フーリエ数列に基づく非パラメトリック回帰モデルの統計的推論と応用
Suliyanto1, Toha Saifudin1, Marisa Rifada1
1Department of Mathematics, Universitas Airlangga, Surabaya, Indonesia.
MethodsX
|August 25, 2025
まとめ
この研究は,フーリエ数列を用いた非パラメトリック回帰の仮説テストを導入し,インドネシアの地域支出データでその有効性を検証します. 結果は,一人当たりの支出に対する予測要因の有意な影響を確認した.
科学分野:
- 統計について
- 経済学
背景:
- 非パラメトリック回帰モデルは,周期的なデータに対して柔軟なソリューションを提供します.
- 以前の研究では 推定に重点を置いていたが 確固たる仮説検証の枠組みは なかった.
研究 の 目的:
- フーリエ数列近似を用いた非パラメトリック回帰の統計推論方法を開発する.
- 仮説テストの手順を導入し,部分テストと同時テストを含む.
- 地域支出分析におけるモデルパラメータの重要性を評価する.
主な方法:
- 非パラメトリック回帰のフーリエ数列近似を用いた.
- 仮説のテストのためのFテストとTテストの統計を実装した.
- 汎用クロス検証 (GCV) による最適な振動パラメータの決定
主要な成果:
- 一人当たりの支出に対する予測変数 (人当たりのGDP,貧困率,労働力参加率) の有意な影響を示した.
- パプア,インドネシアの実際の支出データを用いてモデルの有効性を検証した.
- 一時的な (Fテスト) と部分的な (Tテスト) 意義評価の両方によって確認された結果.
結論:
- 開発された仮説テストフレームワークは,フーリエ数列による非パラメトリック回帰のための堅固な方法を提供します.
- このモデルは,地域一人当たりの支出の重要な予測要因を正確に特定します.
- この研究は,定期的な経済データを分析するための統計的推論能力を高めます.
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