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2629:{\displaystyle \underbrace {\overbrace {estimate} ^{data-driven \choose observed}} _{\begin{pmatrix}computed\ value\ (e.g.,\ scalar\ ,\ vector.\ etc.)\\sample\ data\ dependent\\estimator\ dependent\end{pmatrix}}\longleftrightarrow \underbrace {\overbrace {estimator} ^{observable \choose model}} _{\begin{pmatrix}random\ quantity\\''estimating''\ model,\ method,\ or\ recipe\\controls\ estimate's\ distribution\end{pmatrix}}}
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The succeeding sentence seem to be devoted to showing that a certain statistic is an unbiased estimator of a certain probability of success. Why is that what matters in a section titled "sampling distribution"? It's not telling us anything about a sampling distribution.
1683:) we need to understand the distribution." What is this probability? Obviously the expectation of an estimator depends on its probability distribution. Why are we talking about the "expectation value" anyway? There is no reason what that should be our focus here.
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Under "estimator", the first box looks ok. The "realization" box does not. A realization is what an estimate is, not what as estimator is. And the third box has the same problem: "Special cases"? An estimate, rather than an estimator, is a special case.
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And why does every word except "of" in that last box begin with a capital letter? That's not what is in those other boxes. That is at best substandard. Knowledge generally is fairly sparing in the use of capital letters. See
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An estimate is not the same thing as an estimator: an estimate is a specific value dependent on only the dataset while an estimator is a method for estimation that is realized through random variables.
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is an example of a sampling distribution. Does this section even tell us what a sampling distribution is? It appears that whoever wrote it knows nothing about that.
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the value of the parameter. It does not say with certainty what that value is, but the way this is phrased could give the impression that that is what is meant.
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is the number of trials." So all estimators count the number of observations equal to 0 and divide by the sample size? Obviously that is false.
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The 2nd paragraph of the subsection titled "Unbiased" is quite confusing. I'm not sure what it's trying to say. It should be rewritten.
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may be useful to construct and insert in the article (mostly to aid learners)... We can probably generate a schematic like this?
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The first two boxes under "estimate" look ok. The third, "Provides 'true' value of the parameter" seems at best misleading. It
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The sampling distribution of the sample variance from a normally distributed population is a scaled chi-square distribution.
1560:". Indeed. The sampling distribution of the estimator is the sampling distribution of the estimator. A tautologous sentence.
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591:{\displaystyle X={\begin{cases}-1{\text{ w.p. }}{\frac {1}{2}}\\1{\text{ w.p. }}{\frac {1}{2}}\end{cases}}}
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I agree, the idea behind this figure is terrific, to visually summarize the duality between a (model)
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is the number of trials. To understand why the expectation value is dependent on the probability (
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on
Knowledge. If you would like to participate, please visit the project page, where you can join
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on
Knowledge. If you would like to participate, please visit the project page, where you can join
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This article was the subject of a Wiki
Education Foundation-supported course assignment, between
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Then "The sampling distribution is equivalent to the probability distribution of the estimator
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values fluctuating between samples estimators can be on target regardless of the differences.
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The sampling distribution is equivalent to the probability distribution of the estimator
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Then: "To understand why the expectation value is dependent on the probability (
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One should be able better to define this word without immediately linking it to
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I deleted it for reasons that should be obvious to those who know the subject.
771:{\displaystyle S_{n}^{2}={\frac {1}{n-1}}\sum _{i=1}^{n}(X_{i}-{\bar {X}})^{2}}
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has been defined, and obviously not all estimators are something divided by
510:{\displaystyle S_{n}^{2}={\frac {1}{n-1}}\sum _{i=1}^{n}(X_{i}-X_{n})^{2}}
1173:. Therefore, the sampling distribution S can be seen as the distribution
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373::In mathematics designations need to be redefined. This is fine.
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proving that the property holds regardless of what the value of
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either being a success or not it can be thought of as a
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can be thought of as a binomial distribution, or that
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Wiki
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1042:{\displaystyle S={\frac {Y}{n}}.}
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1603:" What? No statistic called
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