Consistent estimator: Difference between revisions

Content deleted Content added
Biased but consistent: fixed def T_n so that its expectation is exactly \theta+\delta
changed application of Markov-inequality
Line 41:
* In order to demonstrate consistency directly from the definition one can use the inequality {{sfn|Amemiya|1985|loc=equation (3.2.5)}}
:: <math>
\Pr\!\big[h(T_n-\theta)\geq\varepsilon\big] \leq \frac{\operatorname{E}\big[h(T_n-\theta)\big]}{h(\varepsilon)},
</math>
the most common choice for function ''h'' being either the absolute value (in which case it is known as [[Markov inequality]]), or the quadratic function (respectively [[Chebyshev's inequality]]).