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Revisiting Local Asymptotic Normality (LAN) and Passing on to Local Asymptotic Mixed Normality (LAMN) and Local Asymptotic Quadratic (LAQ) Experiments

  • George G. Roussas
  • Debasis Bhattacharya
Chapter

Abstract

Let X 1, , X n be a random sample of size n from an underlying parametric statistical model. Then the basic statistical problem may be stated as follows: On the basis of a random sample, whose probability law depends on a parameter θ, discriminate between two values θ and θ (θ≠θ). When the parameters are sufficiently far apart, any decent statistical procedure will do the job. A problem arises when the parameter points are close together, and yet the corresponding probability measures are substantially or even vastly different. The present paper revolves around ways of resolving such a problem. The concepts and methodology used are those of contiguity, Local Asymptotic Normality (LAN), Local Asymptotic Mixed Normality (LAMN), and Local Asymptotic Quadratic (LAQ) experiments.

Keywords

Probability Measure Exponential Family Inst Stat Math Regular Estimate Local Asymptotic Normality 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  1. 1.Department of StatisticsUniversity of CaliforniaDavisUSA

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