自2020年1月爆發新冠病毒以來，全球陷入一場長期與病毒對抗的戰役。這場疫情不僅影響人們的活動範圍和生活方式，還對經濟造成了嚴重的打擊。截至今日，美國作為全球感染數最多的國家，其經濟重鎮之一的加州也成為受影響最嚴重的地區，因此成為我們研究的焦點。本研究基於Huang等人所提出的模型，並加入了多個感興趣變數，通過簡單克里金方法對加州新冠肺炎資料進行空間預測，旨在提供更詳盡的預測資訊。

Since the outbreak of the COVID-19 virus in January 2020, the world has been engaged in a long-term battle against the virus. This pandemic has not only impacted people's activities and lifestyles but also caused severe economic damage. As of today, the United States, being one of the hardest-hit countries in terms of infection numbers, has experienced significant impacts in one of its economic powerhouses, California. Consequently, California has become the focus of our study. Building upon the model proposed by Huang et al. This research incorporates several variables of interest and utilizes the simple kriging method for spatial prediction on California's COVID-19 data, aiming to provide more detailed predictive information.

1 Introduction and Literature Reviews 1
1.1 Multiresolution spline basis functions 2
1.2 Huber M estimate 2
1.3 Variogram 3
2 Data Source 7
2.1 John Hopsking 7
2.2 American Community Survey (ACS) 7
2.3 COVID19.CA.GOV 8
2.4 COVID19 Forecast HUB 8
2.5 United States Environmental Protection Agency (EPA) 9
3 Methodology 11
3.1 Spatial Model In Kriging 12
4 Real Data Analysis 13
5 Conclusion 29
References 31

[1] Azevedo L, Pereira MJ, Ribeiro MC, Soares A. (2020). Geostatistical COVID-
19 infection risk maps for Portugal. Int J Health Geogr, 19(1), 1-8.

[2] Backer, S., Rezene, A., Kahar, P., Khanna, D. (2022). Socioeconomic determi-
nants of COVID-19 incidence and mortality in Florida. Cureus, 14(2), 1-12.

[3] Chande Aroon, Lee Seolha, Harris Mallory, Nguyen Quan, Beckett Stephen
J., Hilley Troy, Andris Clio, and Weitz Joshua S. (2020). Real-time, interactive
website for US-county-level COVID-19 event risk assessment. Nat. Hum. Behav.
4(12), 1313-1319.

[4] Cressie, N. A. (1985). Fitting variogram models by weighted least-squares. Jour-
nal of The International Association for Mathematical Geology, 17, 563-586.

[5] Cressie, N., Hawkins, D.M. (1980). Robust estimation of the variogram: I.
Journal of the International Association for Mathematical Geology, 12, 115-125.

[6] Cramer EY, Ray EL, Lopez VK,...etc (2022). Evaluation of individual and
ensemble probabilistic forecasts of COVID-19 mortality in the United States.Proc Natl Acad Sci, 119(15), 1-12.

[7] Diggle, P. J., Tawn, J. A., Moyeed, R. A. (1998). Model-based geostatistics.
Journal of the Royal Statistical Society Series C: Applied Statistics, 47(3), 299-350.

[8] Friedson, A. I., McNichols, D., Sabia, J. J., Dave, D. (2021). Shelter‐in‐place orders and public health: evidence from California during the Covid‐19 pandemic. Journal of Policy Analysis and Management, 40(1), 258-283.

[9] Huber, P. J. (2004). Robust statistics (Vol. 523). John Wiley and Sons.

[10] Huang, G., Chen, L. J., Hwang, W. H., Tzeng, S., Huang, H. C. (2018).Real‐time PM2.5 mapping and anomaly detection from AirBoxes in Taiwan.Environmetrics, 29(8), 1-15.

[11] Laslett, G. M. (1994). Kriging and splines: an empirical comparison of their
predictive performance in some applications. Journal of the American Statistical Association, 89(426), 391-400.

[12] Li Wang, Guannan Wang, Xinyi Li, Shan Yu, Myungjin Kim, Yueying Wang,Zhiling Gu, and Lei Gao. (2021). Modeling and forecasting COVID-19. Notices of the American Mathematical Society, 68(04).

[13] Liu Q, Harris JT, Chiu LS, Sun D, Houser PR, Yu M, Duffy DQ, Little MM,Yang C. (2021). Spatiotemporal impacts of COVID-19 on air pollution in California, USA. Science of the Total Environment, 750, 141592.

[14] Mollalo A, Tatar M. (2021). Spatial Modeling of COVID-19 Vaccine Hesitancy in the United States. International Journal of Environmental Research and Public Health, 18(18):9488.

[15] Naeger, A. R. and Murphy, K. (2020). Impact of COVID-19 containment measures on air pollution in California. Aerosol and Air Quality Research, 20(10),2025-2034.

[16] Oh, D.L., Meltzer, D., Wang, K. et al. (2022). Neighborhood Factors Associated with COVID-19 Cases in California. J. Racial and Ethnic Health Disparities,1-10.

[17] Parker HA, Hasheminassab S, Crounse JD, Roehl CM, Wennberg PO. (2020).Impacts of traffic reductions associated with COVID‐19 on Southern California air quality. Geophysical Research Letters, 47(23), 1-9.

[18] Shih-Chia Chen, Chi-Yang Tsai, Chao-Yen Chen, Pi-Yun Teng. (2022).The Impact and Reflections Brought by COVID-19 on Professional Sports Industry: Case Study of the United States. Journal of Sport Culture No, 40, 90-115.

[19] Saelee R, Zell E, Murthy BP, Castro-Roman P, Fast H, Meng L, Shaw L, Gibbs-Scharf L, Chorba T, Harris LQ, Murthy N. (2022). Disparities in COVID-19 Vaccination Coverage Between Urban and Rural Counties - United States, December 14, 2020-January 31, 2022. Morbidity and Mortality Weekly Report,
71(9), 335.

[20] Tzeng, S. and Huang, H.-C. (2018). Resolution adaptive fixed rank kriging.Technometrics, 60(2), 198-208.

[21] Wood, S.N. (2003). Thin plate regression splines. J.R.Statist.Soc.B, 65(1), 95-114