Related papers: Exchangeability, the 'Histogram Theorem', and popu…
We consider studies where multiple measures on an outcome variable are collected over time, but some subjects drop out before the end of follow up. Analyses of such data often proceed under either a 'last observation carried forward' or…
We consider a population distributed between two habitats, in each of which it experiences a growth rate that switches periodically between two values, $1- \varepsilon > 0$ or $ - (1 + \varepsilon) < 0$. We study the specific case where the…
Inspired by sample splitting and the reusable holdout introduced in the field of differential privacy, we consider selective inference with a randomized response. We discuss two major advantages of using a randomized response for model…
Estimating the unknown number of classes in a population has numerous important applications. In a Poisson mixture model, the problem is reduced to estimating the odds that a class is undetected in a sample. The discontinuity of the odds…
We consider basic conceptual questions concerning the relationship between statistical estimation and causal inference. Firstly, we show how to translate causal inference problems into an abstract statistical formalism without requiring any…
Estimating the probability distribution 'q' governing the behaviour of a certain variable by sampling its value a finite number of times most typically involves an error. Successive measurements allow the construction of a histogram, or…
As predictive algorithms grow in popularity, using the same dataset to both train and test a new model has become routine across research, policy, and industry. Sample-splitting attains valid inference on model properties by using separate…
We introduce two new bootstraps for exchangeable random graphs. One, the "empirical graphon bootstrap", is based purely on resampling, while the other, the "histogram bootstrap", is a model-based "sieve" bootstrap. We show that both of them…
Iterative imputation, in which variables are imputed one at a time each given a model predicting from all the others, is a popular technique that can be convenient and flexible, as it replaces a potentially difficult multivariate modeling…
Given only aggregate choice data and limited information about how menus are distributed across the population, we describe what can be inferred robustly about the distribution of preferences (or more general decision rules). We strengthen…
Hidden Markov models (HMMs) are flexible tools for clustering dependent data coming from unknown populations, allowing nonparametric modelling of the population densities. Identifiability fails when the data is in fact independent and…
We consider a population of Bayesian agents who share a common prior over some finite state space and each agent is exposed to some information about the state. We ask which distributions over empirical distributions of posteriors beliefs…
Practical problems with missing data are common, and statistical methods have been developed concerning the validity and/or efficiency of statistical procedures. On a central focus, there have been longstanding interests on the mechanism…
We review approaches to statistical inference based on randomization. Permutation tests are treated as an important special case. Under a certain group invariance property, referred to as the ``randomization hypothesis,'' randomization…
Network regression models, where the outcome comprises the valued edge in a network and the predictors are actor or dyad-level covariates, are used extensively in the social and biological sciences. Valid inference relies on accurately…
The empirical likelihood inference is extended to a class of semiparametric models for stationary, weakly dependent series. A partially linear single-index regression is used for the conditional mean of the series given its past, and the…
A probability model is presented for the dynamics of mutation-selection balance in a haploid infinite-population infinite-sites setting sufficiently general to cover mutation-driven changes in full age-specific demographic schedules. The…
Persistent homology computes topological invariants from point cloud data. Recent work has focused on developing statistical methods for data analysis in this framework. We show that, in certain models, parametric inference can be performed…
We propose a class of evolutionary models that involves an arbitrary exchangeable process as the breeding process and different selection schemes. In those models, a new genome is born according to the breeding process, and then a genome is…
The sum of independent, but not necessary identically distributed, exponential random variables follows hypoexponential distribution. We focus on a particular case when all, but one rate parameters of the exponential variables are…