The complexity of today’s statistical data calls for modern mathematical tools. Many fields of science make use of mathematical statistics and require continuous updating on statistical technologies. Practice makes perfect, since mastering the tools makes them applicable. Our book of exercises and solutions offers a wide range of applications and numerical solutions based on R. In modern mathematical statistics, the purpose is to provide statistics students with a number of basic exercises and also an understanding of how the theory can be applied to real-world problems. The application aspect is also quite important, as most previous exercise books are mostly on theoretical derivations. Also we add some problems from topics often encountered in recent research papers. The book was written for statistics students with one or two years of coursework in mathematical statistics and probability, professors who hold courses in mathematical statistics, and researchers in other fields who would like to do some exercises on math statistics.
The complexity of today’s statistical data calls for modern mathematical tools. Many fields of science make use of mathematical statistics and require continuous updating on statistical technologies. Practice makes perfect, since mastering the tools makes them applicable. Our book of exercises and solutions offers a wide range of applications and numerical solutions based on R. In modern mathematical statistics, the purpose is to provide statistics students with a number of basic exercises and also an understanding of how the theory can be applied to real-world problems. The application aspect is also quite important, as most previous exercise books are mostly on theoretical derivations. Also we add some problems from topics often encountered in recent research papers. The book was written for statistics students with one or two years of coursework in mathematical statistics and probability, professors who hold courses in mathematical statistics, and researchers in other fields who would like to do some exercises on math statistics.
We develop a mixed-frequency, tree-based, gradient-boosting model designed to assess the default risk of privately held firms in real time. The model uses data from publicly-traded companies to construct a probability of default (PD) function. This function integrates high-frequency, market-based, aggregate distress signals with low-frequency, firm-level financial ratios, and macroeconomic indicators. When provided with private firms' financial ratios, the model, which we name signal-knowledge transfer learning model (SKTL), transfers insights gained from 35 thousand publicly-traded firms to more than 4 million private-held ones and performs well as an ordinal measure of privately-held firms' default risk.
Over the last decade, differential privacy (DP) has emerged as the de facto standard privacy notion for research in privacy-preserving data analysis and publishing. The DP notion offers strong privacy guarantee and has been applied to many data analysis tasks. This Synthesis Lecture is the first of two volumes on differential privacy. This lecture differs from the existing books and surveys on differential privacy in that we take an approach balancing theory and practice. We focus on empirical accuracy performances of algorithms rather than asymptotic accuracy guarantees. At the same time, we try to explain why these algorithms have those empirical accuracy performances. We also take a balanced approach regarding the semantic meanings of differential privacy, explaining both its strong guarantees and its limitations. We start by inspecting the definition and basic properties of DP, and the main primitives for achieving DP. Then, we give a detailed discussion on the the semantic privacy guarantee provided by DP and the caveats when applying DP. Next, we review the state of the art mechanisms for publishing histograms for low-dimensional datasets, mechanisms for conducting machine learning tasks such as classification, regression, and clustering, and mechanisms for publishing information to answer marginal queries for high-dimensional datasets. Finally, we explain the sparse vector technique, including the many errors that have been made in the literature using it. The planned Volume 2 will cover usage of DP in other settings, including high-dimensional datasets, graph datasets, local setting, location privacy, and so on. We will also discuss various relaxations of DP.
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