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A method for parameter hypothesis testing in nonparametric regression with Fourier series approach.

Mustain Ramli1, I Nyoman Budiantara1, Vita Ratnasari1

  • 1Department of Statistics, Faculty of Science and Data Analytics, Institut Teknologi Sepuluh Nopember, Kampus ITS-Sukolilo, Surabaya 60111, Indonesia.

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Summary

This study introduces parameter hypothesis testing for nonparametric regression using Fourier series. The likelihood ratio test (LRT) method confirms significant parameter influence on ROA data from Indonesian banks.

Keywords:
Fourier series functionFourier series function, Likelihood ratio testHypothesis testingLikelihood ratio testNonparametric regressionReturn on asset

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Area of Science:

  • Statistics
  • Econometrics
  • Financial Modeling

Background:

  • Nonparametric regression with Fourier series is established for parameter estimation.
  • Existing research lacks parameter hypothesis testing in this model.
  • Parameter hypothesis testing is crucial for assessing parameter significance.

Purpose of the Study:

  • To develop and apply parameter hypothesis testing for nonparametric regression using Fourier series.
  • To determine the significance of estimated parameters in the Fourier series nonparametric regression model.
  • To utilize the Likelihood Ratio Test (LRT) method for hypothesis testing.

Main Methods:

  • The Likelihood Ratio Test (LRT) method was employed for hypothesis testing.
  • The Fourier series function was treated as a non-smooth function.
  • Statistical test form, distribution, and rejection region were derived using LRT.

Main Results:

  • The statistical test derived via LRT follows a specific distribution.
  • Application to ROA data from 47 Indonesian banks in 2020.
  • Estimated parameters demonstrated a significant influence on the ROA model.

Conclusions:

  • The LRT method provides a valid approach for parameter hypothesis testing in Fourier series nonparametric regression.
  • The study successfully identified significant parameters influencing bank ROA.
  • This research fills a gap in hypothesis testing for this specific statistical model.