Tuesday, Aug 5: 2:00 PM - 3:50 PM
4128
Contributed Papers
Music City Center
Room: CC-103A
Main Sponsor
Section on Nonparametric Statistics
Presentations
There is a rich and growing body of research focusing on the development of empirical likelihood (EL) estimation and inference methods. Unlike traditional likelihood-based methods, EL techniques rely on a set of unbiased estimating equations (EE) that summarize the parametric constraints of the model, offering greater flexibility in handling complex data, while solving restricted optimization by using Lagrange Multipliers. In recent years, significant progress has been made leveraging the EL approach for longitudinal data analysis and its adaptation to the Bayesian paradigm. In this work, we combine both ideas. Standard Markov chain Monte Carlo (MCMC) procedures within the Bayesian EL (BEL) framework are particularly challenging due to the nonparametric nature of the EL and the restrictions imposed by EE, presenting several limitations that affect their efficiency, mainly dealing with dependent data. Alternatively, by imposing a simple correlation structure often useful in such studies, we develop a method that jointly estimates regression and correlation parameters via the Hamiltonian Monte Carlo (HMC) algorithm that can efficiently sample from the BEL-based posterior distribution
Keywords
nonparametric estimation
Lagrange multipliers
Bayesian estimation
correlated data
Traditional functional principal component analysis (FPCA) is typically designed for continuous functional observations. In this paper, we address the scenario where the outcome consists of repeated categorical data defined over a bounded interval. Our objective is to develop an FPCA methodology tailored specifically for ordinal functional data. Our approach leverages recent advancements in ordinal data modeling to estimate both the mean function and the eigenfunctions, while employing a computationally efficient method for predicting the scores. The performance of the proposed methodology is evaluated numerically in simulation and data application.
Keywords
Functional Data
Functional Principal Component Analysis
Ordinal Functional Data
Zero-inflated functional data appear when an excessive number of zeros are recorded for some functional variables due to the threshold of detection limits. To analyze this kind of data we propose a two part mixed-effects functional regression model. The first part models the probability function of the functional response taking nonzero values via a mixed-effects functional logistic regression model. The second part models the log-transformed true response function by a mixed-effects functional linear model. We use smoothing splines to estimate both the fixed and random effect functions. The estimation procedures for the two parts are respectively penalized quasi-likelihood and a REML-based EM algorithm. Extensive simulations are presented to evaluate the numerical performance of our method. We also apply the method to a Northwestern ICU study to investigate the relationship between total calcium and albumin measurements in repeated blood tests during each of the multiple ICU visits of a patient. Results show that the proposed approach effectively handles zero inflation while recovering the functional relationship between the variables of interest.
Keywords
Zero-inflated functional data
Functional regression model
Mixed-effects model
Penalized quasi-likelihood
REML based EM algorithm
Analysis of sparse functional data has been primarily conducted under the assumption of an uninformative sampling design. We consider the case where the data follow a visit process that induces dropout dependent on the functional outcomes. Such a case leads to bias in model component estimation when standard functional data analysis techniques are used. Recent research has presented methods to adjust estimation for informative observation times and censoring, though not while also considering dropout informed by prior functional outcomes. We propose a joint visit process and functional data model following that accounts for both informative observation times and dropout while allowing for sparse, irregular observation times. The performance of the proposed method is shown in numerical studies.
Keywords
Functional Data Analysis
Truncated Data
Informative sampling design
Pseudo-Likelihood Methods
Nonparametric statistics
Sparse Functional Principal Component Analysis
Functional data analysis holds transformative potential across fields but often relies on mean regression, with limited focus on quantile regression. Furthermore, the infinite-dimensional nature of the functional predictors necessitates the use of dimension reduction techniques. Therefore, in this work, we address this gap by developing dimension reduction techniques for the conditional quantiles of functional data. The idea is to replace the functional predictors with a few finite predictors without losing important information on the conditional quantile while maintaining a flexible nonparametric model. We derive the convergence rates of the proposed estimators and demonstrate their finite sample performance using simulations and a real dataset from fMRI studies.
Keywords
conditional quantiles
dimension reduction
functional data
Functional regression has become essential for analyzing complex, high-dimensional data collected continuously over time or space. Bayesian methods for functional regression can jointly model functional and scalar outcomes, providing straightforward construction of credible intervals. However, these methods are often limited by computational intensity and difficulties in specifying priors. We propose a Weighted Bayesian Bootstrap (WBB) approach for efficient approximate functional posterior inference by Using randomly weighted optimization of a penalized regression. We conduct an extensive simulation study to evaluate the performance of interval estimation Using the WBB approach across three functional regression models: (1) functional predictor regression, (2) functional response regression, and (3) function-on-function regression. Finally, we present an application of this approach to several real data examples.
Keywords
Functional Data Analysis
Markov chain Monte Carlo
Weighted bootstrap
Functional Regression
To optimize mobile health interventions and advance domain knowledge on intervention design, it is critical to understand how the intervention effect varies over time and with contextual information. This study aims to assess how a push notification suggesting physical activity influences individuals' step counts using data from the HeartSteps micro-randomized trial (MRT). The statistical challenges include the time-varying treatments and longitudinal functional step count measurements. We propose the first semiparametric causal excursion effect model with varying coefficients to model the time-varying effects within a decision point and across decision points in an MRT. The proposed model incorporates double time indices to accommodate the longitudinal functional outcome, enabling the assessment of time-varying effect moderation by contextual variables. We propose a two-stage causal effect estimator that is robust against a misspecified high-dimensional outcome regression nuisance model. We establish asymptotic theory and conduct simulation studies to validate the proposed estimator. Our analysis provides new insights into individuals' change in response profiles.
Keywords
causal inference
varying coefficient model
functional data analysis
splines
longitudinal data
micro-randomized trial