Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 1811.01261

Canonical Least Favorable Submodels:A New TMLE Procedure for Multidimensional Parameters

Jonathan Levy
View original source ↗Read source document ↗Export metadata ↓

Abstract

This paper is a fundamental addition to the world of targeted maximum likelihood estimation (TMLE) (or likewise, targeted minimum loss estimation) for simultaneous estimation of multi-dimensional parameters of interest. TMLE, as part of the targeted learning framework, offers a crucial step in constructing efficient plug-in estimators for nonparametric or semiparametric models. The so-called targeting step of targeted learning, involves fluctuating the initial fit of the model in a way that maximally adjusts the plug-in estimate per change in the log likelihood. Previously for multidimensional parameters of interest, iterative TMLE's were constructed using locally least favorable submodels as defined in van der Laan and Gruber, 2016, which are indexed by a multidimensional fluctuation parameter. In this paper we define a canonical least favorable submodel in terms of a single dimensional epsilon for a $d$-dimensional parameter of interest. One can view the clfm as the iterative analog to the one-step TMLE as constructed in van der Laan and Gruber, 2016. It is currently implemented in several software packages we provide in the last section. Using a single epsilon for the targeting step in TMLE could be useful for high dimensional parameters, where using a fluctuation parameter of the same dimension as the parameter of interest could suffer the consequences of curse of dimensionality. The clfm also enables placing the so-called clever covariate denominator as an inverse weight in an offset intercept model. It has been shown that such weighting mitigates the effect of large inverse weights sometimes caused by near positivity violations.

Explore related subjects

stat.MEmath.STstat.APstat.TH

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Jonathan Levy. 2019-04-11. Canonical Least Favorable Submodels:A New TMLE Procedure for Multidimensional Parameters. https://arxiv.org/abs/1811.01261

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Bridging Impulse Control of Piecewise Deterministic Markov Processes and Markov Decision Processes: Frameworks, Extensions, and Open Challenges

Control theory plays a pivotal role in understanding and optimizing the behavior of complex dynamical systems across various scientific and engineering disciplines. Two key frameworks that have emerged for modeling and solving control problems in stochastic systems are piecewise deterministic Markov processes (PDMPs) and Markov decision processes (MDPs). Each framework has its unique strengths, and their intersection offers promising opportunities for tackling a broad class of problems, particularly in the context of impulse controls and decision-making in complex systems. The relationship between PDMPs and MDPs is a natural subject of exploration, as embedding impulse control problems for PDMPs into the MDP framework could open new avenues for their analysis and resolution. Specifically, this integration would allow leveraging the computational and theoretical tools developed for MDPs to address the challenges inherent in PDMPs. On the other hand, PDMPs can offer a versatile and simple paradigm to model continuous time problems that are often described as discrete-time MDPs parametrized by complex transition kernels. This transformation has the potential to bridge the gap between the two frameworks, enabling solutions to previously intractable problems and expanding the scope of both fields. This paper presents a comprehensive review of two research domains, illustrated through a recurring medical example. The example is revisited and progressively formalized within the framework of thevarious concepts and objects introduced

stat.ME↗
arXiv2026

Decision Theoretic Subgroup Detection With Bayesian Machine Learning

We consider the problem of identifying promising subpopulations in terms of treatment effectiveness or treatment effect heterogeneity, from a Bayesian decision theoretic perspective. We first show that a straight-forward application of Bayesian decision theory to subgroup detection leads to a counter-intuitive risk-seeking (RS) behavior. Motivated by this observation, we introduce the Bayesian Risk-Aware Inference and Detection of Subgroups (BRAIDS) utility and use it to perform subgroup selection and post selection inference. The BRAIDS utility interpolates between risk-seeking (RS) and risk-averse (RA) identifications of subgroups, with a variant of the virtual twins algorithm as its risk-neutral midpoint. We also argue that effective subgroup estimation and inference requires the use of regularization priors to safeguard inferences from the winner's curse. We provide empirical evidence that posterior credible intervals for subgroup effects can still obtain nominal coverage levels, provided that an appropriate prior distribution is chosen. The proposed framework is illustrated on data from clinical trial assessing the efficacy of canagliflozin as a treatment for type 2 diabetes.

stat.ME↗
arXiv2026

Modeling cyclostationarity in time series using ASCA

Modern data analysis across diverse disciplines increasingly relies on time series. Many of these datasets exhibit cyclostationarity, where patterns approximately repeat in a regular manner, often across multiple time scales, such as daily, weekly or yearly cycles. In this context, statistical inference is essential to distinguish genuine underlying effects from random variability. While tools like Analysis of Variance (ANOVA) provide such inference, they often lack interpretability and struggle with the complexities of multivariate data. To address these limitations, we propose a unified pipeline for the exploratory analysis of cyclostationary times series using ANOVA Simultaneous Component Analysis (ASCA). ASCA is an extension of ANOVA that is able to work in both univariate and multivariate cases. Combining inference with the visualization capabilities of Principal Component Analysis (PCA), ASCA provides powerful options for interpretability. ASCA's capabilities have been well-established in the analysis of experimental data, but they remain largely unexplored for observational data like time series. Our workflow introduces an algorithmic approach to modeling time-dependent data using ASCA, enabling control over multiple cyclostationary time scales while also accounting for the specific challenges of this type of data, such as autocorrelation. Furthermore, we observed that ASCA provides a better separation of variability across factors than ANOVA in unbalanced designs due to its multivariate nature. We demonstrate the efficacy of this methodology through two real-world case studies: water temperature trends in mountain lakes in Sierra Nevada, Spain, and airborne pollen trends over 30 years recorded in the city of Granada, Spain.

stat.ME↗