Asymptotic Properties of the Straight Line Estimator for a Renewal Function

GÖKPINAR E., Khaniyev T., GAMGAM H.

SAINS MALAYSIANA, cilt.44, sa.7, ss.1041-1051, 2015 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 44 Sayı: 7
  • Basım Tarihi: 2015
  • Doi Numarası: 10.17576/jsm-2015-4407-17
  • Dergi Adı: SAINS MALAYSIANA
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.1041-1051
  • Anahtar Kelimeler: Asymptotic normality, asymptotic unbiasedness, consistency, nonparametric estimator, renewal function, NONPARAMETRIC-ESTIMATION, MODEL, S,S
  • Gazi Üniversitesi Adresli: Evet

Özet

In estimation problems in renewal function, when the distribution is not known, nonparametric estimators of renewal function are used. Frees (1986a, Warranty analysis and renewal function estimation, Naval Res. Logist. Quart, 33, 361-372) proposed the nonparametric estimator of renewal function for large values of t. Frees's estimator is easy to apply in practice. It is a preferred estimator for large values of t. However, its statistical properties still have not been investigated in detailed. For this reason, in this study, we investigate asymptotic properties of this estimator such as consistency, asymptotic unbiasedness and asymptotic normality. Also Monte Carlo simulation study is given to assess the performance of this estimator according to value of renewal function. Simulation results indicate that in the large values of t, Frees estimator is sufficiently close to the renewal function for the Gamma distribution with various parameters.