Related papers: The Exchangeability Assumption for Permutation Tes…
We propose a general new method, the conditional permutation test, for testing the conditional independence of variables $X$ and $Y$ given a potentially high-dimensional random vector $Z$ that may contain confounding factors. The proposed…
Classical two-sample permutation tests for equality of distributions have exact size in finite samples, but they fail to control size for testing equality of parameters that summarize each distribution. This paper proposes permutation tests…
Relational arrays represent measures of association between pairs of actors, often in varied contexts or over time. Trade flows between countries, financial transactions between individuals, contact frequencies between school children in…
In group sequential designs, where several data looks are conducted for early stopping, we generally assume the vector of test statistics from the sequential analyses follows (at least approximately or asymptotially) a multivariate normal…
Subset selection for multiple linear regression aims to construct a regression model that minimizes errors by selecting a small number of explanatory variables. Once a model is built, various statistical tests and diagnostics are conducted…
Many multiple testing procedures make use of the p-values from the individual pairs of hypothesis tests, and are valid if the p-value statistics are independent and uniformly distributed under the null hypotheses. However, it has recently…
The paper presents some models for the propensity score. Considerable attention is given to a recently popular, but relatively under-explored setting in causal inference where the no-interference assumption does not hold. We lay out some…
Permutation tests are amongst the most commonly used statistical tools in modern genomic research, a process by which p-values are attached to a test statistic by randomly permuting the sample or gene labels. Yet permutation p-values…
Permutation tests are widely used for statistical hypothesis testing when the sampling distribution of the test statistic under the null hypothesis is analytically intractable or unreliable due to finite sample sizes. One critical challenge…
Data analysis based on information from several sources is common in economic and biomedical studies. This setting is often referred to as the data fusion problem, which differs from traditional missing data problems since no complete data…
In regression analysis of multivariate data, it is tacitly assumed that response and predictor variables in each observed response-predictor pair correspond to the same entity or unit. In this paper, we consider the situation of "permuted…
Model checking plays an important role in linear regression as model misspecification seriously affects the validity and efficiency of regression analysis. In practice, model checking is often performed by subjectively evaluating the plot…
We argue for the use of separate exchangeability as a modeling principle in Bayesian nonparametric (BNP) inference. Separate exchangeability is de facto widely applied in the Bayesian parametric case, e.g., it naturally arises in simple…
This note continues study of exchangeability martingales, i.e., processes that are martingales under any exchangeable distribution for the observations. Such processes can be used for detecting violations of the IID assumption, which is…
Regression models describing the joint distribution of multivariate response variables conditional on covariate information have become an important aspect of contemporary regression analysis. However, a limitation of such models is that…
In inference problems involving a multi-dimensional parameter $\theta$, it is often natural to consider decision rules that have a risk which is invariant under some group $G$ of permutations of $\theta$. We show that this implies that the…
In the analysis of machine learning models, it is often convenient to assume that the parameters are IID. This assumption is not satisfied when the parameters are updated through training processes such as SGD. A relaxation of the IID…
We consider linear models with scalar responses and covariates from a separable Hilbert space. The aim is to detect change points in the error distribution, based on sequential residual empirical distribution functions. Expansions for those…
The increasing adoption of machine learning tools has led to calls for accountability via model interpretability. But what does it mean for a machine learning model to be interpretable by humans, and how can this be assessed? We focus on…
In randomized experiments with noncompliance, tests may focus on compliers rather than on the overall sample. Rubin (1998) put forth such a method, and argued that testing for the complier average causal effect and averaging permutation…