高維資料空間零膨脹模型的有效參數估計;Efficient estimation for spatial zero-inflated models with large data

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题名:	高維資料空間零膨脹模型的有效參數估計;Efficient estimation for spatial zero-inflated models with large data
作者:	許卜仁;Hsu, Bu-Ren
贡献者:	統計研究所
关键词:	赤池信息量準則;廣義估計方程式;參數估計;薄板樣條;零膨脹;Akaike’s information criterion;Generalized estimating equations;Parameter estimation;Thin-plate splines;Zero inflation
日期:	2024-07-02
上传时间:	2024-10-09 16:34:30 (UTC+8)
出版者:	國立中央大學
摘要:	空間兩成分混合模型用於分析空間零膨脹計數資料，為了避免對反應變數假設特定分布而導致不正確的推論，我們採用了一種半參數的空間零膨脹模型。對於大型數據集，我們面臨高維度空間相依潛在變量、大量矩陣運算和參數估計過程的收斂速度等議題，導致配適半參數空間零膨脹模型的計算負擔是相當重的。為了應對這些挑戰，我們引入了一種投影的方法，用於降低矩陣運算的維度。這種方法將空間相依的潛在變量投影到一組事先給定的基底函數所定義的低維空間中。然後，我們提出了一種基於廣義估計方程方法的高效率迭代演算法用以估計模型的參數。其中，我們透過赤池信息準則(AIC) 選擇合適的基底函數數量，並且使用區塊刀法(block jackknife method) 評估所提估計式的穩健性。我們透過各式的模擬情境來展示所提參數估計法的有效性，同時分析2016 年台灣日降雨資料來說明所提方法的實用性。;Spatial two-component mixture models provide a robust framework for the analysis of spatial zero-inflated correlated count data. To avoid incorrect inferences from imposing a specific distribution on the response variables, a semiparametric spatial zero-inflated model is utilized. The computational burden of fitting this model, particularly with large datasets, is considerable due to the presence of high-dimensional spatially dependent latent variables, intensive matrix operations, and the slow convergence of the estimation process. To address these challenges, we introduce a projection-based method that reduces the dimensionality of matrix operations. This method projects the spatially dependent latent variables onto a lower dimensional space defined by a predetermined set of basis functions. An efficient iterative algorithm, augmented by a generalized estimation equation approach, is then proposed for parameter estimation. The number of basis functions is selected based on Akaike′s information criterion and the robustness of our estimations is evaluated using the block jackknife method. The efficacy of our proposed method is demonstrated through extensive simulation studies and an application of the analysis of Taiwan′s daily rainfall data for 2016, showcasing its practical utility.
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