What is a good journal for submitting my article on a conjecture in theoretical statistics, re: ancillary complement for correlation?

Question

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 theoretical statistics, albeit a rigorous one—and I'm an applied statistician by training. Normally, I'd start with journals I'm citing (e.g., Electronic Journal of Statistics, Statistical Papers, Statistics and Probability Letters, Communications in Statistics—Theory and Methods, Theory of Probability and Its Applications) but I wonder if journals have a different standard for publishing conjectures.

The title and abstract are below, all suggestions are welcome!

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On a proposed ancillary complement to Pearson’s r and its implications for inferring the population correlation

Pearson’s r is the maximum likelihood estimator (MLE) of the population correlation ρ under bivariate normality. Like most MLEs, r is not a sufficient statistic. One could obtain greater parameter information from the sample, in principle, by conditioning r on an ancillary complement, but none is known to exist. Indeed, no ancillary complement need exist for any MLE, and even if it does, there is no standard method of discovering it.

In this paper, we define a function of a long-abandoned rank correlation statistic called the matching statistic, denoted m, as a pivotal quantity for Pearson’s r. We then modify the pivot to construct an asymptotically ancillary statistic for r. Finally, we propose this statistic is a non-unique, approximate ancillary complement, in finite samples, for r under bivariate normality. While our assertion remains a conjecture, we provide ample evidence it is not a vacuous one, both mathematically and empirically.

To wit, we prove conditioning r on the statistic always reduces r’s mean squared error (MSE) when specified assumptions hold—bivariate normality and ρ nonnegative and not large (ρ < .5). Monte Carlo simulation results illustrate why: r and m are correlated, especially in small samples, and conditioning r on the proposed ancillary complement partially rotates away this correlation without significantly reducing dependence on ρ. More fundamentally, we theorize MSE is reduced by controlling for a sample-specific source of variance in (X, Y): the rank order of observations in Y, conditional on the rank order of observations in X.

Answer 1

Although you describe your article as being "on a conjecture", from what you have described about the content, it looks to me like you do a lot of things first that are of definite substance — e.g., derive a new asymptotically ancillary statistic, prove that it has certain properties, show a simulation of its effect on estimation, give geometric insight into this result, etc. The fact that you also have some conjectures in your paper does not mean that there are no substantive results as well.

In view of this, I think it would be reasonable for you to submit your paper to one of the journals you've named. I would probably try Communications in Statistics—Theory and Methods first, since they do plently of new theory stuff. To ensure that your article is ready for submission, it might be worth running your work past a statistician with more theoretical grounding, just to check with them if there is any known way to prove/disprove your conjectures. If another statistician can provide a proof/disproof of one or more of your conjectures then they would be a good co-author on your paper and could probably improve it considerably.

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Unsolicited critique: Your abstract looks far too long and detailed to me. You don't need to give your specific mathematical notation and results in the abstract; just describe the paper and its contribution in high-level terms. Cut your abstract down to one-third of its present size and remove all the mathematical notation. Here is an example of a cut-down version:

Pearson’s sample correlation coefficient is the maximum likelihood estimator of the population correlation under bivariate normality. It is not a sufficient statistic. One could obtain greater parameter information from the sample by conditioning on an ancillary complement, but none is known to exist. In this paper, we define a function of a rank-correlation statistic called the "matching statistic" as a pivotal quantity for Pearson’s sample correlation coefficient, and we modify the pivot to construct an asymptotically ancillary statistic. We analyse some properties of this latter statistic showing that it can be used to improve estimation, and we also conduct a simulation analysis to this effect and give some geometric insights into why improved estimation occurs. We also propose some further properties as plausible conjuctures.