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The example doesn't state that it is an approximation of the variance of a binomial, rather that it is an approximation of the variance of the limiting normal distribution whose variance does exist. I'd recommend removing the disclaimer.
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Also, more text about the practical implications of this example would be good. The relative risk thing at the end is a start, but what about the proportion itself? What is a concrete, real-world example?
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Perhaps to avoid the subtleties of almost sure convergene, it is best to insert another example with C-infinity transformation on the real line. I can do so later.
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I was the one who added that comment. The support is not positive since a binomial random variable can be zero.
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333:{\displaystyle {\displaystyle \log \left({\frac {X_{n}}{n}}\right)}\log \left({\frac {X_{n}}{n}}\right)}
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0,P(|X_{n}-\theta |<\epsilon )=P({\sqrt {n}}|X_{n}-\theta |<{\sqrt {n}}\epsilon )\to 1}" /: -->
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0,P(|X_{n}-\theta |<\epsilon )=P({\sqrt {n}}|X_{n}-\theta |<{\sqrt {n}}\epsilon )\to 1}": -->
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on
Knowledge. If you would like to participate, please visit the project page, where you can join
89:
on
Knowledge. If you would like to participate, please visit the project page, where you can join
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0,P(|X_{n}-\theta |<\epsilon )=P({\sqrt {n}}|X_{n}-\theta |<{\sqrt {n}}\epsilon )\to 1}
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585:{\displaystyle {\displaystyle {\frac {\hat {p}}{\hat {q}}}}{\frac {\hat {p}}{\hat {q}}}}
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For example, how does this follow? "the logarithm of the estimated relative risk
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I'm sure these are trivial to someone who can already see it, but I don't.
513:{\displaystyle {\displaystyle n\rightarrow \infty }n\rightarrow \infty ..}
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to be large enough for the density at 0 to become vanishingly small.
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For example, how does this follow? "the asymptotic variance of
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It does exist provided you are dealing with positive support
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Someone commented on the variance of the log of a rv.
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620:You do not need normality to use the delta method
254:I could use more comments in the binomial example.
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979:{\displaystyle {\sqrt {n}}\epsilon \to \infty }
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592:has asymptotic variance equal to .."
250:more comments in the binomial example
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184:This article is within the scope of
79:This article is within the scope of
38:It is of interest to the following
1177:Low-importance Statistics articles
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204:Knowledge:WikiProject Mathematics
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698:..". Where does this come from?
691:{\displaystyle X_{n}\to \theta }
207:Template:WikiProject Mathematics
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473:0\right)\rightarrow 1}}" /: -->
408:0\right)\rightarrow 1}}" /: -->
340:does exist and is equal to .."
224:This article has been rated as
119:This article has been rated as
102:Template:WikiProject Statistics
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413:0\right)\rightarrow 1}}": -->
348:0\right)\rightarrow 1}}": -->
198:and see a list of open tasks.
93:and see a list of open tasks.
872:{\displaystyle n\to \infty }
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728:: -->
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220:Low
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