arXiv subjects

Olivia McGough

Publications and source records attributed to Olivia McGough.

4 recordsLinked to original sources

arXiv2026

Valid F-screening in linear regression

Suppose that a data analyst wishes to report the results of a least squares linear regression only if the overall null hypothesis, $H_0^{1:p}: β_1= β_2 = \ldots = β_p=0$, is rejected. This practice, which we refer to as F-screening (since the overall null hypothesis is typically tested using an $F$-statistic), is in fact common across a number of applied fields. Unfortunately, it poses a problem: standard guarantees for the inferential outputs of linear regression, such as Type 1 error control of hypothesis tests and nominal coverage of confidence intervals, hold unconditionally, but fail to hold conditional on rejection of the overall null hypothesis. In this paper, we develop an inferential toolbox for the coefficients in a least squares model that are valid conditional on rejection of the overall null hypothesis. We develop selective p-values that lead to tests that are consistent and control the selective Type 1 error, i.e., the Type 1 error conditional on having rejected the overall null hypothesis. Furthermore, they can be computed without access to the raw data, i.e., using only the standard outputs of a least squares linear regression, and therefore are suitable for use in a retrospective analysis of a published study. We also develop confidence intervals that attain nominal selective coverage, and point estimates that account for having rejected the overall null hypothesis. We derive an expression for the Fisher information about the coefficients resulting from the proposed approach, and compare this to the Fisher information that results from an alternative approach that relies on sample splitting. We investigate the proposed approach in simulation and via re-analysis of two datasets from the biomedical literature.

stat.ME↗

arXiv2026

Infer-and-widen, or not?

In recent years, there has been substantial interest in the task of selective inference: inference on a parameter that is selected from the data. Many of the existing proposals fall into what we refer to as the \emph{infer-and-widen} framework: they produce symmetric confidence intervals whose midpoints do not account for selection and therefore are biased; thus, the intervals must be wide enough to account for this bias. In this paper, we investigate infer-and-widen approaches in three vignettes: the winner's curse, maximal contrasts, and inference after the lasso. In each of these examples, we show that a state-of-the-art infer-and-widen proposal leads to confidence intervals that are wider than a non-infer-and-widen alternative. Furthermore, even an ``oracle'' infer-and-widen confidence interval -- the narrowest possible interval that could be theoretically attained via infer-and-widen -- can be wider than the alternative.

stat.ME↗

arXiv2022

Population-Based Hierarchical Non-negative Matrix Factorization for Survey Data

Motivated by the problem of identifying potential hierarchical population structure on modern survey data containing a wide range of complex data types, we introduce population-based hierarchical non-negative matrix factorization (PHNMF). PHNMF is a variant of hierarchical non-negative matrix factorization based on feature similarity. As such, it enables an automatic and interpretable approach for identifying and understanding hierarchical structure in a data matrix constructed from a wide range of data types. Our numerical experiments on synthetic and real survey data demonstrate that PHNMF can recover latent hierarchical population structure in complex data with high accuracy. Moreover, the recovered subpopulation structure is meaningful and can be useful for improving downstream inference.

stat.CO↗

arXiv2021

Counting weighted maximal chains in the circular Bruhat order

The totally nonnegative Grassmannian $\mathrm{Gr}(k,n)_{\geq0}$ is the subset of the real Grassmannian $\mathrm{Gr}(k,n)$ consisting of points with all nonnegative Plücker coordinates. The circular Bruhat order is a poset isomorphic to the face poset of A. Postnikov's (2005) positroid cell decomposition of $\mathrm{Gr}(k,n)_{\geq0}$. We provide a closed formula for the sum of its weighted chains in the spirit of J. Stembridge (2002).

math.CO↗