Maximum Likelihood¶
Functions for inferences in maximum likelihood models.
-
estimagic.inference.likelihood_covs.
cov_hessian
(hessian)[source]¶ Covariance based on the negative inverse of the hessian of loglike.
- Parameters
hessian (np.array) – 2d array hessian matrix of dimension (nparams, nparams)
- Returns
2d array covariance matrix (nparams, nparams)
- Return type
hessian_matrix (np.array)
Resources: Marno Verbeek - A guide to modern econometrics [Ver08]
-
estimagic.inference.likelihood_covs.
cov_jacobian
(jacobian)[source]¶ Covariance based on outer product of jacobian of loglikeobs.
- Parameters
jacobian (np.array) – 2d array jacobian matrix of dimension (nobs, nparams)
- Returns
2d array covariance matrix (nparams, nparams)
- Return type
jacobian_matrix (np.array)
Resources: Marno Verbeek - A guide to modern econometrics.
-
estimagic.inference.likelihood_covs.
cov_sandwich
(jacobian, hessian)[source]¶ Covariance of parameters based on HJJH dot product.
H stands for Hessian of the log likelihood function and J for Jacobian, of the log likelihood per individual.
- Parameters
jacobian (np.array) – 2d array jacobian matrix of dimension (nobs, nparams)
hessian (np.array) – 2d array hessian matrix of dimension (nparams, nparams)
- Returns
2d array covariance HJJH matrix (nparams, nparams)
- Return type
sandwich_cov (np.array)
- Resources:
-
estimagic.inference.likelihood_covs.
se_from_cov
(cov)[source]¶ Standard deviation of parameter estimates based on the function of choice.
- Parameters
cov (np.array) – 2d array covariance matrix of dimenstions (nparams, nparams)
- Returns
1d array of dimension (nparams) with standard errors
- Return type
standard_errors (np.array)
- Ver08
M. Verbeek. A Guide to Modern Econometrics. Wiley, 2008. ISBN 9780470517697. URL: https://books.google.com/books?id=uEFm6pAJZhoC.