Abstract In time delay estimation the correlator or, equivalently, matched filter estimator is widely used. Examples of its usage can be found in the global positioning system (GPS), radars and code division multiple access (CDMA) communication systems. Although widely used its performance is not studied in general case until recently. Partially this study is done in this thesis. If interfering signals like multipath or multiple access signals exist in addition to additive white Gaussian noise, as in GPS and CDMA, the correlator is not a maximum likelihood (ML) estimator. However, it is known that the correlator produces consistent estimates in the existence of multipath interference if the delay separation is larger than the correlation time of the signal (in direct sequence spread spectrum applications such as GPS and CDMA, the correlation time approximately equals the chip duration of the spreading code). It also performs well in the existence of multiple access interference (MAI), if the powers of the MAI signals are equal to the power of the desired signal. In this thesis the asymptotic distribution of the correlator estimator is derived in multisignal environments. Using the result, it can be analytically shown, that in these benign interference cases the exact ML estimator and the correlator estimators perform equally well in the sense that their asymptotic covariance matrices are equal. The thesis also verifies the well known result that if the signals are orthogonal, then the correlator and ML estimators perform equally. In addition, the correlator's asymptotic performance is investigated also in the inconsistent case by slightly extending the earlier results found in the literature. Also the resolution of the correlator estimator is investigated. It is numerically shown that the correlator estimator can produce consistent estimators even if the delay separation is less that the chip duration, which is commonly believed to be the resolution limit of the correlator. This can happen in fading channels where the multipath amplitudes are uncorrelated or just slightly correlated. This result seems to be fairly unknown. In addition to the classical ML estimator, where all the unknowns are assumed to be deterministic, also an improved ML estimator is investigated. This other ML estimator is obtained by assuming that the amplitudes are Gaussian distributed. It is an improved estimator in the sense that its asymptotic covariance, say CML, is less positive definite than that of the classical ML estimator CCML, i.e., CCML-CML is positive semidefinite. More importantly, this result is valid independent of the fact are the amplitudes really deterministic or Gaussian. This well known result is shown in this thesis to be valid also if the signals contain more than one unknown parameter, which occurs, for example, in direction-of-arrival estimation when two angles per arrival are to be estimated.

Real social graphs datasets are fundamental to understanding a variety of phenomena, such as epidemics, crowd management and political uprisings, yet releasing digital recordings of such datasets exposes the participants to privacy violations. A safer approach to making real social network topologies available is to anonymize them by modifying the graph structure enough as to decouple the node identity from its social ties, yet preserving the graph characteristics in aggregate. At scale, this approach comes with a significant challenge in computational complexity. This thesis questions the need to structurally anonymize very large graphs. Intuitively, the larger the graph, the easier for an individual to be “lost in the crowd”. On the other hand, at scale new topological structures may emerge, and those can expose individual nodes in ways that smaller structures do not. To answer this problem, this work introduces a set of metrics for measuring the indistinguishability of nodes in large-scale social networks independent of attack models and shows how different graphs have different levels of inherent indistinguishability of nodes. Moreover, we show that when varying the size of a graph, the inherent node indistinguishability decreases with the size of the graph. In other words, the larger a graph of a graph structure, the higher the indistinguishability of its nodes.

In this paper we consider conditional maximum likelihood (cml) estimates for item parameters in the Rasch model under random subject parameters. We give a simple approximation for the asymptotic covariance matrix of the cml-estimates. The approximation is stated as a limit theorem when the number of item parameters goes to infinity. The results contain precise mathematical information on the order of approximation. The results enable the analysis of the covariance structure of cml-estimates when the number of items is large. Let us give a rough picture. The covariance matrix has a dominating main diagonal containing the asymptotic variances of the estimators. These variances are almost equal to the efficient variances under ml-estimation when the distribution of the subject parameter is known. Apart from very small numbers n of item parameters the variances are almost not affected by the number n. The covariances are more or less negligible when the number of item parameters is large. Although this picture intuitively is not surprising it has to be established in precise mathematical terms. This has been done in the present paper. The paper is based on previous results [5] of the author concerning conditional distributions of non-identical replications of Bernoulli trials. The mathematical background are Edgeworth expansions for the central limit theorem. These previous results are the basis of approximations for the Fisher information matrices of cmlestimates. The main results of the present paper are concerned with the approximation of the covariance matrices. Numerical illustrations of the results and numerical experiments based on the results are presented in Strasser, [6].

A study into the factors that affect power in an analysis of covariance (ANCOVA) design were examined. Four factors - sample size, significance level, dependent variable-covariate correlations and homogeneity of regression - were varied in a population study. Results indicate that power increased when the dependent variable-covariate correlations increased and when sample size increased. Power also increased when a less stringent alpha level was used. Homogeneity of regression did not effect power. Implications and recommendations for the applied researcher are discussed.

One of the goals of perception is to learn to respond to coherence across space, time and modality. Here we present an abstract framework for the local online unsupervised learning of this coherent information using multi-stream neural networks. The processing units distinguish between feedforward inputs projected from the environment and the lateral, contextual inputs projected from the processing units of other streams. The contextual inputs are used to guide learning towards coherent cross-stream structure. The goal of all the learning algorithms described is to maximize the predictability between each unit output and its context. Many local cost functions may be applied: e.g. mutual information, relative entropy, squared error and covariance. Theoretical and simulation results indicate that, of these, the covariance rule (1) is the only rule that specifically links and learns only those streams with coherent information, (2) can be robustly approximated by a Hebbian rule, (3) is stable with input noise, no pairwise input correlations, and in the discovery of locally less informative components that are coherent globally. In accordance with the parallel nature of the biological substrate, we also show that all the rules scale up with the number of streams.

Space-Time Adaptive Processing is a signal processing technique that uses an adaptive array to help remove nonhomogeneous data points from a dataset. Since the early 1970s, STAP has been used in radar systems for their ability to "filter clutter, interference and jamming signals. One major flaw with early STAP radar systems is the reliance on non-robust estimators to estimate the noise condition. When even a single outlier is present, the earliest STAP radar systems would break down, causing the target to be missed. Many algorithms have been developed to successfully estimate the noise condition of the dataset when outliers are present. As recently as 2007, a STAP radar processing system based on Adaptive Complex Projection Statistics has been proposed and successfully"filters out the noise condition even when outliers are present. However, this algorithm requires the data to be entirely real. Radar data, which consists of amplitude and phase, is complex valued. Therefore, it must be converted into its rectangular components before processing can commence. This introduces many additional processing steps which significantly increase the computing time. The STAP radar algorithm of this thesis overcomes the problems with early radar systems. It is based on the Complex GM Wiener Filter (CGMWF) with the Minimum Covariance Determinant (MCD) for outlier detection. The robustness of the conventional Wiener "lter is enhanced by robust Huber Estimator, and using the MCD enables processing entirely in the complex domain. This results in a STAP radar algorithm with a breakdown point of nearly 35% and that enables processing entirely in the complex domain for fewer computing steps. / Master of Science

Indiana University-Purdue University Indianapolis (IUPUI) / In this dissertation, a potential outcomes (PO) based framework is developed for causally interpretable treatment effect parameters in the multinomial dependent variable regression framework. The specification of the relevant data generating process (DGP) is also derived. This new framework simultaneously accounts for the potential endogeneity of the treatment and loosens inter-category covariance restrictions on the multinomial outcome model (e.g., the independence from irrelevant alternatives restriction). Corresponding consistent estimators for the “deep parameters” of the DGP and the treatment effect parameters are developed and implemented (in Stata). A novel approach is proposed for assessing the inter-category covariance flexibility afforded by a particular multinomial modeling specification [e.g. multinomial logit (MNL), multinomial probit (MNP), and nested multinomial logit (NMNL)] in the context of our general framework. This assessment technique can serve as a useful tool for model selection. The new modeling/estimation approach developed in this dissertation is quite general. I focus here, however, on the NMNL model because, among the three modeling specifications under consideration (MNL, MNP and NMNL), it is the only one that is both computationally feasible and is relatively unrestrictive with regard to inter-category covariance. Moreover, as a logical starting point, I restrict my analyses to the simplest version of the model – the trinomial (three-category) NMNL with an endogenous treatment (ET) variable conditioned on individual-specific covariates only. To identify potential computational issues and to assess the statistical accuracy of my proposed NMNL-ET estimator and its implementation (in Stata), I conducted a thorough simulation analysis. I found that conventional optimization techniques are, in this context, generally fraught with convergence problems. To overcome this, I implement a systematic line search algorithm that successfully resolves this issue. The simulation results suggest that it is important to accommodate both endogeneity and inter-category covariance simultaneously in model design and estimation. As an illustration and as a basis for comparing alternative parametric specifications with respect to ease of implementation, computational efficiency and statistical performance, the proposed model and estimation method are used to analyze the impact of substance abuse/dependence on the employment status using the National Epidemiologic Survey on Alcohol and Related Conditions (NESARC) data.

FMRI datasets allow scientists to assess functionality of the brain by measuring the response of blood flow to a stimulus. Since the responses from neighboring locations within the brain are correlated, simple linear models that assume independence of measurements across locations are inadequate. Mixed models can be used to model the spatial correlation between observations, however selecting the correct covariance structure is difficult. Information criteria, such as AIC are often used to choose among covariance structures. Once the covariance structure is selected, significance tests can be used to determine if a region of interest within the brain is significantly active. Through the use of simulations, this project explores the performance of AIC in selecting the covariance structure. Type I error rates are presented for the fixed effects using the the AIC chosen covariance structure. Power of the fixed effects are also discussed.

Multiple-input Multiple-output (MIMO) wireless communication systems allow increased spectral efficiency and therefore promise significant improvement in performance. However, because of the rapid variation in channel state information (CSI) in networks with mobile nodes or scatterers, it is difficult both to maintain high communication performance and to create channel models that effectively represent the time-varying behavior of the channels. The spatial covariance of the MIMO channel describes the average power gain on each transmit-receive antenna pair as well as the correlation between the complex link gains and thus provides critical information for understanding the performance of the system and for creating models to accurately describe the interaction of the electromagnetic fields with the antennas. Furthermore, in many cases the MIMO signaling scheme uses knowledge of this spatial covariance. This thesis proposes a closed-form analytical model that allows estimation of the full MIMO channel covariance based on knowledge of the power angular spectrum (PAS) of the channel and the antenna radiation patterns. Comparison of covariance matrices computed using this model with those estimated from observed channel samples reveals the appropriate window over which the covariance should be estimated for non-WSS time-varying channels. Two approaches are developed to compare the covariance matrices in order to determine the appropriate window, both based on a metric, correlation matrix distance (CMD). Simulations based on both a two-ring propagation model and raytracing data in a three dimensional urban environment are included. The results reveal that with the optimal window size, the CMD of the estimated covariance is close to that of the analytical covariance. An average window size normalized by the scatterer circle radius is determined for practical estimation of covariance based on knowledge of the average distance to the scatterers. The impact of the number of scatterers on the optimal window size is analyzed as well. The results based on ray-tracing data show that the CMD of the estimated covariance using a 16 – 17λ window match the CMD of the analytical covariance.

Les méthodes du score de propension (PS) sont populaires pour estimer l’effet d’une exposition sur une issue à l’aide de données observationnelles. Cependant, leur mise en place pour l’analyse de données administratives soulève des questions concernant la sélection des covariables confondantes et le risque de covariables confondantes non mesurées. Notre objectif principal consiste à comparer différentes approches d’ajustement pour les covariables confondantes pou réliminer les biais dans le cadre d’études observationnelles basées sur des données administratives. Quatre méthodes de sélection de covariables seront comparées à partir de simulations, à savoir le score de propension à hautes dimensions (hdPS), le score de propension à hautes dimensions modifié (hdPS_0), le LASSO adapté pour l’issue (OAL) et l’estimation ciblée collaborative et évolutive par maximum de vraisemblance (SC-TMLE). Pour hdPS, hdPS_0et OAL, quatre approches d’ajustement sont considérées : 1) la pondération par l’inverse de probabilité de traitement (IPTW), 2) l’appariement, 3) l’appariement pondéré et 4) l’ajustement pour le score de propension. Des simulations avec 1000 observations et 100 covariables potentiellement confondantes ont été réalisées. Les résultats indiquent que la performance des méthodes d’ajustement varie d’un scénario à l’autre, mais l’IPTW, a réussi globalement à réduire le plus le biais et l’erreur quadratique moyenne parmi toutes les méthodes d’ajustement. De surcroît, aucune des méthodes de sélection de covariables ne semble vraiment arriver à corriger le biais attribuable aux covariables confondantes non mesurées. Enfin, la robustesse de l’algorithme hdPS peut être beaucoup améliorée, en éliminant l’étape 2 (hdPS_0). / Propensity score methods (PS) are common for estimating the effect of an exposure on an outcome using observational data. However, when analyzing administrative data, the applicationof PS methods raises questions regarding how to select confounders, and how to adjust forunmeasured ones. Our objective is to compare different methods for confounding adjustmentin the context of observational studies based on administrative data. Four methods for selecting confounders were compared using simulation studies: High-dimensional propensity score(hdPS), modified hdPS (hdPS_0), Outcome-adaptive Lasso (OAL) and Scalable collaborativetargeted maximum likelihood (SC-TMLE). For hdPS, hdPS_0 and OAL, four PS adjustmentapproaches were considered : 1) inverse probability of treatment weighting (IPTW), 2) matching, 3) matching weights and 4) covariate adjustment in the outcome model. Simulations basedon synthetically generated data with 1000 observations and 100 potential confounders havebeen realized. The results indicate that the performance of the adjustment methods variesfrom one scenario to another, but the IPTW, has globally succeeded in reducing the bias andthe mean square error. Moreover, no method for selecting confounders, seem to be able toadjust for unmeasured confounders. Finally, the robustness of the hdPS algorithm can begreatly improved, by eliminating step 2 (hdPS_0).