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Asymptotic Statistics by A.W. van der Vaart

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1

Introduction

           Why asymptotic statistics? The use of asymptotic approximations is two-fold. First, they enable us to find approximate tests and confidence regions. Second, approximations can be used theoretically to study the quality (efficiency) of statistical procedures.

1.1 Approximate Statistical Procedures

To carry out a statistical test, we need to know the critical value for the test statistic. In most cases this means that we must know the distribution of the test statistic under the null hypothesis. Sometimes this is known exactly, but more often only approximations are available. This may be because the distribution of the statistic is analytically intractable, or perhaps the postulated statistical model is considered only ...

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