This article describes the application of spatial statistical epidemiological modeling and its inference and applies it to COVID-19 case data, looking at it from a spatial perspective, and considering time-series data. COVID-19 cases in Indonesia are increasing and spreading in all provinces, including Kalimantan. This study uses applied mathematics and spatiotemporal analysis to determine the factors affecting the constant rise of COVID-19 cases in Kalimantan. The spatiotemporal analysis uses the Geographically Temporally Weighted Regression (GTWR) model by developing a spatial and temporal interaction distance function. The GTWR model was applied to data on positive COVID-19 cases at a scale of 56 districts/cities in Kalimantan between the period of January 2020 and August 2021. The purpose of the study was to determine the factors affecting the cumulative increase in COVID-19 cases in Kalimantan and map the spatial distribution for 56 districts/cities based on the significant predictor variables. The results of the study show that the GTWR model with the development of a spatial and temporal interaction distance function using the kernel Gaussian fixed bandwidth function is a better model compared to the Ordinary Least Squares (OLS) model. According to the significant variables, there are various factors affecting the rise in cases of COVID-19 in the region of Kalimantan, including the number of doctors, the number of TB cases, the percentage of elderly population, GRDP, and the number of hospitals. The highest factors that affect COVID-19 cases are the high number of TB cases, population density, and the lack of health services. Furthermore, an area map was produced on the basis of the significant variables affected by the rise in COVID-19 cases. The results of the study provide local governments with decision-making recommendations to overcome COVID-19-related issues in their respective regions.

This study developed a new method of hypothesis testing of model conformity between truncated spline nonparametric regression influenced by spatial heterogeneity and truncated spline nonparametric regression. This hypothesis test aims to determine the most appropriate model used in the analysis of spatial data. The test statistic for model conformity hypothesis testing was constructed based on the likelihood ratio of the parameter set under H₀ whose components consisted of parameters that were not influenced by the geographical factor and the set under the population parameter whose components consisted of parameters influenced by the geographical factor. We have proven the distribution of test statistics V and verified that each of the numerators and denominators in the statistic test V followed a distribution of χ2. Since there was a symmetric and idempotent matrix S, it could be proved that Y~TS Y~/σ2~χn-lm-12. Matrix Dui,vi was positive semidefinite and contained weighting matrix Wui,vi which had different values in every location; therefore matrix Dui,vi was not idempotent. If Y~TDui,viY~≥0 and Dui,vi was not idempotent and also Y~ was a N0,I distributed random vector, then there were constants k and r; hence Y~TDui,viY~~kχr2; therefore it was concluded that test statistic V followed an F distribution. The modeling is implemented to find factors that influence the unemployment rate in 38 areas in Java in Indonesia.

This study proposes the development of a spatio-temporal model with geographic weights containing elements of location, time and the correlation between the two. The spatio-temporal model is a spatial regression model that combines geographic information and time series simultaneously. The model can overcome the problem of spatial heterogeneity and spatial effects. The spatial temporal model used is the Geographically Weighted Panel Regression (GWPR) model with a within estimator. Therefore, it is necessary to determine the best geographic weighting with the optimal bandwidth value and the lowest Cross Validation (CV). The geographic weights used were the Gaussian kernel function, the Bisquare kernel function and the exponential kernel function. Estimation of spatio-temporal model parameters using Weighted Least Square (WLS). The GWPR model was applied to food security index data in 34 Indonesian provinces. The problem of food security is an important problem to be solved in Indonesia, one way is to find the factors that influence the food security index through spatio-temporal modeling. This study consists of data exploration, descriptive statistics, spatial mapping distribution, selection of geographic weights and GWPR modeling. The results showed that the spatio temporal statistical model of GWPR was more accurate with a good model of 92.78 % and a Root mean Square Error value of 3.41. Some highlights of the proposed approach are.

This article discusses statistical innovations implemented in the health sector. The research is being conducted on the treatment and prevention of Dengue Hemorrhagic Fever (DHF), focusing on the factors contributing to the increase in DHF. Create a nonparametric regression model with a mixed estimator, truncated spline, and Gaussian Kernel to estimate the regression curve. In multiple nonparametric regression, this method can handle differences in data patterns between predictors. Truncated splines are polynomial segments with segmented and continuous properties. Truncated splines contain knot points that can locate their estimated data no matter where the data pattern moves. In addition, the Gaussian Kernel estimator is dependent on bandwidth, which regulates the regression curve's smoothness. The mixed estimators of truncated spline and Gaussian Kernel could model DHF cases according to an empirical analysis of DHF data. The most effective model has a Coefficient of Determination (R²) of 88.46%. Simultaneous hypothesis testing indicates that the model contains at least one significant predictor variable.

Nonparametric regression is a regression approach that is used to determine the relationship between the response variable and the predictor variable if the shape of the regression curve is unknown. One of the popular estimators used in nonparametric regression is the Fourier series estimator. Fourier series nonparametric regression is generally used when the pattern of the investigated data is unknown and there is a tendency for the pattern to repeat. The purpose of this study is to estimate nonparametric regression using the Fourier series approach and to find out the factors that influence the open unemployment rate on the island of Borneo in 2021. The criteria for the goodness of the model used Generalized Cross Validation (GCV) and the coefficient of determination ( ). Based on the results, it was found that the best nonparametric regression model for the Fourier series was the model with 5 oscillations which indicated a minimum GCV of 10.47 and an of 74.22%. Furthermore, based on the results of parameter significance testing either simultaneously or partially, it shows that all predictor variables have a significant effect on the open unemployment rate. The predictor variables include the labor force participation rate, the average length of schooling, the percentage of poor people, economic growth rate, and total population.