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Data from World Health Organization (WHO) in world showed every year more than 1.25 million victims die from traffics accidents. East Java Province had the highest number of traffic accident cases in Indonesia. Then to predict the number of accidents in East Java against predictor variables, it is necessary to build a model. Traffic accident could make victims die, serious injury, and light injury. In this study, the researcher estimate the parametric and nonparametric regression negative binomial model based on the truncated spline estimator. The best model is determined based on Maximum Likelihood Cross-Validation (MLCV). The nonparametric regression model with negative binomial approach with the best-truncated spline estimator is obtained from the combination of knots (2, 1, 2, 3) using the MLCV method. The comparison of the deviance values between parametric and nonparametric regression in this study showed the deviance value nonparametric model less then deviance value parametric model. Deviance values showed the binomial negative using nonparametric regression model approach based on truncated spline estimator is better than the negative binomial using parametric regression model approach. The analysis showed factor traffic accident cause driver is sleepy had the highest influence on the number of traffic accidents cases in East Java Province. [ABSTRACT FROM AUTHOR]

In simple terms, semiparametric regression is a model that combines parametric and nonparametric models. The use of two different components in semiparametric regression practically makes this model broader and developed rapidly in theoretical respect. There are several estimators where two of them are truncated spline and fourier series. Spline has the characteristic of changing patterns at certain sub-intervals while fourier series are smooth and follow the pattern repeated at certain intervals. Furthermore, in multivariable nonparametric regression, it is possible to use different estimators for each predictor. This has encouraged researcher to develop studies with mixed or combined estimators. Ordinary Least Square (OLS) as one of the most common estimation methods cannot be directly used in nonparametric regression because the shape of the curve is unknown. Hence, the OLS method is modified with conditional optimization and referred to Penalized Least Square (PLS). The semiparametric regression curve estimation obtained in this study applied to the Human Development Index (HDI) in 37 regencies across East Java. Based on data from BPS-Statistics of East Java Province, East Java's HDI is the lowest among six provinces on Java island and slightly lower than Indonesia's HDI. Therefore, further studies on East Java's HDI becomes important. In this regard, the objective of this research is to obtain an estimator of multivariable semiparametric regression curve using mixed truncated spline and fourier series model and applying the data of HDI in East Java. The method of selecting smoothing parameter using minimum Generalized Cross Validation (GCV) and the best model was obtained with two knots-two oscillation with minimum GCV equals to 4.58531 which has R2=89.20%. Model interpretations are generally divided for each predictor variable and due to R2 obtained, it can also be said that the model obtained can explain the relationship between response and predictor variables. [ABSTRACT FROM AUTHOR]

The number of confirmed and suspected cases of Covid-19 are type of count data and they correlate each other. A popular regression model of two response variables for count data is bi-response Poisson regression. However, assumptions violation of Poisson regression that frequently occurs is over-dispersion. Negative binomial regression can overcome this over-dispersion case. The goal of this research is to model the number of confirmed and suspected Covid- 19 cases affected by population density using bi-response negative binomial regression based on local linear estimator. The proposed method gave the optimal bandwidth of 609 based on maximum likelihood cross validation criterion, with deviance value of 1.537 which is less than 27.083 of the parametric regression approach. It means that the estimated model of the number of confirmed and suspected cases of Covid-19 affected by population density using bi-response negative binomial regression based on local linear estimator is better than the parametric model approach. [ABSTRACT FROM AUTHOR]

The number of HIV and AIDS cases is a count data correlated with each other. The common model to regress two response variables in the form of count data is bi-response Poisson regression. One infraction of assumptions in the Poisson regression is over dispersion. Negative binomial regression is to be solution to this over dispersion case. This study aims to estimate bi-response negative binomial nonparametric regression model based on local linear estimators for modeling the number of HIV and AIDS cases in East Java. The results give the deviance value as the goodness of fit criterion of bi-response negative binomial nonparametric regression model by using local linear estimator of 2.263 which is smaller than the deviance value of the parametric regression model of 3.926. It means that the bi-response negative binomial nonparametric regression model by using local linear estimator is better than that by using parametric regression model approach to explain the relationship between HIV and AIDS cases affected by drug users in East Java. [ABSTRACT FROM AUTHOR]