Araştırma Makalesi
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Basit Doğrusal Otoregresif Modeller Sisteminde Parametre Tahmini ve Hipotez Testi: Simetrik İnovasyonlar

Yıl 2005, Cilt: 4 Sayı: 1, 75 - 91, 15.04.2005

Öz

Bu çalışmada, simetrik dağılıma sahip hata terimli basit otoregresif modeller sistemi incelenerek normal dağılım varsayımının geçersiz olduğu durumlardaki metodoloji birden fazla bağımsız bilgi kaynağı olduğu durumlara genellenmiş, uyarlanmış en çok olabilirlik yöntemi ile tahmin ediciler elde edilmiş ve parametre vektörünün tüm kaynaklar için değişip değişmediğini test edecek sağlam ve etkin test istatistikleri geliştirilmiştir. Elde edilen tahmin ediciler ve test istatistikleri bu alandaki uygulamalarda sıkça kullanılan en küçük kareler yöntemi ile elde edilen tahmin edici ve test istatistikleri ile karşılaştırılmış ve daha iyi sonuçlar verdiği görülmüştür.

Kaynakça

  • AKKAYA, A.D. ve TIKU, M.L. (200la), Estimating Parameters in Autoregressive Models in Non-Normal Situations: Asymmetric Innovations, Commun. Statist. Theory Meth., 30(3), 517,536.
  • AKKAYA, A.D. ve TIKU, M.L. (2001b), Corrigendum: Time Series Models with Asymetric Innovation, Commun. Statist. Theory Meth., 30(10), 2227-2230.
  • BHATTACHARYA, G.K. (1985), The Asymptotics of Maximum Likelihood and Related Estimators Based on Type II Censored Data, J. Amer. Statist. Assoc., 80, 398-404.
  • DURBIN, J. (1960), Estimation of Parameters in Time Series Regression Model, JRSS B, 22, 139-153.
  • ELVEBACK, L.R, GUILLIER, C.L. ve KERTING, F.R. (1970), Health, Normality and the Ghost of Gauss, J. American Medical Assoc., 211, 69-75.
  • ISLAM, M. Q., TIKU, M.L. ve YILDIRIM, F (2001), Non-Normal Regression I, Commun. Statist. Theory Meth., 30, 993-1020.
  • ISLAM, M. Q. ve TIKU, M.L. (2004), Multiple Linear Regression Models Under Non-Normality, Commun. Stat. - Theory Meth.
  • MALLER, R.A. (1989), Regression with Autoregressive Errors-Some Asymptotic Results, Statistics, 20, 23-39.
  • NAGARAJ, N.K. ve FULLER, W.A. (l992), Least Squares Estimation of the Linear Model with Autoregressive Errors, New Directions in Time Series Analysis, Part I, IMA Vol. Math. Appl. 45, New York: Springer, 215-225.
  • PEARSON, E.S. (1932), the Analysis of Variance in Cases of Nonnormal Variation, Biometrika, 23, 114-133.
  • PUTHENPURA, S. ve SINHA, N.K. (1986), Modified Maximum Likelihood Method for the Robust Estimation of System Parameters from Very Noisy Data, Automatica, 22, 231-235.
  • SCHAFFLER, S. (1991), Maximum Likelihood Estimation for Linear Regression Model with Autoregressive Errors, Statistics, 22, 191-198.
  • TIKU, M.L. (1967), Estimating the Mean and Standard Deviation from Censored Normal Samples, Biometrika, 54, 155-165.
  • TIKU, M. L. ve KUMRA, S. (1981), Expected Values and Variances and Covariances of Order Statistics for a Family of Symmetrical Distributions (Student’s t), Selected Tables in Mathematical Statistics 8, Providence, RI: American Mathematical Society, 141-270.
  • TIKU, M. L., TAN, W.Y. ve BALAKRISHNAN, N. (1986), Robust Inference, New York, Marcel Dekker.
  • TIKU, M.L. ve SURESH. R.P. (1992), a New Method of Estimation for Location and Scale Parameter's, J. Stat. Plann. and Inf., 30, 281-292.
  • TIKU, M.L., WONG, W.K. ve BIAN, G. (1999), Estimating Parameters in Autoregressive Models in Non-Normal Situations; Symmetric Innovations, Commun. Statist. Theory Meth., 28(2), 315-341.
  • TIKU, M. L., ISLAM M. Q., and SELÇUK, A. S. (2001), Non-Normal Regression II, Commun. Statist. Theory Meth., 30, 1021-1045.
  • TSE, Y. K. (1991), Price and Volume in the Tokyo Stock Exchange: an Explanatory Study, Japanese Financial Market Research (W.T. Ziemba, W. Bailey and Y. Hamano, Eds.), New York: Elsevier Science Publishers B. V., 91-119.
  • VAUGHAN, D. C. (1992), on the Tiku-Suresh Method of Estimation, Commun. Statist. Theory Meth., 21, 451-469.
  • VAUGHAN, D. C. ve TIKU, M. L. (2000), Estimation and Hypothesis Testing for a Non-Normal Bivariate Distribution and Applications, J. Mathematical and Computer Modelling, 32, 53-67.
  • VELU, R. ve GREGORY, C. (1987), Reduced Rank Regression with Autoregressive Errors, Econometrics, 35, 317-335.
  • VINOD, H. D. ve SHENTON, L. R. (1996) Exact Moments for Autoregressive and Random Walk Models for a Zero or Stationary Initail Value, Econometric Theory, 21, 391-404.

Estimation of Parameters and Hypothesis Testing in the System of Simple Autoregressive Models: Symmetric Innovations

Yıl 2005, Cilt: 4 Sayı: 1, 75 - 91, 15.04.2005

Öz

In this study, the simple autoregressive models system having symmetric innovations have been investigated and the methodology under non-normality has been extended to various independent sources of information. Modified likelihood estimators are obtained; robust and efficient statistics for testing whether the parameter vector remains the same from one source to another are developed. The estimators and the test statistics obtained are compared to the corresponding least squares statistics which are widely used in this context in applications, and found to give more accurate results.

Kaynakça

  • AKKAYA, A.D. ve TIKU, M.L. (200la), Estimating Parameters in Autoregressive Models in Non-Normal Situations: Asymmetric Innovations, Commun. Statist. Theory Meth., 30(3), 517,536.
  • AKKAYA, A.D. ve TIKU, M.L. (2001b), Corrigendum: Time Series Models with Asymetric Innovation, Commun. Statist. Theory Meth., 30(10), 2227-2230.
  • BHATTACHARYA, G.K. (1985), The Asymptotics of Maximum Likelihood and Related Estimators Based on Type II Censored Data, J. Amer. Statist. Assoc., 80, 398-404.
  • DURBIN, J. (1960), Estimation of Parameters in Time Series Regression Model, JRSS B, 22, 139-153.
  • ELVEBACK, L.R, GUILLIER, C.L. ve KERTING, F.R. (1970), Health, Normality and the Ghost of Gauss, J. American Medical Assoc., 211, 69-75.
  • ISLAM, M. Q., TIKU, M.L. ve YILDIRIM, F (2001), Non-Normal Regression I, Commun. Statist. Theory Meth., 30, 993-1020.
  • ISLAM, M. Q. ve TIKU, M.L. (2004), Multiple Linear Regression Models Under Non-Normality, Commun. Stat. - Theory Meth.
  • MALLER, R.A. (1989), Regression with Autoregressive Errors-Some Asymptotic Results, Statistics, 20, 23-39.
  • NAGARAJ, N.K. ve FULLER, W.A. (l992), Least Squares Estimation of the Linear Model with Autoregressive Errors, New Directions in Time Series Analysis, Part I, IMA Vol. Math. Appl. 45, New York: Springer, 215-225.
  • PEARSON, E.S. (1932), the Analysis of Variance in Cases of Nonnormal Variation, Biometrika, 23, 114-133.
  • PUTHENPURA, S. ve SINHA, N.K. (1986), Modified Maximum Likelihood Method for the Robust Estimation of System Parameters from Very Noisy Data, Automatica, 22, 231-235.
  • SCHAFFLER, S. (1991), Maximum Likelihood Estimation for Linear Regression Model with Autoregressive Errors, Statistics, 22, 191-198.
  • TIKU, M.L. (1967), Estimating the Mean and Standard Deviation from Censored Normal Samples, Biometrika, 54, 155-165.
  • TIKU, M. L. ve KUMRA, S. (1981), Expected Values and Variances and Covariances of Order Statistics for a Family of Symmetrical Distributions (Student’s t), Selected Tables in Mathematical Statistics 8, Providence, RI: American Mathematical Society, 141-270.
  • TIKU, M. L., TAN, W.Y. ve BALAKRISHNAN, N. (1986), Robust Inference, New York, Marcel Dekker.
  • TIKU, M.L. ve SURESH. R.P. (1992), a New Method of Estimation for Location and Scale Parameter's, J. Stat. Plann. and Inf., 30, 281-292.
  • TIKU, M.L., WONG, W.K. ve BIAN, G. (1999), Estimating Parameters in Autoregressive Models in Non-Normal Situations; Symmetric Innovations, Commun. Statist. Theory Meth., 28(2), 315-341.
  • TIKU, M. L., ISLAM M. Q., and SELÇUK, A. S. (2001), Non-Normal Regression II, Commun. Statist. Theory Meth., 30, 1021-1045.
  • TSE, Y. K. (1991), Price and Volume in the Tokyo Stock Exchange: an Explanatory Study, Japanese Financial Market Research (W.T. Ziemba, W. Bailey and Y. Hamano, Eds.), New York: Elsevier Science Publishers B. V., 91-119.
  • VAUGHAN, D. C. (1992), on the Tiku-Suresh Method of Estimation, Commun. Statist. Theory Meth., 21, 451-469.
  • VAUGHAN, D. C. ve TIKU, M. L. (2000), Estimation and Hypothesis Testing for a Non-Normal Bivariate Distribution and Applications, J. Mathematical and Computer Modelling, 32, 53-67.
  • VELU, R. ve GREGORY, C. (1987), Reduced Rank Regression with Autoregressive Errors, Econometrics, 35, 317-335.
  • VINOD, H. D. ve SHENTON, L. R. (1996) Exact Moments for Autoregressive and Random Walk Models for a Zero or Stationary Initail Value, Econometric Theory, 21, 391-404.
Toplam 23 adet kaynakça vardır.

Ayrıntılar

Birincil Dil Türkçe
Konular İstatistik
Bölüm Araştırma Makaleleri
Yazarlar

Özlem Türker Bu kişi benim

Ayşen D. Akkaya Bu kişi benim

Yayımlanma Tarihi 15 Nisan 2005
Yayımlandığı Sayı Yıl 2005 Cilt: 4 Sayı: 1

Kaynak Göster

APA Türker, Ö., & Akkaya, A. D. (2005). Basit Doğrusal Otoregresif Modeller Sisteminde Parametre Tahmini ve Hipotez Testi: Simetrik İnovasyonlar. İstatistik Araştırma Dergisi, 4(1), 75-91.