高維資料空間零膨脹模型的有效參數估計

以作者查詢圖書館館藏

、以作者查詢臺灣博碩士

、以作者查詢全國書目

、勘誤回報

、線上人數：55

、訪客IP：13.59.182.74

姓名

許卜仁(Bu-Ren Hsu) 查詢紙本館藏

畢業系所

統計研究所

論文名稱

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)

相關論文

★ A Compression-Based Partitioning Estimate Classifier	★ Data adaptive median filters for image denoising based on a prediction criterion
★ Fixed effect estimation and spatial prediction via universal kriging	★ Two-stage model selection under a misspecified spatial covariance function
★ 時空過程的配適研究	★ 空間變異係數模型
★ 非監督式廣義學習NEM分類演算法	★ Spline-based Approach for Image Restoration
★ 固定秩克里金法的圖像重建	★ 克利金模型中基於Kullback-Leibler損失的共變異函數選擇
★ A Spatio-temporal Hierarchical PGEV Model for Extreme Value Analysis

檔案

[Endnote RIS 格式]

[Bibtex 格式]

[相關文章]

[文章引用]

[完整記錄]

[館藏目錄]

至系統瀏覽論文 (2026-8-1以後開放)

摘要(中)

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。

摘要(英)

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.

關鍵字(中)

★ 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

關鍵字(英)

★ Akaike’s information criterion
★ Generalized estimating equations
★ Parameter estimation
★ Thin-plate splines
★ Zero inflation

論文目次

摘要I
Abstract II
致謝辭III
Contents IV
List of Figures VI
List of Tables VII
1 Introduction 1
2 Spatial zero-inflated models 4
2.1 Discrete type . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
2.1.1 ZIP models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
2.1.2 Semiparametric spatial zero-inflated count model . . . . . . . . . . . . 5
2.2 Semi-continuous type . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.2.1 ZIT models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.2.2 Semiparametric spatial zero-inflated semi-continuous model . . . . . . 10
3 Dimension reduction for covariance structures 12
3.1 Thin-plate splines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
3.2 Applications of TPS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
4 Estimation of model parameters 17
4.1 Parameter estimation for covariance matrix . . . . . . . . . . . . . . . . . . . 17
4.2 Parameter estimation for regression coefficients . . . . . . . . . . . . . . . . . 19
4.3 Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
4.4 Variance estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
5 Simulation study 24
5.1 Setups . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
5.2 The results of parameter estimation . . . . . . . . . . . . . . . . . . . . . . . . 26
5.2.1 Small samples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
5.2.2 Large samples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
6 Application 35
7 Conclusion and discussion 40
References 42

參考文獻

Adegboye, O. A., Leung, D. H., and Wang, Y. G. (2018). Analysis of spatial data with a nested correlation structure. Journal of the Royal Statistical Society: Series C (Applied Statistics), 67, 329-354.

Agarwal, D. K., Gelfand, A. E., and Citron-Pousty, S. (2002). Zero-inflated models with application to spatial count data. Environmental and Ecological Statistics, 9, 341-355.

Akaike, H. (1973). Information theory and an extension of the maximum likelihood principle. International Symposium on Information Theory, eds. V. Petrov, and F. Cs´aki, Budapest: Akad´emiai Kiad´o, 267-281.

Banerjee, S., Gelfand, A. E., Finley, A. O., and Sang, H. (2008). Gaussian predictive process models for large spatial data sets. Journal of the Royal Statistical Society: Series B, 70, 825-848.

Böhning, D., Dietz, E., Schlattmann, P., Mendonga, L., and Kirchner, U. (1999). The zero-inflated Poisson model and the decayed, missing and filled teeth index in dental epidemiology. Journal of the Royal Statistical Society. Series A (Statistics in Society), 162, 195-209.

Cressie, N. (1993). Statistics for Spatial Data (revised edition). New York: Wiley.

Cressie, N. and Johannesson, G. (2008). Fixed rank kriging for very large spatial data sets. Journal of the Royal Statistical Society: Series B, 70, 209-226.

Farewell, V. T. and Sprott, D. A. (1988). The use of a mixture model in the analysis of count data. Biometrics, 44, 1191-1194.

Green, P. J. and Silverman, B. W. (1993). Nonparametric Regression and Generalized Linear Models: A Roughness Penalty Approach. Boca Raton: CRC Press.

Guan, Y. and Haran, M. (2018). A computationally efficient projection-based approach for spatial generalized linear mixed models. Journal of Computational and Graphical Statistics,
27, 701-714.

Hall, D. B. (2000). Zero-inflated Poisson and binomial regression with random effects: a case study. Biometrics, 56, 1030-1039.

Hall, D. B., and Zhang, Z. (2004). Marginal models for zero-inflated clustered data. Statistical Modelling, 4(3), 161-180.

Harville, D. A. (1997). Matrix Algebra From a Statistician′s Perspective. New York: Springer.

He, H., Wang, W. J., Hu, J., Gallop, R., Crits-Christoph, P., and Xia, Y. L. (2015). Distribution-free inference of zero-inflated binomial data for longitudinal studies. Journal of Applied Statistics, 42, 2203-2219.

Katzfuss, M. (2017). A multi-resolution approximation for massive spatial datasets. Journal of the American Statistical Association, 112, 201-214.

Lambert, D. (1992). Zero-inflated Poisson regression, with an application to defects in manufacturing. Technometrics, 34, 1-14.

Lee, C. E. and Kim, S. (2017). Applicability of zero-inflated models to fit the torrential rainfall count data with extra zeros in South Korea. Water, 9, 123.

Liang, K. Y. and Zeger, S. L. (1986). Longitudinal data analysis using generalized linear models. Biometrika, 73, 13-22.

McCullagh, P. and Nelder, J. A. (1989). Generalized Linear Models. Boca Raton: Chapman and Hall/CRC.

Moulton, L. H. and Halsey, N. A. (1995). A mixture model with detection limits for regression analyses of antibody response to vaccine. Biometrics, 51, 1570-1578.

Neelon, B., Zhu, L., and Neelon, S. E. B. (2015). Bayesian two-part spatial models for semicontinuous data with application to emergency department expenditures. Biostatistics, 16, 465-479.

Nychka, D., Bandyopadhyay, S., Hammerling, D., Lindgren, F., and
Sain, S. (2015). A multiresolution Gaussian process model for the analysis of large spatial datasets. Journal of Computational and Graphical Statistics, 24, 579-599.

Park, J. and Haran, M. (2020). Reduced-dimensional Monte Carlo maximum likelihood for latent Gaussian random field models. Journal of Computational and Graphical Statistics, 30, 269-283.

Rathbun, S. L. and Fei, S. (2006). A spatial zero-inflated Poisson regression model for oak regeneration. Environmental and Ecological Statistics, 13, 409-426.

Shen, C. W. and Chen, C. S. (2024). Estimation and selection for spatial zero-inflated count models. Environmetrics, 35(4), e2847.

Taiwan Climate Change Projection Information and Adaptation Knowledge Platform (TCCIP) (2023). https://tccip.ncdr.nat.gov.tw/.

Tobin, J. (1958). Estimation of Relationships for Limited Dependent Variables. Econometrica, 26, 24-36.

Tzeng, S. L. and Huang, H. C. (2018). Resolution Adaptive Fixed Rank Kriging. Technometrics, 60, 198-208.

Wahba, G. (1985). A comparison of GCV and GML for choosing the smoothing parameter in the generalized spline smoothing problem. Annals of Statistics, 13, 1378-1402.

Wahba, G. (1990). Spline Models for Observational Data. Philadelphia: Society for Industrial and Applied Mathematics.

Wikle, C. K. (2010). Low-Rank Representations for Spatial Processes. In Handbook of Spatial Statistics, eds. A. E. Gelfand, P. J. Diggle, M. Fuentes, and P. Guttorp, Boca Raton, FL: CRC Press, 107-118.

指導教授

陳春樹(Chun-Shu Chen)

審核日期

2024-7-2

推文