Arbitrary Correlation Structure Research Articles

Sensitivity, specificity and ROC-curves in multiple reader diagnostic trials—A unified, nonparametric approach

In diagnostic trials, the performance of a product is most frequently measured in terms such as sensitivity, specificity and the area under the ROC-curve (AUC). In multiple-reader trials, correlated data appear in a natural way since the same patient is observed under different conditions by several readers. The repeated measures may have quite an involved correlation structure. Even though sensitivity, specificity and the AUC are all assessments of diagnostic ability, a unified approach to analyze all such measurements allowing for an arbitrary correlation structure does not exist. Thus, a unified approach for these three effect measures of diagnostic ability will be presented in this paper. The fact that sensitivity and specificity are particular AUCs will serve as a basis for our method of analysis. As the presented theory can also be used in set-ups with correlated binomial random-variables, it may have a more extensive application than only in diagnostic trials.

An Approach to the Triple Branch Selection Diversity Analysis Over Correlated α-μ Fading Channels in the Presence of CCI

In this paper, an approach to derivation of the joint trivariate ?-μ probability density function (pdf) and cumulative distribution function (cdf) expressions will be presented. Capitalizing on this, closed-form expressions for the cdf and pdf at the output of triple branch selective combiner (SC) in the presence of correlated co-channel interference (CCI) will be determined. The main contribution of this paper is generality of our model, since the expressions accommodate arbitrary correlation structures. General results, from this paper, could be reduced to the specific ones for various fading models and types of correlation. Important performance measures like outage probability (Pout) and average output signal-to-interference ratio (SIR) will also be determined and graphically illustrated for various values of existing parameters.

Noncircularity restoral for multi-antenna blind beamforming

Blind beamforming for extracting noncircular signals without the prior knowledge about the objective steering vector is considered. Three second-order blind techniques via NonCircularity REstoral (NCRE) are proposed to recover a dominant noncircular signal from circular interferences plus sensor noise with arbitrary and unknown correlation structure. These schemes are labeled as NCRE1, NCRE2, and NCRE3, respectively. For the high-rank environments where a number of rectilinear/circular interfering signals are present a Mixed-Order BEamspace (MOBE) technique, using simultaneously the second- and fourth-order cumulants, is developed. The performance of these proposed methods is studied based on numerical simulations. NCRE1 is computationally simple but performs well only in the case of very weak interferences and moderate noise, NCRE3 can provide good performance in the presence of medium or weak interferences, while NCRE2 is very suitable for adverse signal environments. NCRE2 outperforms NCRE1 and NCRE3 in terms of convergence rate, over a wide range of signal to interference plus noise ratio values. It is demonstrated that all the three NCRE methods are better than the traditional sample matrix inversion technique in the presence of look direction mismatch. They are also more attractive than the high-order cumulant method when non-Gaussian circular interferences are encountered. The MOBE method is shown to be competent for handling rectilinear/circular interfering signals, with respect to the attainable output signal to interference plus noise ratio.

New results for the multivariate Nakagami-𝓂 fading model with arbitrary correlation matrix and applications

New results for the multichannel Nakagami-m fading model with an arbitrary correlation matrix are presented in this paper. By using an efficient tridiagonalization method based on Householder matrices, the inverse of the Gaussian correlation matrix is transformed to tridiagonal, managing to derive a closed-form union upper bound for the joint Nakagami-m probability density function and an exact analytical expression for the moment generating function of the sum of identically distributed gamma random variables. Our analysis considers an arbitrary correlation structure, which includes as special cases the exponential, constant, circular, and linear correlation ones. Based on the proposed mathematical analysis, we obtain a tight union upper bound for the outage probability of multibranch selection diversity receivers as well as exact analytical expressions for the outage and the average error probability of multibranch maximal-ratio diversity receivers. Our analysis is verified by comparing numerically evaluated with extensive computer simulation performance evaluation results, showing the usefulness of the proposed approach.

Exact distribution of the Mann–Kendall trend test statistic for persistent data

The distribution-free Mann–Kendall test is widely used for the assessment of significance of trends in many hydrologic and climatic time series. Previous studies have suggested both exact and approximate formulas for the calculation of the variance of the test statistic when the data are serially correlated. This paper outlines a procedure for the calculation of the exact distribution of the Mann–Kendall trend test statistic for persistent data with an arbitrary correlation structure. The particular cases of the AR(1) (first order autoregressive) model and the Fractional Gaussian Noise (FGN) model are presented for sample sizes between 3 and 9. While it has been previously shown that the Normal distribution gives a reasonable approximation to the exact distribution for large values of sample size n , a more accurate approximation based on the Beta distribution is proposed for moderate values of n . The application of the test to small samples is illustrated by testing the significance of recent trends starting in 1990 in 58 world river flow time series. The results confirm the effect of scaling in small samples and the benefits of using the Beta distribution as an approximation.

Further Results on the Capacity and Error Probability Analysis of Noncoherent MIMO Systems in the Low SNR Regime

The noncoherent single-user multiple-input-multiple-output (MIMO) channel in the low signal-to-noise ratio (SNR) regime is investigated from two viewpoints: capacity and probability of error analysis. The novelty in both viewpoints is that we allow an arbitrary correlation structure for the Gaussian observation noise. First, we look at the capacity of the spatially correlated Rayleigh fading channel. We investigate the impact of channel and noise correlation on the mutual information for the on-off and Gaussian signaling schemes. Our findings establish that, in the low SNR regime, mutual information is maximized when the transmit antennas are fully correlated (the same holds for the receive array). Then, the deterministic channel setup is considered and a pairwise error probability (PEP) analysis for the generalized likelihood ratio test (GLRT) receiver is performed. This leads to a codebook design criterion on which we base the construction of new space-time constellations. Their performance is assessed by computer simulations and, as a byproduct, we show that our codebooks are also of interest for Bayesian receivers, which decode constellations with nonuniform priors.

Bayesian learning for a class of priors with prescribed marginals

We discuss three learning rules for generalized Bayesian updating of an imprecise probability: (a modified version of) the generalized Bayes’ rule, the maximum likelihood update rule (after Gilboa and Schmeidler) and a newly developed hybrid rule. We investigate the general methodology for a special class of multivariate probability measures with prescribed marginals but arbitrary correlation structure. Both the choice and analysis of this class are motivated by expert interviews that we conducted with modelers in the field of climatic change. We argue that both updating rules from the literature have strong limitations, the generalized Bayes’ rule is too conservative, i.e., too inclusive, while the maximum likelihood update rule being too exclusive, adding spurious information. As a powerful extension we introduce a new rule for Bayesian updating of an imprecise measure: a “weighted likelihood update method,” which bases Bayesian updating on the whole set of priors but weights the influence of its members. We study the different rules in the case of bivariate Gaussian priors. Our investigation shows that the new rule combines certain attractive features of the generalized Bayes’ rule and the maximum likelihood update rule. In this article we aim at highlighting the sequence of not yet fully resolved statistical issues a practitioner on complex mechanistic models would face when updating imprecise prior knowledge.

Noncoherent Communication in Multiple-Antenna Systems: Receiver Design and Codebook Construction

In this paper, we address the problem of space-time codebook design for noncoherent communications in multiple-antenna wireless systems. In contrast with other approaches, the channel matrix is modeled as an unknown deterministic parameter at both the receiver and the transmitter, and the Gaussian observation noise is allowed to have an arbitrary correlation structure, known by the transmitter and the receiver. In order to handle the unknown deterministic space-time channel, a generalized likelihood ratio test (GLRT) receiver is considered. A new methodology for space-time codebook design under this noncoherent setup is proposed. It optimizes the probability of error of the GLRT receiver's detector in the high signal-to-noise ratio (SNR) regime by solving a high-dimensional nonlinear nonsmooth optimization problem in a two-step approach. First, a convex semidefinite programming (SDP) relaxation of the codebook design problem yields a rough estimate of the optimal codebook. This is then refined through a geodesic descent optimization algorithm that exploits the Riemannian geometry imposed by the power constraints on the space-time codewords. The results obtained through computer simulations illustrate the advantages of our method. For the specific case of spatio-temporal white observation noise, our codebook constructions replicate the performance of state-of-the-art known solutions. The main point here is that our methodology permits extending the codebook construction to any given correlated noise environment. The simulation results show good performance of these new designed codes in colored noise setups.

A Closed-Form BER Expression for BPSK Using MRC in Correlated CCI and Rayleigh Fading

An exact closed-form expression for the average bit error rate (BER) of coherent BPSK using maximal ratio combining (MRC) with correlated branches in the presence of cochannel interference (CCI) and noise is derived. This expression is valid for an arbitrary correlation structure under the assumption that the branch gains of the desired user signal and interfering signals experience correlated Rayleigh fading with the same correlation eigenvector matrix.

Precoding of space-time block coded signals for joint transmit-receive correlated MIMO channels

A memoryless linear precoder is designed for orthogonal space-time block codes (OSTBC) for improved performance over block-fading flat correlated Rayleigh fading multiple-input multiple-output (MIMO) channels. Original features of the proposed technique include 1) the precoder can handle both transmit and receive correlation, and 2) the precoder handles any arbitrary joint correlation structure, including the so-called Kronecker (non-Kronecker) correlation models. The precoder is designed to minimize a symbol error-based metric as function of the joint slowly-varying channel correlation coefficients, which are supposed to be known to the transmitter. Several useful properties of the optimal precoder are given, evidencing the impact of receive correlation on transmitter optimization in certain situations. An iterative fast-converging numerical optimization algorithm is proposed. Monte Carlo simulations over fading channels are used to validate our claims.

Missing responses in generalised linear mixed models when the missing data mechanism is nonignorable

SUMMARY We propose a method for estimating parameters in the generalised linear mixed model with nonignorable missing response data and with nonmonotone patterns of missing data in the response variable. We develop a Monte Carlo EM algorithm for estimating the parameters in the model via the Gibbs sampler. For the normal random effects model, we derive a novel analytical form for the E- and M-steps, which is facilitated by integrating out the random effects. This form leads to a computationally feasible and extremely efficient Monte Carlo EM algorithm for computing maximum likelihood estimates and standard errors. In addition, we propose a very general joint multinomial model for the missing data indicators, which can be specified via a sequence of one-dimensional conditional distributions. This multinomial model allows for an arbitrary correlation structure between the missing data indicators, and has the potential of reducing the number of nuisance parameters. Real datasets from the International Breast Cancer Study Group and an environmental study involving dyspnoea in cotton workers are presented to illustrate the proposed methods.

Adapting sample size calculations to repeated measurements in clinical trials

Many of the repeated-measures sample size calculation methods presented in the literature are not suitable when: ” the different treatments are assumed to be equal on average at baseline time due to randomization, ” and the experimenters are interested in a pre-specified difference to be detected after a specific time period. The method presented here has been developed for those cases where a multivariate normal distribution can reasonably be assumed. It is likelihood-based and has been designed to be flexible enough to handle repeated-measures models, including a non-linear change in time, and an arbitrary correlation structure.

Streamflow Simulation: 1. A new look at Markovian Models, fractional Gaussian noise, and Crossing Theory

A broken line process is presented as a potential hydrologic simulation model. The process is composed of the sum across a series of broken lines. By proper choice of the number of broken lines considered and of their parameters, various statistical characteristics may be modeled. These include an arbitrary monotonic correlation structure and memory. In addition, the second derivative of the correlation function at the origin may be preserved. This preservation of the second derivative is an important property in crossing theory.