i Abstract In the environment of a large group of analysts who are willing to share their investment ideas publicly, it is a challenging task to find the ones who have a great skill and whose recommendations generate abnormal returns. We explore one such famous group, Value Investors Club, consisting of 1223 analysts be- tween the years 2000 and 2019. We separate the analysts into multiple groups, each representing their inherent abilities. The commonly used method of single hypothesis testing cannot be used as we test many analysts at once, and the multiple hypothesis testing methods need to be employed. Using these meth- ods, we are able to detect the subgroup of analysts who have abnormal returns from the Fama-French 4 factor portfolio. However, different methods lead to different groups of analysts deemed to be skilled. An overall portfolio consist- ing of all analysts generates large abnormal returns, which diminish with the increases in the holding period. Furthermore, analyses from analysts estimated to be skilled are used to form portfolios. We find that there are methods that have significantly larger abnormal returns compared to the overall portfolio; however, the methods are not consistent at producing such portfolios. Keywords multiple hypothesis testing, luck and skill, in- vestment ideas Title...

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Testing the equality between two high-dimensional covariance matrices is challenging. As the most efficient way to measure evidential discrepancies in observed data, the likelihood ratio test is expected to be powerful when the null hypothesis is violated. However, when the data dimensionality becomes large and potentially exceeds the sample size by a substantial margin, likelihood ratio based approaches face practical and theoretical challenges. To solve this problem, this study proposes a method by which we first randomly project the original high-dimensional data into lower-dimensional space, and then apply the corrected likelihood ratio tests developed with random matrix theory. We show that testing with a single random projection is consistent under the null hypothesis. Through evaluating the power function, which is challenging in this context, we provide evidence that the test with a single random projection based on a random projection matrix with reasonable column sizes is more powerful when the two covariance matrices are unequal but component-wise discrepancy could be small -- a weak and dense signal setting. To more efficiently utilize this data information, we propose combined tests from multiple random projections from the class of meta-analyses. We establish the foundation of the combined tests from our theoretical analysis that the p-values from multiple random projections are asymptotically independent in the high-dimensional covariance matrices testing problem. Then, we show that combined tests from multiple random projections are consistent under the null hypothesis. In addition, our theory presents the merit of certain meta-analysis approaches over testing with a single random projection. Numerical evaluation of the power function of the combined tests from multiple random projections is also provided based on numerical evaluation of power function of testing with a single random projection. Extensive simulations and two real genetic data analyses confirm the merits and potential applications of our test. / Statistics

Use of spatial data has become an important aspect of data analysis. Use of location information can provide useful insight into the dataset. Advancement of sensor technologies and improved data connectivity have made it possible to the generation of large amounts of passively generated user location data. Apart from passively generated data from users, explicit effort has been made by commercial vendors to curate large amounts of location related data such as residential histories from a variety of sources such as credit records, litigation data, driving license records etc. Such spatial data, when linked with other datasets can provide useful insights. In this dissertation, we show that spatial information of data enables us to derive useful insights in domains of text analysis and epidemiology. We investigated primarily two types of data having spatial information - text data with location information and disease related data having residential address information. We show that in the case of text data, spatial information helps us find spatially informative topics. In the case of epidemiological data, we show residential information can be used to identify high risk spatial regions. There are instances where a primary analysis is not sufficient to establish a statistically robust conclusion. For instance, in domains such as epidemiology, where a finding is not considered to be relevant unless some statistical significance is established. We proposed techniques for significant tests which can be applied to text analysis, topic modelling, and disease mapping tasks in order to establish significance of the findings. / Computer and Information Science

In many hypothesis testing problems such as one-sample and two-sample test problems, the test statistics are degenerate U-statistics. One of the challenges in practice is the computation of U-statistics for a large sample size. Besides, for degenerate U-statistics, the limiting distribution is a mixture of weighted chi-squares, involving the eigenvalues of the kernel of the U-statistics. As a result, it’s not straightforward to construct the rejection region based on this asymptotic distribution. In this research, we aim to reduce the computation complexity of degenerate U-statistics and propose an easy-to-calibrate test statistic by using the divide-and-conquer method. Specifically, we randomly partition the full n data points into kn even disjoint groups, and compute U-statistics on each group and combine them by averaging to get a statistic Tn. We proved that the statistic Tn has the standard normal distribution as the limiting distribution. In this way, the running time is reduced from O(n^m) to O( n^m/km_n), where m is the order of the one sample U-statistics. Besides, for a given significance level , it’s easy to construct the rejection region. We apply our method to the goodness of fit test and two-sample test. The simulation and real data analysis show that the proposed test can achieve high power and fast running time for both one and two-sample tests.

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Recent technological advances in fields like medicine and genomics have produced high-dimensional data sets and a challenge to correctly interpret experimental results. The Optimal Discovery Procedure (ODP) (Storey 2005) builds on the framework of Neyman-Pearson hypothesis testing to optimally test thousands of hypotheses simultaneously. The method relies on the assumption of normally distributed data; however, many applications of this method will violate this assumption. This thesis investigates the sensitivity of this method to detection of significant but nonnormal data. Overall, estimation of the ODP with the method described in this thesis is satisfactory, except when the nonnormal alternative distribution has high variance and expectation only one standard deviation away from the null distribution.

The Neotropical region is the most biologically diverse region on the planet. The region encompasses a variety of ecosystems and has long been the target of researchers interested in patterns of species diversity and distribution. More recently, molecular data have been incorporated into methods for reconstructing the historical relationships among geographical areas and their biotas. Molecular phylogenetics has provided insights into diversification patterns and the influence of Late Cenozoic events on the evolutionary history of the region. Nevertheless, considering the vast extent and complexity of the region, more studies are needed to fully appreciate the patterns of biogeography and the mechanisms that generate and maintain its biodiversity. Therefore, in Chapter 1 I employed molecular methods to reconstruct the phylogenetic relationships of the subfamily Sigmodontinae, which is the most diverse and widespread radiation of Neotropical rodents. I was able to evaluate controversial hypotheses about the paleogeographic scenarios implicated to explain the biogeography of sigmodontines. Advances in sequencing technology and analytical approaches have revolutionized the role of historical biogeography in elucidating the spatial and temporal context of diversification, and the integrative field of phylogeography was fundamental to the development of biogeography at the intraspecific level. However, the potential of phylogeography to unravel diverse historical scenarios in a tractable statistical framework has been largely unexplored for the Neotropics as a whole. In order to integrate more robust hypothesis testing to elucidate the evolutionary history of Amazonia's biota, I devoted Chapter 2 to a review of Amazonian phylogeography that I anticipate will improve the basis for interpreting the patterns and processes of diversification in Amazonia. Chapter 3 is a thorough species account of spiny rats of the genus Proechimys, which is poorly known taxonomically despite its diversity and widespread distribution in the Neotropics. This taxonomic revision will benefit researchers interested in using such information with coalescent-based methods of species delimitation aimed at an integrative and stable taxonomy. Lastly, Chapter 4 deals with the phylogeography of P. roberti. This species occurs in southeastern Amazonia and the Cerrado of central Brazil. I employed a dense taxon sampling and used coalescent-based methods to demonstrate that rivers and topography have a causal link to the geographic structure of P. roberti populations. In my dissertation, I used a combination of molecular genetics tools to provide a better understanding of the biogeography and evolution of some of the most diverse groups of Neotropical mammals. My dissertation interacts in many levels with my future research interests. These present and future efforts hold promise for unraveling the evolutionary history of the Neotropical region and its biota, and will assist in conservation decisions aiming at preserving its unparalleled biodiversity.

This study compared the results of his chi square text of independence and the corrected chi square statistic against Fisher's exact probability test (the hypergeometric distribution) in contection with sampling from a finite population. Data were collected by advancing the minimum call size from zero to a maximum which resulted in a tail area probability of 20 percent for sample sizes from 10 to 100 by varying increments. Analysis of the data supported the rejection of the null hypotheses regarding the general rule-of-thumb guidelines concerning sample size, minimum cell expected frequency and the continuity correction factor. it was discovered that the computation using Yates' correction factor resulted in values which were so overly conservative (i.e. tail area porobabilities that were 20 to 50 percent higher than Fisher's exact test) that conclusions drawn from this calculation might prove to be inaccurate. Accordingly, a new correction factor was proposed which eliminated much of this discrepancy. Its performance was equally consistent with that of the uncorrected chi square statistic and at times, even better.

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