The semiparametric regression is one of the three forms of regression analysis which is made up of parametric and nonparametric. While the parametric is based on linear estimator, this nonparametric component is an innovation. This research proposes all the possible trigonometric basis usually used in Fourier series as nonparametric component estimator, its advantage, which includes its ability to overcome data with oscillation patterns. This study discusses nonparametric regression based on complete and sine Fourier series. Both estimators are developed using the cosine Fourier series concept. The outputs are two estimators which are used for parametric and nonparametric components with the corresponding form in semiparametric regression. In addition, all of these can be applied in real problems, and the best estimator is determined based on the smallest GCV and MSE for an oscillation parameter which gives the highest coefficient of determination for the selected one.

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Stunting is a kind of chronic nutritional problem among under-five years children that characterized by a shorter height compared to other children of their age. The ordinal logistic regression is one statistical method that used to analyze the ordinal response variable with three or more categories and predictor variables that are categorical or continuous. This method has been used in various fields, one of them is in the health field. In this study, ordinal logistic regression is used to describe the correlation between stunting status of children and birth weight, birth length, mother's age, mother's height, mother's knowledge about nutrition, parenting, health services, hygiene and sanitation, number of children and number of family members. The stunting status of children in this study is divided into three kind which are severely stunted, moderately stunted, and normal stunted. The aim of this study is to describe the characteristics of children and to determine the factors that influence the stunting status of children in priority villages for stunting prevention i.e. Bucorwetan and Alaspandan village in the Probolinggo district, East Java, Indonesia. The prevalence of stunting was 30% (22.5% moderately, 7.5% severely). The mother's height and health services were the important determinants of stunting.

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