We give a tutorial exposition of the analogue filtering equation for quantum systems focusing on probabilistic framework and developing ideas from classical theory. Quantum covariances conditional expectations von Neumann algebras play an essential part in presentation.

The increase in trading frequency of Exchanged Traded Funds (ETFs) presents a positive externality for financial risk management when the price ETF is available at higher than component stocks. spillover consists improving accuracy pre-estimators integrated covariance stocks included ETF. proposed Beta Adjusted Covariance (BAC) equals pre-estimator plus minimal adjustment matrix such that covar...

For longitudinal data, when the within-subject covariance is misspecified, the semiparametric regression estimator may be inefficient. We propose a method that combines the efficient semiparametric estimator with nonparametric covariance estimation, and is robust against misspecification of covariance models. We show that kernel covariance estimation provides uniformly consistent estimators for...