arXiv subjects

Wayne Oldford

Publications and source records attributed to Wayne Oldford.

5 recordsLinked to original sources

arXiv2023

Recursive random binning to detect and display pairwise dependence

Random binnings generated via recursive binary splits are introduced as a way to detect, measure the strength of, and to display the pattern of association between any two variates, whether one or both are continuous or categorical. This provides a single approach to ordering large numbers of variate pairs by their measure of dependence and then to examine any pattern of dependence via a common display, the departure display (colouring bins by a standardized Pearson residual). Continuous variates are first ranked and their rank pairs binned. The Pearson's goodness of fit statistic is applicable but the classic $\chi^2$ approximation to its null distribution is not. Theoretical and empirical investigations motivate several approximations, including a simple $\chi^2$ approximation with real-valued, yet intuitive, degrees of freedom. Alternatively, applying an inverse probability transform from the ranks before binning returns a simple Pearson statistic with the classic degrees of freedom. Recursive random binning with different approximations is compared to recent grid-based methods on a variety of non-null dependence patterns; the method with any of these approximations is found to be well-calibrated and relatively powerful against common test alternatives. Method and displays are illustrated by applying the screening methodology to a publicly available data set having several continuous and categorical measurements of each of 6,497 Portuguese wines. The software is publicly available as the R package AssocBin.

stat.ME↗

arXiv2023

Balancing central and marginal rejection when combining independent significance tests

A common approach to evaluating the significance of a collection of $p$-values combines them with a pooling function, in particular when the original data are not available. These pooled $p$-values convert a sample of $p$-values into a single number which behaves like a univariate $p$-value. To clarify discussion of these functions, a telescoping series of alternative hypotheses are introduced that communicate the strength and prevalence of non-null evidence in the $p$-values before general pooling formulae are discussed. A pattern noticed in the UMP pooled $p$-value for a particular alternative motivates the definition and discussion of central and marginal rejection levels at $α$. It is proven that central rejection is always greater than or equal to marginal rejection, motivating a quotient to measure the balance between the two for pooled $p$-values. A combining function based on the $χ^2_κ$ quantile transformation is proposed to control this quotient and shown to be robust to mis-specified parameters relative to the UMP. Different powers for different parameter settings motivate a map of plausible alternatives based on where this pooled $p$-value is minimized.

stat.ME↗

arXiv2018

A framework for measuring dependence between random vectors

A framework for quantifying dependence between random vectors is introduced. With the notion of a collapsing function, random vectors are summarized by single random variables, called collapsed random variables in the framework. Using this framework, a general graphical assessment of independence between groups of random variables for arbitrary collapsing functions is provided. Measures of association computed from the collapsed random variables are then used to measure the dependence between random vectors. To this end, suitable collapsing functions are presented. Furthermore, the notion of a collapsed distribution function and collapsed copula are introduced and investigated for certain collapsing functions. This investigation yields a multivariate extension of the Kendall distribution and its corresponding Kendall copula for which some properties and examples are provided. In addition, non-parametric estimators for the collapsed measures of dependence are provided along with their corresponding asymptotic properties. Finally, data applications to bioinformatics and finance are presented.

stat.ME↗

arXiv2017

Visualizing Dependence in High-Dimensional Data: An Application to S&P 500 Constituent Data

The notion of a zenpath and a zenplot is introduced to search and detect dependence in high-dimensional data for model building and statistical inference. By using any measure of dependence between two random variables (such as correlation, Spearman's rho, Kendall's tau, tail dependence etc.), a zenpath can construct paths through pairs of variables in different ways, which can then be laid out and displayed by a zenplot. The approach is illustrated by investigating tail dependence and model fit in constituent data of the S&P 500 during the financial crisis of 2007-2008. The corresponding Global Industry Classification Standard (GICS) sector information is also addressed. Zenpaths and zenplots are useful tools for exploring dependence in high-dimensional data, for example, from the realm of finance, insurance and quantitative risk management. All presented algorithms are implemented using the R package zenplots and all examples and graphics in the paper can be reproduced using the accompanying demo SP500.

stat.AP↗

arXiv2016

Euclidean distance matrix completion and point configurations from the minimal spanning tree

The paper introduces a special case of the Euclidean distance matrix completion problem (edmcp) of interest in statistical data analysis where only the minimal spanning tree distances are given and the matrix completion must preserve the minimal spanning tree. Two solutions are proposed, one an adaptation of a more general method based on a dissimilarity parameterized formulation, the other an entirely novel method which constructs the point configuration directly through a guided random search. These methods as well as three standard edcmp methods are described and compared experimentally on real and synthetic data. It is found that the constructive method given by the guided random search algorithm clearly outperforms all others considered here. Notably, standard methods including the adaptation force peculiar, and generally unwanted, geometric structure on the point configurations their completions produce.

math.OC↗