Curve Estimation of Multivariable Nonparametric Kernel Regression on the Percentage of Households with Access to Decent and Affordable Housing
Tiaranisa^i Fadhilla, I Nyoman Budiantara, and Ismaini Zain

3Institut Teknologi Sepuluh Nopember

Abstract

Nonparametric regression methods, such as spline, Fourier, and kernel regression, are essential for modeling real cases where the relationships between variables cannot be easily defined. Among these methods, kernel regression is particularly useful when the underlying data patterns are unknown and do not follow a specific trend, periodicity, or interval-based changes. This research focuses on obtaining curve estimates through kernel regression using multiple predictor variables. The study aims to enhance our understanding of multivariable kernel regression and its practical applications. The bandwidth selection method employed is Generalized Cross Validation. The research investigates the percentage of households with access to decent and affordable housing, considering predictor variables like population density, floor area per capita, access to drinking water, and access to sanitation. The study focuses on cities and districts in Java Island, encompassing six provinces: DKI Jakarta, West Java, Central Java, DI Yogyakarta, East Java, and Banten, with a total of 119 observations. The relationship patterns observed between the predictor variables indicate non-monotonic associations, where an increase in the predictor value does not necessarily correspond to an increase or decrease in the response value. Consequently, the research employs kernel nonparametric regression with multiple variables to address this complexity.

Keywords: Affordable Housing, Curve Estimation, Generalized Cross Validation, Kernel, Nonparametric Regression

Topic: Mathematics and Statistics