In this article, we study a count time‐series data of weekly dengue cases in Kaohsiung City, Taiwan during the period 2009–2012, where the problems of a large number of zeros or zero‐inflation and seasonality arise together. To capture both features, we consider an application‐oriented zero‐inflated seasonal PINAR framework based on zero‐inflated Poisson innovations. We also incorporate an exogenous variable, namely the weekly maximum temperature, in the innovations to study the effect of temperature on the number of dengue cases as many studies have found that temperature is a significant factor in spreading dengue infections globally. The proposed model can capture both the non‐recovery cases from the previous time point and the new cases coming at the current time point. The distributional and forecasting properties of the proposed model are derived. The consistency and asymptotic normality of the CLS estimator are established under suitable regularity conditions, and simulation experiments are used to examine the finite‐sample estimation and forecasting performance of the proposed model. The proposed model is compared with some existing INAR models. Finally, we analyze the data of weekly dengue cases in Kaohsiung for practical illustration.
Subhankar Chattopadhyay, A. Biswas, Samarjit Das et al.· Environmetrics· 0 citations
Estimating multiple precision matrices in high-dimension presents significant challenges, particularly when distinct datasets share a common conditional dependency structure but exhibit population-specific interaction strengths. We address this problem by introducing the Multiplicative Graphical Lasso (Mglasso), a method for jointly estimating precision matrices across multiple Gaussian graphical models under a shared sparsity constraint. Each precision matrix is decomposed as a Schur-Hadamard product of a shared structural matrix $\boldsymbol{\Theta}$, which encodes the common conditional independence graph, and a population-specific matrix $\boldsymbol{\Gamma}_{l}$, which captures variation in edge strengths across populations. We optimize a penalized log-likelihood that utilizes an $\ell_1$-penalty to enforce common sparsity and a Frobenius norm penalty to regulate population-specific variations. The optimization is efficiently performed using the Alternating Direction Method of Multipliers (ADMM) algorithm integrated with gradient descent. Theoretically, we establish the local strict convexity of the objective function and provide rigorous high-dimensional consistency guarantees, including supremum norm error bounds and exact support recovery under sub-Gaussian tail conditions. Extensive simulations show superior model selection consistency at smaller sample sizes compared to the benchmark Group Graphical Lasso (GGL). Finally, the method's practical utility is further validated through real-world applications.
S. Bhowal, Debashis Paul, Gopal K. Basak et al.· 0 citations
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