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Birth is one of the factors that influence the rate of population growth, one of the birth measures is the Total Fertility Rate (TFR). TFR is the average number of children born to a woman during her childbearing age can be measured using the number of children born alive. East Java Province is one of the provinces where the TFR value has reached the government's target, so that it is necessary to analyze the factors that are suspected to affect the number of children born alive in East Java Province. In this study using SDKI 2017 data in East Java Province with a sample of 2737 Women of Childbearing Age (WCA) and factors that are thought to affect the number of children born alive are the mother's age, the area of residence, the last education, the status of work, the quantile of wealth, the number of children died, the number of ideal children, the age of the first sexual relationship, the use of contraception tools, the first age of pregnancy, and the failure of pregnancy. Because of the response variable used an ordinal scale so that one of the statistical methods suitable for use is the method of ordinal logistic regression. The results of the analysis obtained that the most WCA in East Java has two children with factors that affect are the area of residence, and the number of children died. [ABSTRACT FROM AUTHOR]

Due to the lack of prior knowledge regarding the type of relationship between the response and the predictor variable, not all patterns of the regression curve are identifiable in regression analysis. Hence, nonparametric regression becomes a reasonable solution since no prespecified functional form is assumed. In nonparametric regression, curve estimation using a mixed estimator is rather complex, notably when there are two or more correlated response variables. In this study, we developed the curve estimation of bi-response nonparametric regression with a mixed truncated spline and Fourier series estimator model. The main objective was to estimate the regression curve using penalized weighted least square and weighted least square optimization. Based on the estimation results, numerical simulations with various sample sizes and correlations were implemented with generalized cross validation as the criterion. Thus, the model with a large sample size and high correlation was performed with the best outcome. [ABSTRACT FROM AUTHOR]

In regression analysis, not all pattern of regression curve is known due to absence of prior information about the kind of relationship between response and predictor variable. In this case, nonparametric regression becomes an alternative solution since there is no assumption about parametric form. There are several functions in nonparametric regression one of which is truncated spline that is more flexible to fit the data, good at visual interpretation, and able to handle data that have changed behavior at certain subintervals. Moreover, some application involves more than one response variables that are correlated between responses. Therefore, this study aims to obtain the curve estimation of truncated spline estimators on bi-response nonparametric regression along with estimation of error variance-covariance matrix. The curve estimation of the truncated spline estimator was obtained by Weighted Least Square (WLS) optimization with Generalized Cross Validation (GCV) as optimal knot point selection method. Then, the curve estimation of the model was applied to a real dataset of the 2019 Human Development Index (HDI) and Gender Development Index (GDI) in East Java Province, Indonesia. HDI and GDI become indicators of Sustainable Development Goals (SDGs) achievement, particularly social and economic pillars. An adequate coefficient determination from the best model indicates that the model provides good performance in modeling the data. [ABSTRACT FROM AUTHOR]

This research aims to develop an algorithm of the quasi maximum likelihood estimation method. The model used is the spatial Durbin panel model with dynamic effects for the single equation. The weighted matrix used in this study is equal for each variable This study proposes the generalized estimation equation approach and the Gauss-Newton iteration method for parameter estimation. Modeling of Foreign Direct Investment (FDI) in ASEAN countries from 2010 - 2017 is used for illustration. The best model selection is based on the smallest correlation information criterion (CIC) value. [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]

Education is widely accepted to be a fundamental resource, both for individuals and societies. Mean Years of Schooling (MYS) is one of the two education indicators in UNDP’s Human Development Index (HDI) and can reflect important aspects related to the degree of education in some countries or regencies. The results of the preliminary identification show that the relationship patterned between MYS as response and all predictor variables does not follow particular pattern (linear or a certain degree polynomial). Therefore the analysis of nonparametric regression should be performed. The scatter plot between response and predictors variables shows patterns that change at certain sub-intervals so the suitable method used is the nonparametric regression with truncated spline estimation. Truncated polynomial spline regression is used because it has an advantage which the model tends to find its own estimate of the data pattern wherever it moves. In this regard, the objective of this research is to get estimator of nonparametric truncated spline regression and investigate the significant factors affecting mean years of schooling of 119 regencies across Java in 2017. The numbers of knot points used are one, two, three, and combination of knot points. The method of selecting optimum knots uses minimum Generalized Cross Validation (GCV) and the best model is obtained with combination knots with a coefficient of determination 87.99 percent. Based on the result of a statistical significance test, the factors that significantly affect MYS are population density, student-teacher ratio, per capita gross regional domestic products, and student-school ratio. The results of this study are expected to be the input for the government to regulate policy in order to improve the overall national mean years of schooling. [ABSTRACT FROM AUTHOR]

Nonparametric regression is a method used to analyze the relation between response variables and predictor variables that do not follow a particular pattern. One common approach used in nonparametric regression is truncated spline, because of its high flexibility and good visual interpretation. The study of partial hypothesis testing in nonparametric regression is important in statistical inference. The likelihood ratio test will be used in order to define the test statistic. Theoretical study resulted in a the statistical test for partial hypothesis testing, denoted by Q* and following Student's t-distribution with (n-(1+(m+r)h) degrees of freedom. [ABSTRACT FROM AUTHOR]

Semiparametric regression contains two components, i.e. parametric and nonparametric component. Semiparametric regression model is represented by yti= μ(xti, zti)+εti where ?μ(x'ti,zti) =x'tiβ g(zti), and yti is response variable. It is assumed to have a linear relationship with the predictor variables x'ti=(x1/1,x2/2....xt/t). Random error εti i=1....n t=1....T is normally distributed with zero mean and variance σ² and g (zti) is a nonparametric component. The results of this study showed that the PLS approach on longitudinal semiparametric regression models obtain estimators... The result also show that bootstrap was valid on longitudinal semiparametric regression model with ... as nonparametric component estimator. [ABSTRACT FROM AUTHOR]