# Documentation

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# Multivariate Normal Regression

Regression analysis, with or without missing data, using likelihood-based methods for multivariate normal regression

## Functions

 `ecmnfish` Fisher information matrix `ecmmvnrfish` Fisher information matrix for multivariate normal regression model `ecmnhess` Hessian of negative log-likelihood function `ecmninit` Initial mean and covariance `ecmnobj` Multivariate normal negative log-likelihood function `ecmnmle` Mean and covariance of incomplete multivariate normal data `ecmnstd` Standard errors for mean and covariance of incomplete data `ecmmvnrstd` Evaluate standard errors for multivariate normal regression model `mvnrmle` Multivariate normal regression (ignore missing data)
 `ecmmvnrobj` Log-likelihood function for multivariate normal regression with missing data `ecmlsrmle` Least-squares regression with missing data `ecmlsrmle` Least-squares regression with missing data `mvnrfish` Fisher information matrix for multivariate normal or least-squares regression `mvnrobj` Log-likelihood function for multivariate normal regression without missing data `mvnrstd` Evaluate standard errors for multivariate normal regression model
 `convert2sur` Convert multivariate normal regression model to seemingly unrelated regression (SUR) model

## Examples and How To

Multivariate Normal Regression Functions

Financial Toolbox™ has a number of functions for multivariate normal regression with or without missing data.

Portfolios with Missing Data

This example illustrates how to use the missing data algorithms for portfolio optimization and for valuation.

Valuation with Missing Data

Estimating the coefficients of the Capital Asset Pricing Model with incomplete stock price data.

Capital Asset Pricing Model with Missing Data

This example illustrates implementation of the Capital Asset Pricing Model (CAPM) in the presence of missing data.

## Concepts

Multivariate Normal Regression Types

Estimating the parameters of the regression model using multivariate normal regression.

Multivariate Normal Regression

Using likelihood-based methods for the multivariate normal regression model.

Maximum Likelihood Estimation with Missing Data

Estimating the parameters of the multivariate normal regression model using maximum likelihood estimation.

## Troubleshooting

Troubleshooting Multivariate Normal Regression

Handling various technical and operational difficulties with multivariate normal regression.