Exercise B.1 The MATLAB file DataCauchy contains observations from a Cauchy distribution

(see Appendix A.6.16) with density

Assume that the data are independent. We want to estimate μ and σ > 0.
The log-likelihood function to maximize is

(a) Using the MATLAB function EstCauchy, find ˆμ and ˆσ. Note that the observations have been simulated with μ = 10 and σ = 5!

(b) Extend the function EstCauchy so that the covariance matrix between the estimators is an output. Use the exact gradients to estimate the Fisher information.

Transcribed Image Text:

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