Julian Aronowitz | Searcharxiv

arXiv2026

Non-asymptotic bounds for quasi-MLE, misspecified models, and dependence under group sequential sampling

We derive asymptotic multivariate normal limits and explicit non-asymptotic normal approximation bounds for group sequential quasi-maximum likelihood estimators under possible model misspecification and within-group dependence. The bounds, obtained using Stein's method, have known constants and apply to a class of dependent-data estimating problems in which the likelihood used for estimation may differ from the true data-generating mechanism. We compute the limiting covariance structure and finite-sample bound explicitly for a Poisson generalized linear mixed model with random group effects and illustrate the results using data from an epilepsy clinical trial.

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arXiv2023

Finite-sample bounds to the normal limit under group sequential sampling

In group sequential analysis, data is collected and analyzed in batches until pre-defined stopping criteria are met. Inference in the parametric setup typically relies on the limiting asymptotic multivariate normality of the repeatedly computed maximum likelihood estimators (MLEs), a result first rigorously proved by Jennison and Turbull (1997) under general regularity conditions. In this work, using Stein's method we provide optimal order, non-asymptotic bounds on the distance for smooth test functions between the joint group sequential MLEs and the appropriate normal distribution under the same conditions. Our results assume independent observations but allow heterogeneous (i.e., non-identically distributed) data. We examine how the resulting bounds simplify when the data comes from an exponential family. Finally, we present a general result relating multivariate Kolmogorov distance to smooth function distance which, in addition to extending our results to the former metric, may be of independent interest.

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