Modern Statistical Methods and Theory Published online by Cambridge University Press: aN Invalid Date NaN
We trace the evolution of statistics from its origins in the seventeenth century, contrasting twentieth-century data sets and approaches with those seen frequently today. This discussion motivates the approach taken in the book, which focuses on the bias--variance tradeoff as opposed to unbiased estimation, and on finite-sample guarantees as opposed to asymptotics, which can often be misleading in problems whose difficulty is controlled by several parameters. We introduce the decision-theoretic framework that underpins our assessment of the performance of statistical procedures, and discuss the concepts of minimaxity and adaptation. One of our perspectives is to seek to understand the behaviour of methods with respect to as wide a class of data generating mechanisms as possible, and in particular under model misspecification --- where an idealised model that motivates a procedure fails to hold. We discuss the use of the book for teaching and prerequisites for students, concluding with notation used throughout the book.
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