Some Limit Theorems

  • Lucien Le Cam
Part of the Springer Series in Statistics book series (SSS)


The purpose of this chapter is to describe some of the relations that occur when a net {ℰ’v} of experiments converges to a limit in the weak sense of Chapter 2. Several of the results obtained in the previous chapters indicate that even the convergence Δ(ℰv, ℰ) → 0 is not a very strong relation. It is certainly much weaker than many of the stochastic process convergences often used as assumptions in the statistical literature. However, as we shall show below, even weak convergence is already rich in recognizable statistical implications.


Limit Theorem Loss Function Risk Function Weak Topology Cluster Point 
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Copyright information

© Springer-Verlag New York Inc. 1986

Authors and Affiliations

  • Lucien Le Cam
    • 1
  1. 1.Department of StatisticsUniversity of CaliforniaBerkeleyUSA

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