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distribution is, in a sense, locally uniform. This is often considered desirable and leads to the convenient property that a small change in the parameter does not dramatically change the distribution of the estimator.
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273:{\displaystyle {\sqrt {n}}\left({\hat {\theta }}_{n}-\psi (\theta +h/{\sqrt {n}})\right){\stackrel {\theta +h/{\sqrt {n}}}{\rightarrow }}L_{\theta }}
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Beran, R. (1995). THE ROLE OF HAJEK'S CONVOLUTION THEOREM IN STATISTICAL THEORY
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Vaart AW van der. Asymptotic
Statistics. Cambridge University Press; 1998.
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that satisfy certain regularity conditions which make them amenable to
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where the convergence is in distribution under the law of
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are non-regular estimators when the population parameter
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313:{\displaystyle \theta +h/{\sqrt {n}}}
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72:{\displaystyle {\hat {\theta }}_{n}}
128:is said to be regular if for every
324:Examples of non-regular estimators
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30:analysis. The convergence of a
16:Class of statistical estimators
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101:{\displaystyle \psi (\theta )}
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108:based on a sample of size
349:{\displaystyle \theta }
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24:statistical estimators
381:James-Stein estimator
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334:James-Stein estimator
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32:regular estimator's
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20:Regular estimators
376:Hodges' estimator
330:Hodges' estimator
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141:{\displaystyle h}
121:{\displaystyle n}
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371:Cramér-Rao bound
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43:An estimator
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387:References
39:Definition
28:asymptotic
430:Estimator
366:Estimator
344:θ
328:Both the
290:θ
266:θ
236:θ
231:→
198:θ
192:ψ
189:−
177:^
174:θ
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58:^
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424:Category
360:See also
332:and the
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