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We investigate the bias and error in estimates of the cosmological parametercovariance matrix, due to sampling or modelling the data covariance matrix, forlikelihood width and peak scatter estimators. We show that these estimators donot coincide unless the data covariance is exactly known. For sampled datacovariances, with Gaussian distributed data and parameters, the parametercovariance matrix estimated from the width of the likelihood has a Wishartdistribution, from which we derive the mean and covariance. This mean is biasedand we propose an unbiased estimator of the parameter covariance matrix.Comparing our analytic results to a numerical Wishart sampler of the datacovariance matrix we find excellent agreement. An accurate ansatz for the meanparameter covariance for the peak scatter estimator is found, and we fit itscovariance to our numerical analysis. The mean is again biased and we proposean unbiased estimator for the peak parameter covariance. For sampled datacovariances the width estimator is more accurate than the peak scatterestimator. We investigate modelling the data covariance, or equivalently datacompression, and shown that the peak scatter estimator is less sensitive tobiases in the model data covariance matrix than the width estimator, butrequires independent realisations of the data to reduce the statistical error.If the model bias on the peak estimator is sufficiently low this is promising,otherwise the sampled width estimator is preferable.

Estimating Cosmological Parameter Covariance