arXiv subjects

Pratim Guha Niyogi

Publications and source records attributed to Pratim Guha Niyogi.

9 recordsLinked to original sources

arXiv2026

Nonparametric Regression with Measurement Error in Banach Spaces

We consider nonparametric regression with a Banach-space-valued predictor where the covariate takes values in a general separable Banach space. Our primary objective is to develop a unified framework for estimating the regression operator without relying on an inner-product structure, thereby extending classical and functional nonparametric regression beyond Euclidean and Hilbert spaces in the presence of measurement error. We establish the fundamental properties of the proposed estimator and develop its large-sample theory under conditions formulated in terms of the geometry and local concentration of the Banach-valued predictor. In particular, we study pointwise estimation and inference and discuss the construction of pointwise confidence intervals and uniform confidence bands. Our proposed framework is further extended to accommodate error-in-variables settings, where the predictor is observed with contamination. We also investigate related inverse problems arising from the construction of inverse weighting functions and consider partial contamination models. These developments provide a general framework for nonparametric regression and inference with complex infinite-dimensional predictors and identify several statistical and mathematical challenges that arise when the usual Hilbert-space structure is unavailable.

math.ST↗

arXiv2026

Covariate-Adjusted Functional Principal Components Analysis for Modeling Hazard Rates of Physical Activity in the US Population

Physical activity plays a vital role in human health. Its entire distribution differs among people. Commonly used summary measures cannot describe this distributional pattern. We present a distribution-based analytical approach to describe physical activity by modeling individual-level activity-intensity patterns through hazard functions derived from wrist-worn accelerometer data. We analyzed minute-level Monitor-Independent Movement Summary (MIMS) data of 4297 adults with seven continuous days of device wear from the 2011- 2012 National Health and Nutrition Examination Survey (NHANES). We derived a nonparametric activity-intensity hazard using a survival-based approach for each individual on a common intensity grid, treating both the hazard curves from MIMS and their log-transformed MIMS as functional objects. We used functional principal component analysis (FPCA) on both scales of MIMS to characterize dominant modes of variation in activity-intensity distributions. Group-wise mean hazard functions showed little difference at lower intensity levels, while we observed a substantial difference at higher intensity levels. Our results demonstrate that hazard-based functional representations for capturing differences in physical activity intensity distributions across individuals offer a flexible and interpretable way to characterize heterogeneity. This approach works better than mean-based summaries and supports principled comparisons of physical activity patterns across population subgroups.

stat.AP↗

arXiv2026

Scalar-on-distribution regression via generalized odds with applications to accelerometry-assessed disability in multiple sclerosis

Distributional representations of data collected using digital health technologies have been shown to outperform scalar summaries for clinical prediction, with carefully quantified tail-behavior often driving the gains. Motivated by these findings, we propose a unified generalized odds (GO) framework that represents subject-specific distributions through ratios of probabilities over arbitrary regions of the sample space, subsuming hazard, survival, and residual life representations as special cases. We develop a scale-on-odds regression model using spline-based functional representations with penalization for efficient estimation. Applied to wrist-worn accelerometry data from the HEAL-MS study, generalized odds models yield improved prediction of Expanded Disability Status Scale (EDSS) scores compared to classical scalar and survival-based approaches, demonstrating the value of odds-based distributional covariates for modeling DHT data.

stat.ME↗

arXiv2025

Identifying arbitrary transformation between the slopes in scalar-on-function regression

In this article, we study whether the slope functions of two scalar-on-function regression models in two samples are associated with any arbitrary transformation along the vertical axis. The problem is formally stated as a statistical hypothesis test, and corresponding test statistic is formed based on the estimated second derivative of the unknown transformation. The asymptotic properties of the test statistic are investigated using some advanced techniques related to the empirical process. Moreover, to implement the test for small sample size data, a bootstrap algorithm is proposed, and it is shown that the bootstrap version of the test is as good as the original test for sufficiently large sample size. Furthermore, the utility of the proposed methodology is shown for simulated datasets, and DTI data is analyzed using the proposed methodology.

stat.ME↗

arXiv2025

Hazard and Beyond: Exploring Five Distributional Representations of Accelerometry Data for Disability Discrimination in Multiple Sclerosis

Research on modeling the distributional aspects in sensor-based digital health (sDHT) data has grown significantly in recent years. Most existing approaches focus on using individual-specific density or quantile functions. However, there has been limited exploration to assess the practical utility of alternative distributional representations in clinical contexts collecting sDHT data. This study is motivated by accelerometry data collected on 246 individuals with multiple sclerosis (MS)representing a wide range of disability (Expanded Disability Status Scale, EDSS: 0-7). We consider five different individual-level distributional representations of minute-level activity counts: density, survival, hazard, quantile, and total time on test functions. For each of the five distributional representations, scalar-on-function regression fits linear discriminators for binary and continuously measured MS disability, and cross-validated discriminatory performance of these linear discriminators is compared across. The results show that individual-level hazard functions provide the highest discriminatory accuracy, more than double the accuracy compared to density functions. Individual-level quantile functions provided the second-highest discriminatory accuracy. These findings highlight the importance of focusing on distributional representations that capture the tail behavior of distributions when analyzing digital health data, especially in clinical contexts.

stat.AP↗

arXiv2024

Functional varying-coefficient model under heteroskedasticity with application to DTI data

In this paper, we develop a multi-step estimation procedure to simultaneously estimate the varying-coefficient functions using a local-linear generalized method of moments (GMM) based on continuous moment conditions. To incorporate spatial dependence, the continuous moment conditions are first projected onto eigen-functions and then combined by weighted eigen-values, thereby, solving the challenges of using an inverse covariance operator directly. We propose an optimal instrument variable that minimizes the asymptotic variance function among the class of all local-linear GMM estimators, and it outperforms the initial estimates which do not incorporate the spatial dependence. Our proposed method significantly improves the accuracy of the estimation under heteroskedasticity and its asymptotic properties have been investigated. Extensive simulation studies illustrate the finite sample performance, and the efficacy of the proposed method is confirmed by real data analysis.

stat.ME↗

arXiv2024

Quadratic inference with dense functional responses

We address the challenge of estimation in the context of constant linear effect models with dense functional responses. In this framework, the conditional expectation of the response curve is represented by a linear combination of functional covariates with constant regression parameters. In this paper, we present an alternative solution by employing the quadratic inference approach, a well-established method for analyzing correlated data, to estimate the regression coefficients. Our approach leverages non-parametrically estimated basis functions, eliminating the need for choosing working correlation structures. Furthermore, we demonstrate that our method achieves a parametric $\sqrt{n}$-convergence rate, contingent on an appropriate choice of bandwidth. This convergence is observed when the number of repeated measurements per trajectory exceeds a certain threshold, specifically, when it surpasses $n^{a_{0}}$, with $n$ representing the number of trajectories. Additionally, we establish the asymptotic normality of the resulting estimator. The performance of the proposed method is compared with that of existing methods through extensive simulation studies, where our proposed method outperforms. Real data analysis is also conducted to demonstrate the proposed method.

stat.ME↗

arXiv2024

Inspecting discrepancy between multivariate distributions using half-space depth based information criteria

This article inspects whether a multivariate distribution is different from a specified distribution or not, and it also tests the equality of two multivariate distributions. In the course of this study, a graphical tool-kit using well-known half-space depth based information criteria is proposed, which is a two-dimensional plot, regardless of the dimension of the data, and it is even useful in comparing high-dimensional distributions. The simple interpretability of the proposed graphical tool-kit motivates us to formulate test statistics to carry out the corresponding testing of hypothesis problems. It is established that the proposed tests based on the same information criteria are consistent, and moreover, the asymptotic distributions of the test statistics under contiguous/local alternatives are derived, which enable us to compute the asymptotic power of these tests. Furthermore, it is observed that the computations associated with the proposed tests are unburdensome. Besides, these tests perform better than many other tests available in the literature when data are generated from various distributions such as heavy tailed distributions, which indicates that the proposed methodology is robust as well. Finally, the usefulness of the proposed graphical tool-kit and tests is shown on two benchmark real data sets.

stat.ME↗

arXiv2023

A tensor based varying-coefficient model for multi-modal neuroimaging data analysis

All neuroimaging modalities have their own strengths and limitations. A current trend is toward interdisciplinary approaches that use multiple imaging methods to overcome limitations of each method in isolation. At the same time neuroimaging data is increasingly being combined with other non-imaging modalities, such as behavioral and genetic data. The data structure of many of these modalities can be expressed as time-varying multidimensional arrays (tensors), collected at different time-points on multiple subjects. Here, we consider a new approach for the study of neural correlates in the presence of tensor-valued brain images and tensor-valued predictors, where both data types are collected over the same set of time points. We propose a time-varying tensor regression model with an inherent structural composition of responses and covariates. Regression coefficients are expressed using the B-spline technique, and the basis function coefficients are estimated using CP-decomposition by minimizing a penalized loss function. We develop a varying-coefficient model for the tensor-valued regression model, where both predictors and responses are modeled as tensors. This development is a non-trivial extension of function-on-function concurrent linear models for complex and large structural data where the inherent structures are preserved. In addition to the methodological and theoretical development, the efficacy of the proposed method based on both simulated and real data analysis (e.g., the combination of eye-tracking data and functional magnetic resonance imaging (fMRI) data) is also discussed.

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