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Abstract:
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The time-average covariance matrix (TACM) is the variance of the sample mean when there is serially correlated data. Estimation of the TACM is of interest in various fields such as time series, econometrics, and Markov chain Monte Carlo simulations. Spectral variance (SV) estimators are one of the most common estimation methods, but they suffer from a negative bias. An alternative lugsail estimator has been proposed which uses a linear combination of the common SV estimators that induces a positive bias to correct the issue. With the lugsail estimators new tuning parameters are introduced to control the induced positive bias. We typically use a TACM for hypothesis testing, and to create confidence regions for parameters. Current methods focus on optimizing these TACM estimators according to their mean squared error (MSE). Instead we can use alternative loss functions that optimize our parameters according to the type 1 and type 2 error rates of testing procedures, in contrast to controlling them indirectly with MSE. With these new tuning parameters and alternative loss functions we can eliminate the bias, control the variance, and obtain a testing optimal estimator.
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