Related papers: Some Impossibility Results for Inference With Clus…
This paper proposes a novel, nonparametric, interpoint distance-based measure to investigate whether there exist any groups in a set of given data, and if so then, how many groups are prevailing in total. It is a cluster accuracy index…
Causal inference with observational data can be performed under an assumption of no unobserved confounders (unconfoundedness assumption). There is, however, seldom clear subject-matter or empirical evidence for such an assumption. We…
Recent work by Gao et al. (JASA 2022) has laid the foundations for post-clustering inference, establishing a theoretical framework allowing to test for differences between means of estimated clusters. Additionally, they studied the…
Classical causal and statistical inference methods typically assume the observed data consists of independent realizations. However, in many applications this assumption is inappropriate due to a network of dependences between units in the…
In many modern statistical problems, the limited available data must be used both to develop the hypotheses to test, and to test these hypotheses-that is, both for exploratory and confirmatory data analysis. Reusing the same dataset for…
Clustered sampling is prevalent in empirical regression discontinuity (RD) designs, but it has not received much attention in the theoretical literature. In this paper, we introduce a general model-based framework for such settings and…
A cluster tree provides a highly-interpretable summary of a density function by representing the hierarchy of its high-density clusters. It is estimated using the empirical tree, which is the cluster tree constructed from a density…
I introduce a generic method for inference on entire quantile and regression quantile processes in the presence of a finite number of large and arbitrarily heterogeneous clusters. The method asymptotically controls size by generating…
The determination of cluster centers generally depends on the scale that we use to analyze the data to be clustered. Inappropriate scale usually leads to unreasonable cluster centers and thus unreasonable results. In this study, we first…
This paper develops a general asymptotic theory for nonparametric kernel regression in the presence of cluster dependence. We examine nonparametric density estimation, Nadaraya-Watson kernel regression, and local linear estimation. Our…
Clustering is a central approach for unsupervised learning. After clustering is applied, the most fundamental analysis is to quantitatively compare clusterings. Such comparisons are crucial for the evaluation of clustering methods as well…
Clustering is part of unsupervised analysis methods that consist in grouping samples into homogeneous and separate subgroups of observations also called clusters. To interpret the clusters, statistical hypothesis testing is often used to…
Interference arises when an individual's potential outcome depends on the individual treatment level, but also on the treatment level of others. A common assumption in the causal inference literature in the presence of interference is…
The asymptotic results that underlie applications of extreme random fields often assume that the variables are located on a regular discrete grid, identified with $\mathbb{Z}^2$, and that they satisfy stationarity and isotropy conditions.…
A celebrated result of Pollard proves asymptotic consistency for $k$-means clustering when the population distribution has finite variance. In this work, we point out that the population-level $k$-means clustering problem is, in fact,…
This paper studies analytic inference along two dimensions of clustering. In such setups, the commonly used approach has two drawbacks. First, the corresponding variance estimator is not necessarily positive. Second, inference is invalid in…
Persistence is considered in diffusion--limited cluster--cluster aggregation, in one dimension and when the diffusion coefficient of a cluster depends on its size $s$ as $D(s) \sim s^\gamma$. The empty and filled site persistences are…
In unsupervised ensemble learning, one obtains predictions from multiple sources or classifiers, yet without knowing the reliability and expertise of each source, and with no labeled data to assess it. The task is to combine these possibly…
We provide finite-sample distribution approximations, that are uniform in the parameter, for inference in linear mixed models. Focus is on variances and covariances of random effects in cases where existing theory fails because their…
The main question is: why and how can we ever predict based on a finite sample? The question is not answered by statistical learning theory. Here, I suggest that prediction requires belief in "predictability" of the underlying dependence,…