Related papers: Some Impossibility Results for Inference With Clus…

We provide a complete asymptotic distribution theory for clustered data with a large number of independent groups, generalizing the classic laws of large numbers, uniform laws, central limit theory, and clustered covariance matrix…

The problem of change-point estimation is considered under a general framework where the data are generated by unknown stationary ergodic process distributions. In this context, the consistent estimation of the number of change-points is…

In an age of increasingly large data sets, investigators in many different disciplines have turned to clustering as a tool for data analysis and exploration. Existing clustering methods, however, typically depend on several nontrivial…

This paper introduces a novel nonparametric criterion for determining the appropriate number of clusters, which is derived from the spatial median. The method is constructed to reconcile two competing objectives of cluster analysis: the…

To cluster data is to separate samples into distinctive groups that should ideally have some cohesive properties. Today, numerous clustering algorithms exist, and their differences lie essentially in what can be perceived as ``cohesive…

We derive a consistency result, in the $L_1$-sense, for incomplete U-statistics in the non-standard case where the kernel at hand has infinite second-order moments. Assuming that the kernel has finite moments of order $p(\geq 1)$, we obtain…

When people share the same documents and observations yet reach different conclusions, the disagreement often shifts into a judgment that the other party is cognitively defective, irrational, or acting in bad faith. This paper argues that…

Background: When planning a cluster randomized trial, evaluators often have access to an enumerated cohort representing the target population of clusters. Practicalities of conducting the trial, such as the need to oversample clusters with…

We consider the robust algorithms for the $k$-means clustering problem where a quantizer is constructed based on $N$ independent observations. Our main results are median of means based non-asymptotic excess distortion bounds that hold…

We use a measure of clustering derived from the nearest neighbour distribution and the void probability function to distinguish between regular and clustered structures. This measure offers a succinct way to incorporate additional…

We consider the challenging problem of statistical inference for exponential-family random graph models based on a single observation of a random graph with complex dependence. To facilitate statistical inference, we consider random graphs…

Identifying causal treatment (or exposure) effects in observational studies requires the data to satisfy the unconfoundedness assumption which is not testable using the observed data. With sensitivity analysis, one can determine how the…

Determining the quality of the results obtained by clustering techniques is a key issue in unsupervised machine learning. Many authors have discussed the desirable features of good clustering algorithms. However, Jon Kleinberg established…

This paper discusses the fundamental principles of causal inference - the area of statistics that estimates the effect of specific occurrences, treatments, interventions, and exposures on a given outcome from experimental and observational…

Using multi-wavelength imaging from the Wide Field Camera 3 on the Hubble Space Telescope we study the stellar cluster populations of two adjacent fields in the nearby face-on spiral galaxy, M83. The observations cover the galactic centre…

We develop a simple and unified approach to investigate several aspects of the cluster statistics of random expansive (multi-)sets. In particular, we determine the limiting distribution of the size of the smallest and largest clusters, we…

We develop a clustering framework for observations from a population with a smooth probability distribution function and derive its asymptotic properties. A clustering criterion based on a linear combination of order statistics is proposed.…

Recent research has established sufficient conditions for finite mixture models to be identifiable from grouped observations. These conditions allow the mixture components to be nonparametric and have substantial (or even total) overlap.…

Causal inference from observational data provides strong evidence for the best action in decision-making without performing expensive randomized trials. The effect of an action is usually not identifiable under unobserved confounding, even…

We propose some axioms for hierarchical clustering of probability measures and investigate their ramifications. The basic idea is to let the user stipulate the clusters for some elementary measures. This is done without the need of any…