Jianqing Fan

In contemporary science and engineering applications, the volume of available data is growing at an enormous rate. Spectral methods have emerged as a simple yet surprisingly effective approach for extracting information from massive, noisy and incomplete data. A diverse array of applications have been found in machine learning, imaging science, financial and econometric modeling, and signal processing.This monograph presents a systematic, yet accessible introduction to spectral methods from a modern statistical perspective, highlighting their algorithmic implications in diverse large-scale applications. The authors provide a unified and comprehensive treatment that establishes the theoretical underpinnings for spectral methods, particularly through a statistical lens.Building on years of research experience in the field, the authors present a powerful framework, called leave-one-out analysis, that proves effective and versatile for delivering fine-grained performance guarantees for a variety of problems. This book is essential reading for all students, researchers and practitioners working in Data Science.

Financial econometrics is an interdisciplinary subject that uses statistical methods and economic theory to address a variety of quantitative problems in finance. This compact, master's-level textbook focuses on methodology and includes real financial data illustrations throughout. The mathematical level is purposely kept moderate, allowing the power of the quantitative methods to be understood without too much technical detail. Wherever possible, the authors indicate where to find the relevant R codes to implement the various methods. This book grew out of a course at Princeton University which is one of the world's flagship programs in computational finance and financial engineering. It will therefore be useful for those with an economics and finance background who are looking to sharpen their quantitative skills, and also for those with strong quantitative skills who want to learn how to apply them to finance.

Amongmanyexcitingdevelopmentsinstatisticsoverthelasttwodecades, nonlineartimeseriesanddata-analyticnonparametricmethodshavegreatly advanced along seemingly unrelated paths. In spite of the fact that the - plication of nonparametric techniques in time series can be traced back to the 1940s at least, there still exists healthy and justi?ed skepticism about the capability of nonparametric methods in time series analysis. As - thusiastic explorers of the modern nonparametric toolkit, we feel obliged to assemble together in one place the newly developed relevant techniques. Theaimofthisbookistoadvocatethosemodernnonparametrictechniques that have proven useful for analyzing real time series data, and to provoke further research in both methodology and theory for nonparametric time series analysis. Modern computers and the information age bring us opportunities with challenges. Technological inventions have led to the explosion in data c- lection (e.g., daily grocery sales, stock market trading, microarray data). The Internet makes big data warehouses readily accessible. Although cl- sic parametric models, which postulate global structures for underlying systems, are still very useful, large data sets prompt the search for more re?nedstructures,whichleadstobetterunderstandingandapproximations of the real world. Beyond postulated parametric models, there are in?nite other possibilities. Nonparametric techniques provide useful exploratory tools for this venture, including the suggestion of new parametric models and the validation of existing ones.

Statistical Foundations of Data Science gives a thorough introduction to commonly used statistical models, contemporary statistical machine learning techniques and algorithms, along with their mathematical insights and statistical theories. It aims to serve as a graduate-level textbook and a research monograph on high-dimensional statistics, sparsity and covariance learning, machine learning, and statistical inference. It includes ample exercises that involve both theoretical studies as well as empirical applications.The book begins with an introduction to the stylized features of big data and their impacts on statistical analysis. It then introduces multiple linear regression and expands the techniques of model building via nonparametric regression and kernel tricks. It provides a comprehensive account on sparsity explorations and model selections for multiple regression, generalized linear models, quantile regression, robust regression, hazards regression, among others. High-dimensional inference is also thoroughly addressed and so is feature screening. The book also provides a comprehensive account on high-dimensional covariance estimation, learning latent factors and hidden structures, as well as their applications to statistical estimation, inference, prediction and machine learning problems. It also introduces thoroughly statistical machine learning theory and methods for classification, clustering, and prediction. These include CART, random forests, boosting, support vector machines, clustering algorithms, sparse PCA, and deep learning.

Data-analytic approaches to regression problems, arising from many scientific disciplines are described in this book. The aim of these nonparametric methods is to relax assumptions on the form of a regression function and to let data search for a suitable function that describes the data well. The use of these nonparametric functions with parametric techniques can yield very powerful data analysis tools. Local polynomial modeling and its applications provides an up-to-date picture on state-of-the-art nonparametric regression techniques. The emphasis of the book is on methodologies rather than on theory, with a particular focus on applications of nonparametric techniques to various statistical problems. High-dimensional data-analytic tools are presented, and the book includes a variety of examples. This will be a valuable reference for research and applied statisticians, and will serve as a textbook for graduate students and others interested in nonparametric regression.