The analyzed system model in this paper is a distributed parallel detection network in which each secondary user (SU) evaluates the energy-based test statistic from the received observations and sends it to a fusion center (FC), which makes the final decision. Uncertainty in the noise variance at each SU is modeled as an unknown constant in a certain interval around the nominal noise variance. It is assumed that the SUs are heterogeneous in that the nominal noise variances and the uncertainty intervals can be different for different SUs. Moreover, the received signal power at each SU may be different. For the considered system model, the paper presents important results for two interrelated themes on cooperative energy detection (CED) in the presence of noise uncertainty (NU). First, the expressions for generalized SNR walls are derived for the classical CED fusion rule, i.e., sum of energies from all SUs. Second, a Dempster-Shafer theory (DST) based CED is proposed in the presence of NU with heterogeneous sensors. In the proposed scheme, the test statistic from each SU is the energy-based basic mass assignment (BMA) values, which are first discounted depending on the uncertainty level associated with the SU and then fused at the FC using the Dempster rule of combination to arrive at the global decision. It is shown that the proposed scheme outperforms the traditional sum fusion rule in terms of detection performance as well as the location of SNR wall.
Extended Bayesian information criterion (EBIC) and extended Fisher information criterion (EFIC) are two popular criteria for model selection in sparse high-dimensional linear regression models. However, EBIC is inconsistent in scenarios when the signal-to-noise-ratio (SNR) is high but the sample size is small, and EFIC is not invariant to data scaling, which affects its performance under different signal and noise statistics. In this paper, we present a refined criterion called EBIC R where the 'R' stands for robust. EBIC R is an improved version of EBIC and EFIC. It is scale-invariant and a consistent estimator of the true model as the sample size grows large and/or when the SNR tends to infinity. The performance of EBIC R is compared to existing methods such as EBIC, EFIC and multi-beta-test (MBT). Simulation results indicate that the performance of EBIC R in identifying the true model is either at par or superior to that of the other considered methods.
Model selection in linear regression models is a major challenge when dealing with high-dimensional data where the number of available measurements (sample size) is much smaller than the dimension of the parameter space. Traditional methods for model selection such as Akaike information criterion, Bayesian information criterion (BIC) and minimum description length are heavily prone to overfitting in the high-dimensional setting. In this regard, extended BIC (EBIC), which is an extended version of the original BIC and extended Fisher information criterion (EFIC), which is a combination of EBIC and Fisher information criterion, are consistent estimators of the true model as the number of measurements grows very large. However, EBIC is not consistent in high signal-to-noise-ratio (SNR) scenarios where the sample size is fixed and EFIC is not invariant to data scaling resulting in unstable behaviour. In this paper, we propose a new form of the EBIC criterion called EBIC-Robust, which is invariant to data scaling and consistent in both large sample size and high-SNR scenarios. Analytical proofs are presented to guarantee its consistency. Simulation results indicate that the performance of EBIC-Robust is quite superior to that of both EBIC and EFIC.
In this paper, we propose a novel model selection method named multi-beta-test (MBT) for the sparse high-dimensional linear regression model. The estimation of the correct subset in the linear regression problem is formulated as a series of hypothesis tests where the test statistic is based on the relative least-squares cost of successive parameter models. The performance of MBT is compared to existing model selection methods for high-dimensional parameter space such as extended Bayesian information criterion (EBIC), extended Fisher Information criterion (EFIC), residual ratio thresholding (RRT) and orthogonal matching pursuit (OMP) with a priori knowledge of the sparsity. Simulation results indicate that the performance of MBT in identifying the true support set surpasses that of EBIC, EFIC and RRT in certain regions of the considered parameter settings.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.