arXiv subjects

Ismail Shah

Publications and source records attributed to Ismail Shah.

3 recordsLinked to original sources

arXiv2026

Functional Liu Regression for Scalar-on-Functional Models in High-Dimensional Settings

This study develops a functional Liu-type shrinkage estimator (fLiu) for scalar-on-function regression in the presence of strong multicollinearity and high-dimensional functional predictors. The approach extends the classical Liu estimator to the functional setting by combining directional shrinkage with smoothness regularization, providing flexible control over the bias-variance trade-off. Theoretical analysis is used to examine the behavior of the estimator and the associated parameter selection problem. In particular, an explicit mean squared error (MSE) decomposition is derived, characterizing the risk of the estimator in terms of variance reduction and shrinkage bias. This further yields an explicit optimal choice of the shrinkage parameter of the fLiu estimator through a one-dimensional convex risk minimization problem, leading to a practical plug-in tuning rule. Moreover, it is shown that in high-dimensional (underdetermined) settings, commonly used criterion such as GCV (and equivalently PRESS/LOO-CV) become constant with respect to the parameter d, thus uninformative for tuning. This provides a theoretical explanation for the predominant focus on the overdetermined regime in existing Liu-type methods. Numerical results demonstrate that the estimator achieves competitive predictive accuracy relative to existing methods. Implementation is carried out in R using the fda package, and in Python via the fLiu.py package developed for this study.

stat.OT↗

arXiv2026

Partition-Based Functional Ridge Regression for High-Dimensional Data

This paper proposes a partition-based functional ridge regression framework to address multicollinearity, overfitting, and interpretability in high-dimensional functional linear models. The coefficient function vector \( \boldsymbol{\beta}(s) \) is decomposed into two components, \( \boldsymbol{\beta}_1(s) \) and \( \boldsymbol{\beta}_2(s) \), representing dominant and weaker functional effects. This partition enables differential ridge penalization across functional blocks, so that important signals are preserved while less informative components are more strongly shrunk. The resulting approach improves numerical stability and enhances interpretability without relying on explicit variable selection. We develop three estimators: the Functional Ridge Estimator (FRE), the Functional Ridge Full Model (FRFM), and the Functional Ridge Sub-Model (FRSM). Under standard regularity conditions, we establish consistency and asymptotic normality for all estimators. Simulation results reveal a clear bias--variance trade-off where FRSM performs best in small samples through strong variance reduction, whereas FRFM achieves superior accuracy in moderate to large samples by retaining informative functional structure through adaptive penalization. An empirical application to Canadian weather data further demonstrates improved predictive performance, reduced variance inflation, and clearer identification of influential functional effects. Overall, partition-based ridge regularization provides a practical and theoretically grounded method for high-dimensional functional regression.

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arXiv2025

Exponentially weighted moving average chart using zero-inflated negative binomial distribution

Zero-inflated models are frequently used to deal with data having many zeros. A commonly used model for over-dispersed data containing zeros is known as the zero-inflated Poisson model. However, to account for the heterogeneity of counts that leads to excess variance besides inflation of zeros in the data using a more flexible model than the zero-inflated Poisson model, a zero-inflated negative binomial (ZINB) is suggested. In the present study, Shewhart and exponentially weighted moving average (EWMA) control charts are suggested to monitor the ZINB data. The charts are compared using the average run length and standard deviation of run length by using extensive Monte Carlo simulations. Besides a comprehensive simulation study assuming different settings of parameters of ZINB, a real data set is used to show the practicality of the proposed charts. The results indicate that the EWMA chart is better than the Shewhart chart.

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