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<p>This work covers the efficient estimation problem in an arbitrary-order self-exciting threshold generalized integer-valued autoregressive <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(\left( SET-GINAR\right)\)</EquationSource> <EquationSource Format="MATHML"><math> <mfenced close=")" open="("> <mi>S</mi> <mi>E</mi> <mi>T</mi> <mo>-</mo> <mi>G</mi> <mi>I</mi> <mi>N</mi> <mi>A</mi> <mi>R</mi> </mfenced> </math></EquationSource> </InlineEquation> model. The local asymptotic normality <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(\left( LAN\right)\)</EquationSource> <EquationSource Format="MATHML"><math> <mfenced close=")" open="("> <mi>L</mi> <mi>A</mi> <mi>N</mi> </mfenced> </math></EquationSource> </InlineEquation> property is obtained via the adapted (Drost et al.&#xa0;in J&#xa0;Time Ser Anal 29:783–801 (2008) representation of the transition scores. Secondly, using these results, the efficient locally asymptotically minimax <InlineEquation ID="IEq5"> <EquationSource Format="TEX">\(\left( LAM\right)\)</EquationSource> <EquationSource Format="MATHML"><math> <mfenced close=")" open="("> <mi>L</mi> <mi>A</mi> <mi>M</mi> </mfenced> </math></EquationSource> </InlineEquation> estimators are constructed based on the optimality criterion due to Hájek (Proceeding of Sixth berkeley symposium on mathematical statistics and probability, vol 1. University of California Press, pp 175–194, 1972). Finally, the performances of the established method are shown via simulation studies and real data sets. Further, the superiority of this efficient procedure, over the existing approaches in the literature concerning the estimation is also assessed via a numerical illustration study.</p>

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Local asymptotic normality and optimal estimation for self-excited threshold generalized \(INAR\left( p\right)\) models

  • 期刊论文

  • 发表日期：

    2025年6月26日

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  • Mohamed Sadoun,
  • Mohamed Bentarzi

摘要

This work covers the efficient estimation problem in an arbitrary-order self-exciting threshold generalized integer-valued autoregressive \(\left( SET-GINAR\right)\) S E T - G I N A R model. The local asymptotic normality \(\left( LAN\right)\) L A N property is obtained via the adapted (Drost et al. in J Time Ser Anal 29:783–801 (2008) representation of the transition scores. Secondly, using these results, the efficient locally asymptotically minimax \(\left( LAM\right)\) L A M estimators are constructed based on the optimality criterion due to Hájek (Proceeding of Sixth berkeley symposium on mathematical statistics and probability, vol 1. University of California Press, pp 175–194, 1972). Finally, the performances of the established method are shown via simulation studies and real data sets. Further, the superiority of this efficient procedure, over the existing approaches in the literature concerning the estimation is also assessed via a numerical illustration study.