Asymptotic expansions and the deficiency concept

The purpose of this book is to present some means for the comparison of the quality of estimators constructed from samples with random sizes with that of estimators constructed from samples with non-random sizes. As this means it is proposed to use the deficiency. We also demonstrate that all those statistics that are regarded as asymptotically normal in the classical sense become asymptotically Laplace or Student if the sample size is random. We especially separate the case where the Student distribution parameter (“the number degrees of freedom”) is small. Thus the Laplace and Student distributions may be used as an asymptotic approximation in descriptive statistics being a convenient heavy-tailed alternative to stable laws.