandwidth (see [Description]), with

α_{b} = (1 - α) \times Band Width Alpha

. Here,

α

is the Significance Level.

Constraint:

Band Width Alpha > 0.0

Band Width Method

The method used to calculate the bandwidth used in the calculation of the asymptotic covariance matrix

Σ

and

H^{- 1}

Interval Method ='HKS'

'KERNEL'

'IID'

(see [Description]).

Constraint:

Band Width Method ='SHEATHER HALL'

'BOFINGER'

Big

This parameter should be set to something larger than the biggest value supplied in dat and y.

Constraint:

Big > 0.0

Bootstrap Interval Method

Interval Method ='BOOTSTRAP XY'

, Bootstrap Interval Method controls how the confidence intervals are calculated from the bootstrap estimates.

$Bootstrap Interval Method ='T'$: $t$ intervals are calculated. That is, the covariance matrix, $Σ = \{σ_{i j} : i, j = 1, 2, \dots, p\}$ is calculated from the bootstrap estimates and the limits calculated as $β_{i} \pm t_{(n - p, (1 + α) / 2)} σ_{i i}$ where $t_{(n - p, (1 + α) / 2)}$ is the $(1 + α) / 2$ percentage point from a Student's $t$ distribution on $n - p$ degrees of freedom, $n$ is the effective number of observations and $α$ is given by the optional parameter Significance Level.
$Bootstrap Interval Method ='QUANTILE'$: Quantile intervals are calculated. That is, the upper and lower limits are taken as the $(1 + α) / 2$ and $(1 - α) / 2$ quantiles of the bootstrap estimates, as calculated using g01am.

Constraint:

Bootstrap Interval Method ='T'

'QUANTILE'

Bootstrap Iterations

The number of bootstrap samples used to calculate the confidence limits and covariance matrix (if requested) when

Interval Method ='BOOTSTRAP XY'

Constraint:

Bootstrap Iterations > 1

Bootstrap Monitoring

Bootstrap Monitoring ='YES'

and

Interval Method ='BOOTSTRAP XY'

, then the parameter estimates for each of the bootstrap samples are displayed. This information is sent to the unit number specified by Unit Number.

Constraint:

Bootstrap Monitoring ='YES'

'NO'

Calculate Initial Values

Calculate Initial Values ='YES'

then the initial values for the regression parameters,

β

, are calculated from the data. Otherwise they must be supplied in b.

Constraint:

Calculate Initial Values ='YES'

'NO'

Defaults

This special keyword is used to reset all optional parameters to their default values.

Drop Zero Weights

If a weighted regression is being performed and

Drop Zero Weights ='YES'

then observations with zero weight are dropped from the analysis. Otherwise such observations are included.

Constraint:

Drop Zero Weights ='YES'

'NO'

Epsilon

ε_{u}

, the tolerance used when calculating the covariance matrix and the initial values for

u

and

v

. For additional details see [Calculation of Covariance Matrix] and [Additional information] respectively.

Constraint:

Epsilon \geq 0.0

Interval Method

The value of Interval Method controls whether confidence limits are returned in bl and bu and how these limits are calculated. This parameter also controls how the matrices returned in ch are calculated.

$Interval Method ='NONE'$: No limits are calculated and bl, bu and ch are not referenced.
$Interval Method ='KERNEL'$: The Powell Sandwich method with a Gaussian kernel is used.
$Interval Method ='HKS'$: The Hendricks–Koenker Sandwich is used.
$Interval Method ='IID'$: The errors are assumed to be identical, and independently distributed.
$Interval Method ='BOOTSTRAP XY'$: A bootstrap method is used, where sampling is done on the pair $(y_{i}, x_{i})$ . The number of bootstrap samples is controlled by the parameter Bootstrap Iterations and the type of interval constructed from the bootstrap samples is controlled by Bootstrap Interval Method.

Constraint:

Interval Method ='NONE'

'KERNEL'

'HKS'

'IID'

'BOOTSTRAP XY'

Iteration Limit

The maximum number of iterations to be performed by the interior point optimization algorithm.

Constraint:

Iteration Limit > 0

Matrix Returned

The value of Matrix Returned controls the type of matrices returned in ch. If

Interval Method ='NONE'

, this parameter is ignored and ch is not referenced. Otherwise:

$Matrix Returned ='NONE'$: No matrices are returned and ch is not referenced.
$Matrix Returned ='COVARIANCE'$: The covariance matrices are returned.
$Matrix Returned ='H INVERSE'$: If $Interval Method ='KERNEL'$ or $'HKS'$ , the matrices $J$ and $H^{- 1}$ are returned. Otherwise no matrices are returned and ch is not referenced.

The matrices returned are calculated as described in [Description], with the algorithm used specified by Interval Method. In the case of

Interval Method ='BOOTSTRAP XY'

the covariance matrix is calculated directly from the bootstrap estimates.

Constraint:

Matrix Returned ='NONE'

'COVARIANCE'

'H INVERSE'

Monitoring

Monitoring ='YES'

then the duality gap is displayed at each iteration of the interior point optimization algorithm. In addition, the final estimates for

β

are also displayed.

The monitoring information is sent to the unit number specified by Unit Number.

Constraint:

Monitoring ='YES'

'NO'

QR Tolerance

The tolerance used to calculate the rank,

k

, of the

p \times p

cross-product matrix,

X^{T} X

. Letting

Q

be the orthogonal matrix obtained from a

Q R

decomposition of

X^{T} X

, then the rank is calculated by comparing

Q_{i i}

with

Q_{11} \times QR Tolerance

If the cross-product matrix is rank deficient, then the parameter estimates for the

p - k

columns with the smallest values of

Q_{i i}

are set to zero, along with the corresponding entries in bl, bu and ch, if returned. This is equivalent to dropping these variables from the model. Details on the

Q R

decomposition used can be found in f08bf.

Constraint:

QR Tolerance > 0.0

Return Residuals

Return Residuals ='YES'

, the residuals are returned in res. Otherwise res is not referenced.

Constraint:

Return Residuals ='YES'

'NO'

Sigma

The scaling factor used when calculating the affine scaling step size (see equation (8)).

Constraint:

0.0 < Sigma < 1.0

Significance Level

α

, the size of the confidence interval whose limits are returned in bl and bu.

Constraint:

0.0 < Significance Level < 1.0

Tolerance

Convergence tolerance. The optimization is deemed to have converged if the duality gap is less than Tolerance (see [Update and convergence]).

Constraint:

Tolerance > 0.0

Unit Number

The unit number to which any monitoring information is sent.

Constraint:

Unit Number > 1

Inheritance Hierarchy

System..::..Object
NagLibrary..::..G02..::..g02qgOptions

Syntax

Description of the Optional Parameters

Inheritance Hierarchy

See Also