Asymptotic minimax risk of predictive density estimation for non-parametric regression

We consider the problem of estimating the predictive density of future observations from a non-parametric regression model. The density estimators are evaluated under Kullback--Leibler divergence and our focus is on establishing the exact asymptotics of minimax risk in the case of Gaussian errors. We derive the convergence rate and constant for minimax risk among Bayesian predictive densities under Gaussian priors and we show that this minimax risk is asymptotically equivalent to that among all density estimators.Comment: Published in at http://dx.doi.org/10.3150/09-BEJ222 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm

Digital RoF Aided Cooperative Distributed Antennas with FFR in Multicell Multiuser Networks

The achievable throughput of the entire cellular area is investigated, when employing fractional frequency reuse techniques in conjunction with realistically modelled imperfect optical fibre aided distributed antenna systems (DAS). Given a fixed total transmit power, a substantial improvement of the cell-edge area’s throughput can be achieved without reducing the cell-centre’s throughput. The cell-edge’s throughput supported in the worst-case direction is significantly enhanced by the cooperative linear transmit processing technique advocated. Explicitly, a cell-edge throughput of η = 5 bits/s/Hz may be maintained for a imperfect optical fibre model, regardless of the specific geographic distribution of the users

Improved minimax predictive densities under Kullback--Leibler loss

Let $X| \mu \sim N_p(\mu,v_xI)$ and $Y| \mu \sim N_p(\mu,v_yI)$ be independent p-dimensional multivariate normal vectors with common unknown mean $\mu$. Based on only observing $X=x$, we consider the problem of obtaining a predictive density $\hat{p}(y| x)$ for $Y$ that is close to $p(y| \mu)$ as measured by expected Kullback--Leibler loss. A natural procedure for this problem is the (formal) Bayes predictive density $\hat{p}_{\mathrm{U}}(y| x)$ under the uniform prior $\pi_{\mathrm{U}}(\mu)\equiv 1$, which is best invariant and minimax. We show that any Bayes predictive density will be minimax if it is obtained by a prior yielding a marginal that is superharmonic or whose square root is superharmonic. This yields wide classes of minimax procedures that dominate $\hat{p}_{\mathrm{U}}(y| x)$, including Bayes predictive densities under superharmonic priors. Fundamental similarities and differences with the parallel theory of estimating a multivariate normal mean under quadratic loss are described.Comment: Published at http://dx.doi.org/10.1214/009053606000000155 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Imperfect Digital Fibre Optic Link Based Cooperative Distributed Antennas with Fractional Frequency Reuse in Multicell Multiuser Networks

The achievable throughput of the entire cellular area is investigated, when employing fractional frequency reuse techniques in conjunction with realistically modelled imperfect optical fibre aided distributed antenna systems (DAS) operating in a multicell multiuser scenario. Given a fixed total transmit power, a substantial improvement of the cell-edge area's throughput can be achieved without reducing the cell-centre's throughput. The cell-edge's throughput supported in the worst-case direction is significantly enhanced by the cooperative linear transmit processing technique advocated. Explicitly, a cell-edge throughput of $\eta=5$ bits/s/Hz may be maintained for an imperfect optical fibre model, regardless of the specific geographic distribution of the users

Admissible predictive density estimation

Let $X|\mu\sim N_p(\mu,v_xI)$ and $Y|\mu\sim N_p(\mu,v_yI)$ be independent $p$-dimensional multivariate normal vectors with common unknown mean $\mu$. Based on observing $X=x$, we consider the problem of estimating the true predictive density $p(y|\mu)$ of $Y$ under expected Kullback--Leibler loss. Our focus here is the characterization of admissible procedures for this problem. We show that the class of all generalized Bayes rules is a complete class, and that the easily interpretable conditions of Brown and Hwang [Statistical Decision Theory and Related Topics (1982) III 205--230] are sufficient for a formal Bayes rule to be admissible.Comment: Published in at http://dx.doi.org/10.1214/07-AOS506 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Two Rules on the Protein-Ligand Interaction

So far, we still lack a clear molecular mechanism to explain the protein-ligand interaction on the basis of electronic structure of a protein. By combining the calculation of the full electronic structure of a protein along with its hydrophobic pocket and the perturbation theory, we found out two rules on the protein-ligand interaction. One rule is the interaction only occurs between the lowest unoccupied molecular orbitals (LUMOs) of a protein and the highest occupied molecular orbital (HOMO) of its ligand, not between the HOMOs of a protein and the LUMO of its ligand. The other rule is only those residues or atoms located both on the LUMOs of a protein and in a surface pocket of a protein are activity residues or activity atoms of the protein and the corresponding pocket is the ligand binding site. These two rules are derived from the characteristics of energy levels of a protein and might be an important criterion of drug design

Effects of practical impairments on cooperative distributed antennas combined with fractional frequency reuse

Cooperative Multiple Point (CoMP) transmission aided Distributed Antenna Systems (DAS) are proposed for increasing the received Signal-to-Interference-plus-Noise-Ratio (SINR) in the cell-edge area of a cellular system employing Fractional Frequency Reuse (FFR) in the presence of realistic imperfect Channel State Information (CSI) as well as synchronisation errors between the transmitters and the receivers. Our simulation results demonstrate that the CoMP aided DAS scenario is capable of increasing the attainable SINR by up to 3dB in the presence of a wide range of realistic imperfections