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.
This paper seeks to guide the reform of fiscal frameworks in Asia-Pacific in the context of calls for a more active fiscal policy in a shock-prone world. It highlights that the cost of fiscal support is large and that fiscal frameworks, including fiscal rules, are being put to the test given the sharp increase in debt, high interest and weaker growth prospects. The stress is only compounded by long-term challenges like aging populations, climate change and the need to deliver on the sustainable development goals. In this context, it is timely to review the effectiveness of fiscal policy in Asia-Pacific and seek for ways to strengthen fiscal frameworks. After the global financial crisis, fiscal policy in Asia-Pacific became more countercylical and stronger than in other regions—especially in advanced economies. The paper shows that the degree of countercyclicality has been asymetric, with larger responses during periods of weak growth, and in particular in response to large shocks—the global financial crisis and the pandemic. It highlights that responses to the pandemic were large and used a wide range of tools, and how fiscal and monetary policy complemented each as they responded to large shocks. It looks into the deterioration of debt dynamics in Asia-Pacific, as public debt has been rising persistently across most countries driven by declining growth and rising deficits—particualrly after the global financial crisis for advanced economies and after the pandemic for emerging market and low income countries. The paper reviews fiscal frameworks across Asia-Pacific, including the use of fiscal rules, medium-term fiscal frameworks, and fiscal councils. It describes the characteristics of fiscal rules, which usually focus on debt and budget balances and are set by law but tend to lack well-specified enforcement mechanism or escape clauses. It highlights that compliance with the rules has worsened following the pandemic as—in contrast with the outturns before the pandemic--Asia-Pacific countries tend to show larger deviations relative to other regions. It also shows that despite the increase adoption of medium-term fiscal frameworks in Asia-Pacific forward guidance has been hampered by the lack of binding targets and ex-post analysis. Moreover, they do not seem to have resulted in better macro-fiscal forecast in part due to weak capacity and enforcement, lack of integration with the annual budget, and exposure to shocks—with risk analysis mostly limited to qualitative discussions. Proposed reforms seek to implement a comprehensive, risk-based approach to public finances. They focus on strengthening the medium-term orientation of fiscal policy through credible medium-term fiscal plans, fiscal rules linked to the medium-term strategy and the annual budgets, and a stronger reliance on fiscal councils. They also emphasize the need for a broader view of the public sector as fiscal policy is being conducted through multiple channels, which requires assessing and managing vulnerabilities and a significant improvement in fiscal statistics. They also address aging and climate change by focusing on assessing large intergenerational trade-offs, reporting on long-term debt dynamics, and on green medium-term fiscal frameworks that incorporate the effects of climate change and climate policies.
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.
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