Related papers: Statistical Tests for Large Tree-structured Data
This paper develops a smooth test of goodness-of-fit for elliptical distributions. The test is adaptively omnibus, invariant to affine-linear transformations and has a convenient expression that can be broken into components. These…
Traditionally, the Dirichlet-multinomial distribution has been recognized as a key model for contingency tables generated by cluster sampling schemes. There are, however, other possible distributions appropriate for these contingency…
Suppose that we are interested in the comparison of two independent categorical variables. Suppose also that the population is divided into subpopulations or groups. Notice that the distribution of the target variable may vary across…
Estimating phylogenetic trees is an important problem in evolutionary biology, environmental policy and medicine. Although trees are estimated, their uncertainties are discarded by mathematicians working in tree space. Here we explicitly…
A novel goodness-of-fit strategy is introduced for testing models of angular power spectra with unknown parameters. Using this strategy, it is possible to assess the validity of such models without specifying the distribution of the angular…
Left-truncated survival data commonly arise in prevalent cohort studies, where only individuals who have experienced disease onset and survived until enrollment in the study. When the onset process follows a stationary Poisson process, the…
We consider multivariate two-sample tests of means, where the location shift between the two populations is expected to be related to a known graph structure. An important application of such tests is the detection of differentially…
We propose a goodness-of-fit measure for probability densities modeling observations with varying dimensionality, such as text documents of differing lengths or variable-length sequences. The proposed measure is an instance of the kernel…
Experiments often yield non-identically distributed data for statistical analysis. Tests of hypothesis under such set-ups are generally performed using the likelihood ratio test, which is non-robust with respect to outliers and model…
As researchers collect increasingly large molecular data sets to reconstruct the Tree of Life, the heterogeneity of signals in the genomes of diverse organisms poses challenges for traditional phylogenetic analysis. A class of phylogenetic…
In this paper new two-dimensional goodness of fit tests are proposed. They are of supremum-type and are based on different types of characterizations. For the first time a characterization based on independence of two statistics is used for…
A key object of study in stochastic topology is a random simplicial complex. In this work we study a multi-parameter random simplicial complex model, where the probability of including a $k$-simplex, given the lower dimensional structure,…
Mixed-effects logistic regression is widely used for binary outcomes in hierarchical data, yet formal goodness-of-fit tests remain limited to random-intercept models and do not address sparse cluster settings. We extend a grouping-based…
Random forest (RF) stands out as a highly favored machine learning approach for classification problems. The effectiveness of RF hinges on two key factors: the accuracy of individual trees and the diversity among them. In this study, we…
We study the size of the automorphism group of two different types of random trees: Galton--Watson trees and rooted P\'olya trees. In both cases, we prove that it asymptotically follows a log-normal distribution and provide asymptotic…
Due to the broad applications of elliptical models, there is a long line of research on goodness-of-fit tests for empirically validating them. However, the existing literature on this topic is generally confined to low-dimensional settings,…
The analysis of large-scale datasets, especially in biomedical contexts, frequently involves a principled screening of multiple hypotheses. The celebrated two-group model jointly models the distribution of the test statistics with mixtures…
We propose a tree-based algorithm for classification and regression problems in the context of functional data analysis, which allows to leverage representation learning and multiple splitting rules at the node level, reducing…
Latent tree analysis seeks to model the correlations among a set of random variables using a tree of latent variables. It was proposed as an improvement to latent class analysis --- a method widely used in social sciences and medicine to…
Personalized medicine is the future of medical practice. In oncology, tumor heterogeneity assessment represents a pivotal step for effective treatment planning and prognosis prediction. Despite new procedures for DNA sequencing and…