Accelerating the pace of engineering and science

# mvnrstd

Evaluate standard errors for multivariate normal regression model

## Syntax

```[StdParameters, StdCovariance] = mvnrstd(Data, Design, Covariance,CovarFormat)
```

## Arguments

 Data NUMSAMPLES-by-NUMSERIES matrix with NUMSAMPLES samples of a NUMSERIES-dimensional random vector. If a data sample has missing values, represented as NaNs, the sample is ignored. (Use ecmmvnrmle to handle missing data.) 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. 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] = mvnrstd(Data, Design, Covariance, CovarFormat) evaluates standard errors for a multivariate normal regression model without missing data. The model has the form

$Dat{a}_{k}\sim N\left(Desig{n}_{k}×Parameters,\text{\hspace{0.17em}}Covariance\right)$

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

mvnrstd 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.

 Note   mvnrstd operates slowly when you calculate the standard errors associated with the covariance matrix Covariance.

## 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.