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!
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.