Bahadur, R. R.
(1960)
*On the asymptotic efficiency of tests and estimates*
Sankhya, 22
(3-4).
pp. 229-252.
ISSN 0972-7671

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Official URL: http://sankhya.isical.ac.in/search/2234/2234013.ht...

## Abstract

Let x_{1}, x_{2}, ... be a sequence of independent and identically distributed observations with distributions determined by a real valued parameter θ. For each n=1, 2, ..., let T_{n} = T_{n} (x_{1}, x_{2}... x_{n}) be a statistic such that the sequence T_{n} is a consistent estimate of θ. It is shown, under weak regularity conditions on the sample space of a single observation, that the asymptotic effective standard deviation of T_{n} cannot be less than [nI(θ)]^{{½}}. The asymptotic effective standard deviation of T_{n} is defined, roughly speaking, as the solution τ of the equation P(|T_{n}-θ|≥ ε|θ)=P(|N|≥ ε/τ) when n is large and ε is a small positive number, where N denotes a standard normal variable. It is also shown, under stronger regularity conditions, that the asymptotic effective standard deviation of the maximum likelihood estimate of θ is [nI(θ)]^{-{½}}. These conclusions concerning estimates are derived from certain conclusions concerning the relative efficiency of alternative statistical tests based on large samples.

Item Type: | Article |
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Source: | Copyright of this article belongs to Indian Statistical Institute. |

ID Code: | 27033 |

Deposited On: | 08 Dec 2010 12:49 |

Last Modified: | 11 May 2011 04:42 |

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