Financial Toolbox™

ecmmvnrstd - Evaluate standard errors for multivariate normal regression model

Syntax

[StdParameters, StdCovariance] = ecmmvnrstd(Data, Design, 
Covariance, Method, CovarFormat)

Arguments

`Data`	`NUMSAMPLES`-by-`NUMSERIES` matrix with `NUMSAMPLES` samples of a `NUMSERIES`-dimensional random vector. Missing values are represented as `NaN`s. Only samples that are entirely `NaN`s are ignored. (To ignore samples with at least one `NaN`, use `mvnrstd`.)
`Design`	A matrix or a cell array that handles two model structures: If `NUMSERIES = 1`, `Design` is a `NUMSAMPLES`-by-`NUMPARAMS` matrix with known values. This structure is the standard form for regression on a single series. If `NUMSERIES` ≥ `1`, `Design` is a cell array. The cell array contains either one or `NUMSAMPLES` cells. Each cell contains a `NUMSERIES`-by-`NUMPARAMS` matrix of known values. If `Design` has a single cell, it is assumed to have the same `Design` matrix for each sample. If `Design` has more than one cell, each cell contains a `Design` matrix for each sample.
`Covariance`	`NUMSERIES`-by-`NUMSERIES` matrix of estimates for the covariance of the regression residuals.
`Method`	(Optional) String that identifies method of calculation for the information matrix: `hessian` - Default method. Use the expected Hessian matrix of the observed log-likelihood function. This method is recommended since the resultant standard errors incorporate the increased uncertainties due to missing data. `fisher` - Use the Fisher information matrix.
`CovarFormat`	(Optional) String that specifies the format for the covariance matrix. The choices are: `'full'` - Default method. The covariance matrix is a full matrix. `'diagonal'` - The covariance matrix is a diagonal matrix.

Description

[StdParameters, StdCovariance] = ecmmvnrstd(Data, Design, Covariance, Method, CovarFormat) evaluates standard errors for a multivariate normal regression model with missing data. The model has the form

for samples k = 1, ... , NUMSAMPLES.

ecmmvnrstd computes two outputs:

StdParameters is a NUMPARAMS-by-1 column vector of standard errors for each element of Parameters, the vector of estimated model parameters.
StdCovariance is a NUMSERIES-by-NUMSERIES matrix of standard errors for each element of Covariance, the matrix of estimated covariance parameters.

Notes

You can configure Design as a matrix if NUMSERIES = 1 or as a cell array if NUMSERIES ≥ 1.

If Design is a cell array and NUMSERIES = 1, each cell contains a NUMPARAMS row vector.
If Design is a cell array and NUMSERIES > 1, each cell contains a NUMSERIES-by-NUMPARAMS matrix.

References

Roderick J. A. Little and Donald B. Rubin, Statistical Analysis with Missing Data, 2nd ed., John Wiley & Sons, Inc., 2002.

Examples

See Multivariate Normal Regression, Least-Squares Regression, Covariance-Weighted Least Squares, Feasible Generalized Least Squares, and Seemingly Unrelated Regression.