Questions tagged [ancillary-statistics]
The ancillary-statistics tag has no usage guidance.
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Why does the sufficient statistic for the bivariate normal not imply a sufficient statistic for the correlation under bivariate normality?
This question links to a document by Jon Wellner that defines the sufficient statistic for the multivariate normal (p. 7, Example 2.7). The result follows from the factorization theorem and is proven ...
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What is a good journal for submitting my article on a conjecture in theoretical statistics, re: ancillary complement for correlation?
I'm working on a draft of a statistics article, and I'd like to plan for the journal where I'll ultimately submit. My problem is, the article topic is somewhat abstract—it's a conjecture in ...
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Show that Sample Mean and Sample Range are independently distributed for a random sample from Normal Distribution
Let $X_{1},\ldots {, X_{n}}$ be iid random variables with $X_{1} ∼ N(µ,\sigma ^{2}).$Let $\bar{X}= \sum_{i=1}^{n} \frac{X_{i}}{n}$, $R=max_{1\le i \le n} \{X_{i}\}$-$min_{1\le i \le n}\{X_{i}\}$.Show ...
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Does this distribution belong to the exponential family? [duplicate]
I was looking at a problem in the book of "Statistical Inference" second edition by George Casella and Roger L. Berger from chapter 6 that deals with sufficient statistics, minimal ...
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Ancillary function of a random vector, which is independent of change of origin and scale
Let
$(X_1,\ldots,X_n)$ be a random vector, whose distribution involves unknown: location parameter $\mu$ and a scale parameter $\sigma>0$. It follows, that any measurable function $f(X_1,\ldots,X_n)...
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How can I show that $(\bar{X}, S^2)$ is independent of $(X_{(n)}-\bar{X})/S$?
Let $X_1,\ldots,X_n$ be a random sample from $N(\mu,\sigma^2)$ with both parameters unknown. How can I show that $(\bar{X}, S^2)$ is independent of $(X_{(n)}-\bar{X})/S$?
Work:
I am quite confident ...
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What does the assumption of the Fisher test that "The row and column totals should be fixed" mean?
As this source states, one of the assumptions to perform Fisher's exact test of independence is that the row and column totals should be fixed. However, I find the explanation coming with it pretty ...
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What are the broadest class of distributions for which the range statistic is ancillary to the expectation of the random variable?
Let $X_1,X_2,X_3$ be iid random variables such that $E(X_1)=\mu$
Define $X_{(3)}$ and $X_{(1)}$ as the maximum and minimum order statistics respectively.
I know that if $X$ is normal, $R=X_{(3)}-X_{...
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Is Dixon's Q statistic ancillary for normal data?
Dixon's Q statistic is the ratio of the "gap" between an outlier and the nearest value, over the range of the data.
I would like to know is if this is ancillary to the parameters of the normal ...
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Prove that $X_{(n)} - X_{(1)}$ is an ancillary statistics
Let $X_{1},X_{2},\ldots,X_{n}$ be an independent and equally distributed random sample whose distribution is uniform on the interval $(\theta,\theta+1)$, $-\infty<\theta<+\infty$. Then consider ...
user242554
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Proof that the mean is a complete sufficient statistic and the sample variance is an ancillary statistic
I have $X_1, X_2, ..., X_n $ that are random samples from the single variate $N(\mu,\sigma^2) $. I want to prove that the mean $\bar{X}$ and the sample variance $s_x ^2 = \frac{1}{(n- 1)} \sum_{i=1}^...
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Showing these statistics are ancillary
Let $Z_i = X_{(n)} - X_{(i)}$ for $i=1,2,\dots,n$ where $X \sim N(\mu, 1)$, and $X_{(i)}$ is the ith order statistic of the sample.
I want to show $Z=(Z_1,\dots,Z_{n-1})$ are ancillary for $\mu$.
My ...
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Rss and sample variance indipendence in simple linear regression
Suppose that $ (X_1 ,Y_1...X_n,Y_n) $ is an i.i.d. random sample from a simple homoschedastic linear model $Y=\alpha +\beta X+e $ , with $e|X \sim N(0,\sigma_e^2)$.
I want to understand if $ \frac{...
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Is Uniform distribution [a,b] always symmetric?
I want to know whether any uniform distributed random variable is symmetric on any interval [a,b].
My thinking is it is symmetric on any interval [a,b].
i tried to think about a counter-example. But I ...
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What is an approximate ancillary statistic?
In the article Assessing the Accuracy of the Maximum Likelihood Estimator: Observed Versus Expected Fisher Information the authors use the expression "approximate ancillary statistic". This expression ...
