Examples of estimation problems

  • Jiunn Tzon Hwang


Two examples of estimation problems are given. In the first example,X1,X2 andX3 are independent random variables withX1 having a Poisson distribution with mean θ1,X2 being N(θ1,1) and X33 having a chi-square distribution withn degrees of freedom. Based on these three observations, an estimator of (θ123), strictly better than the standard one (X1,X2,X3/(n+2)), is constructed by solving an inequality. In the second example, we establish a counter-example to the assertion that the lack of a nontrivial solution to a difference inequality (corresponding to the problem of improving upon an estimator δ through an identity of Hudson's (1974,Technical Report No. 58, Stanford University), and Stein's type (1973,Proc. Prague Symp. Asymptotic Statist., 345–381)) implies the admissibility of δ. Implications of these two examples are discussed.

AMS 1970 subject classification

Primary 62C15, 62F10 Secondary 62H99, 39A10 

Key words and phrases

Admissibility loss function differential inequality difference inequality Poisson distribution normal distribution and chi-square distribution 


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Copyright information

© The Institute of Statistical Mathematics, Tokyo 1982

Authors and Affiliations

  • Jiunn Tzon Hwang
    • 1
  1. 1.Cornell UniversityUSA

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