Markov inequality
Markov inequality
[′mar‚kȯf ‚in·i′kwäl·əd·ē] (statistics)
If x is a random variable with probability P and expectation E, then, for any positive number a and positive number n P (| x | ≥ a) ≤ E (| x |n/ a n).
References in periodicals archive
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We will need the following Markov inequality (see, e.g., [18]): Let p [member of] (0, [infinity]], k e {1,d}, and S [subset]Rd be abounded convex set with nonempty interior; one has
Since [tau] < 3, the Markov inequality and a basic property (see e.g.
It follows from (3.10), (3.11) and the Markov inequality that for any t > 0 and some constant C > 0,
By using (3.9) and the Markov inequality we obtain [X.sub.4] = [O.sub.p](1).
Markov inequality entails that the conditional probability that [tau.sub.n] [less than or equal to] [3.sub.t]/4 is larger than 1/3.
Solution by the Markov inequality. Let a [member of] I be such that [q.sub.n] attains its norm at this point.
Both Remez and Markov inequalities are well developed in the multivariate setting but the approach using Markov inequality seems to be more suitable for several variables.
WILHELMSEN, A Markov inequality in several dimensions, J.
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