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Summary

This study introduces statistical inference for nonparametric regression using Fourier series functions. Analysis of East Java life expectancy data shows the model significantly predicts outcomes, with an R-square of 96.24%.

Keywords:
Fourier Series FunctionFourier seriesLife expectancy dataLikelihood ratio testNonparametric regressionStatistical inference

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Area of Science:

  • Statistics
  • Econometrics

Background:

  • Nonparametric regression offers curve approximation without assuming a known regression function.
  • Fourier series functions are a key tool for nonparametric curve approximation.
  • Statistical inference, especially partial hypothesis testing, remains underexplored in this context.

Purpose of the Study:

  • To investigate statistical inference for nonparametric regression models utilizing Fourier series function approximation.
  • To cover parameter and model estimation, alongside simultaneous and partial hypothesis testing.
  • To apply the developed methods to real-world life expectancy data.

Main Methods:

  • Utilized the Fourier series function as defined by Bilodeau (1992).
  • Determined the optimal number of oscillation parameters for accurate model estimation.
  • Employed the Likelihood Ratio Test (LRT) method for statistical testing.

Main Results:

  • Achieved a high model estimation accuracy with an R-square value of 96.24%.
  • Simultaneous hypothesis testing indicated significant influence of parameters on the model at a 5% significance level.
  • Partial hypothesis testing revealed four non-significant parameters, yet overall predictor variables significantly impacted life expectancy.

Conclusions:

  • The nonparametric regression model with Fourier series approximation provides a robust framework for statistical inference.
  • The model effectively explains variations in life expectancy, demonstrating practical applicability.
  • Further research can expand inferential capabilities for complex nonparametric models.