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I am not a mathematician, so apologises in advance for confused terminology. I think this question is related to the analytical/numerical dichotomy, but having researched these terms, I'm not clear. (see this question)

I am trying to replicate this paper and am confused by their confidence intervals. This is a maths question because I'm asking about the type of calculations used, not about the statistic itself.

Specifically, the confidence interval I'm talking about is: (- inifinty, -39.2] U [5.3, infinity) (Column 5, Row 2, page 47).

To me this interval seems to have been found both by ‘working out’ (numerical) calculations and by mathemitical reasoning (analytical). I say this because my intuition/common sense suggests you can’t arrive at infinity as a numerical solution for an answer, conversly, an analytical solution won’t delimit bounds by - 39.2 and 5.3.

Let me add that my motivation for asking this question stems from trying to replicate this interval using R. After coding up the test statistic it became obvious to me that R wouldn’t magically spit out infinity as an answer, because computer algorightms solve numerical, not analytical problems.

EDIT:

The test statistic I am talking about here is the Anderson-Rubin stat. According to this paper, an AR confidence set can take one of four values, which are found by solving a quadratic inequality, including the whole Real line and a union of two infinite intervals (Page 6).

So to re-phrase my question: I can conceptually see how R might calculate a finite interval and likewise how mathematical reasoning cold calculate an infinite interval. But I'm confused about the middle case: A union of two infinite intervals.

SeánMcK
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  • Usually a confidence interval for an unknown population parameter $\theta$ is based on a point estimate $\hat theta$ computed from data, a random sample of observations from the population. Then $\hat \theta$ is typically contained in the confidence interval (but $\hat \theta$ is not necessarily the center of the CI. In the link, the set $(-\infty, -39.2)\cup(5.3,\infty)$ seems to be the complement of the interval $(-39.,2,5.3).$ I cannot imagine that a correct confidence interval would be of the form $(-\infty, -39.2)\cup(5.3,\infty).$ That might be the rejection region for a test.$ – BruceET Feb 21 '18 at 00:07
  • If you can describe clearly a population, a sample from that population, and a population parameter you are trying to estimate, then maybe we can be of some help in a discussion about point and interval estimates. – BruceET Feb 21 '18 at 00:09
  • Hi @BruceET, thanks for your comments. I've added some additional info to the question, hopefully that clarify what I'm talking about? Please let me know if I'm still not clear. – SeánMcK Feb 23 '18 at 12:45

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