Performance and Robustness Analysis of Co-Prime and Nested Sampling

Coprime and nested sampling are well known deterministic sampling techniques that operate at rates significantly lower than the Nyquist rate, and yet allow perfect reconstruction of the spectra of wide sense stationary signals. However, theoretical guarantees for these samplers assume ideal conditions such as synchronous sampling, and ability to perfectly compute statistical expectations. This thesis studies the performance of coprime and nested samplers in spatial and temporal domains, when these assumptions are violated. In spatial domain, the robustness of these samplers is studied by considering arrays with perturbed sensor locations (with unknown perturbations). Simplified expressions for the Fisher Information matrix for perturbed coprime and nested arrays are derived, which explicitly highlight the role of co-array. It is shown that even in presence of perturbations, it is possible to resolve $O(M^2)$ under appropriate conditions on the size of the grid. The assumption of small perturbations leads to a novel ``bi-affine" model in terms of source powers and perturbations. The redundancies in the co-array are then exploited to eliminate the nuisance perturbation variable, and reduce the bi-affine problem to a linear underdetermined (sparse) problem in source powers. This thesis also studies the robustness of coprime sampling to finite number of samples and sampling jitter, by analyzing their effects on the quality of the estimated autocorrelation sequence. A variety of bounds on the error introduced by such non ideal sampling schemes are computed by considering a statistical model for the perturbation. They indicate that coprime sampling leads to stable estimation of the autocorrelation sequence, in presence of small perturbations. Under appropriate assumptions on the distribution of WSS signals, sharp bounds on the estimation error are established which indicate that the error decays exponentially with the number of samples. The theoretical claims are supported by extensive numerical experiments.

Warning Against Faking: Boon or Bane? Effects on Test Score Validity

Previous research found personality test scores to be inflated on average among individuals who were motivated to present themselves in a desirable fashion in high stakes situations, such as during the employee selection process. One apparently effective way to reduce the undesirable test score inflation in such situations was to warn participants against faking. This research set out to investigate whether warning against faking would indeed affect personality test scores in the theoretically expected fashion. Contrary to expectations, the results did not support the hypothesized causal chain. Results across three studies show that while a warning may lower test scores in participants motivated to respond desirably (i.e., to fake), the effect of warning on test scores was not fully mediated by: a reduction in motivation to do well and self-reports of exaggerated responses in the personality test. Theoretical and practical implications are discussed.