# Questions tagged [ancillary-statistics]

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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 ...
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### Is Complete Statistic Uncorrelated with Ancillary Statistic

By Basu's theorem, we know that any ancillary statistic is independent of a statistic that is both sufficient and complete. I was wondering if the assumption of sufficiency and completeness can be ...
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### Can someone explain the concept of ancillary statistics in layman's terms?

I'm having a hard time trying to relate or understand it in the simplest way (without solving). "Without solving" in a sense that I don't have to solve for the marginal distribution of T2, if for ...
An i.i.d sample $X_1,\dots,X_n$ from a scale family with c.d.f. $F(\frac{x}{\sigma})$ has $S(X)$ as an ancillary statistic if $S(X)$ depends on the sample only through $\frac{X_1}{X_n},\cdots,\frac{X_{... 1answer 243 views ### Ancillary statistics:Beta distribution is free of$\beta$? I am reading Robert V. Hogg Introduction to Mathematical Statistics 6th Version page 409, second paragraph.$X_1, X_2$is a random sample from a Gamma$\text{G}(\alpha,\beta)$distribution with ... 1answer 2k views ### What is the difference between conditioning on regressors vs. treating them as fixed? Sometimes we assume that regressors are fixed, i.e. they are non-stochastic. I think that means all our predictors, parameter estimates etc. are unconditional then, right? Might I even go so far that ... 0answers 423 views ### How to show ancillary statistic of normal random sample? Let$X_i \sim N(\mu,\sigma^2)$and$X_i$are independent. Then how to show that: $$T = \left(\frac{X_1-\bar{X}}{S},\frac{X_2-\bar{X}}{S},\ldots,\frac{X_n-\bar{X}}{S}\right)$$$T\$ is an ancillary ...
Working through a HW problem, and a hint is that for a decision rule $$T(X) = \frac{X_{(1)} + X_{(n)}}{2}$$ Then $$T - \bar{X}$$ is ancillary. Intuitively this makes complete sense, but I am ...