Analysis of Multivariate and High-Dimensional Data 532pages

This book is about data in many – and sometimes very many – variables and about analysing such data. The book attempts to integrate classical multivariate methods with contemporary methods suitable for high-dimensional data and to present them in a coherent and transparent framework. Writing about ideas that emerged more than a hundred years ago and that have become increasingly relevant again in the last few decades is exciting and challenging.With hindsight, we can reflect on the achievements of those who paved the way, whose methods we apply to ever bigger and more complex data and who will continue to influence our ideas and guide our research. Renewed interest in the classical methods and their extension has led to analyses that give new insight into data and apply to bigger and more complex problems. There are two players in this book: Theory and Data. Theory advertises its wares to lure Data into revealing its secrets, but Data has its own ideas. Theory wants to provide elegant solutions which answer many but not all of Data’s demands, but these lead Data to pose new challenges to Theory. Statistics thrives on interactions between theory and data, and we develop better theory when we ‘listen’ to data. Statisticians often work with experts in other fields and analyse data from many different areas. We, the statisticians, need and benefit from the expertise of our colleagues in the analysis of their data and interpretation of the results of our analysis. At times, existing methods are not adequate, and new methods need to be developed. This book attempts to combine theoretical ideas and advances with their application to data, in particular, to interesting and real data. I do not shy away from stating theorems as they are an integral part of the ideas and methods. Theorems are important because they summarise what we know and the conditions under which we know it. They tell us when methods may work with particular data; the hypotheses may not always be satisfied exactly, but a method may work nevertheless. The precise details do matter sometimes, and theorems capture this information in a concise way. Yet a balance between theoretical ideas and data analysis is vital. An important aspect of any data analysis is its interpretation, and one might ask questions like: What does the analysis tell us about the data?What new insights have we gained from a particular analysis? How suitable is my method formy data?What are the limitations of a particular method, and what other methods would produce more appropriate analyses? In my attempts to answer such questions, I endeavour to be objective and emphasise the strengths and weaknesses of different approaches.