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1 Abstract: Rana et. al. in 2008 proposed modification Goldfield-Quant test for detection of heteroscedasiticity in the presence of outliers by using Least Trimmed Squares (LTS). The proposes method assumed trimming ten percent from dataset. In this situation may take place losing in clean data where the real percentage of outliers is less than (10%) or the estimator may be misleading where the outliers percentage is more than (10%). The researcher propose another modification of Goldfield- Quant test to be robust. The results show our proposed method is better than the last modification of Goldfield- Quant test and the classical one. F LTS

2 1. املقدمة 2 2 exp( z / ) t t z t X (1) (18) (Rana and et.al, 2008) 2 2 c t t حيث c t كمية غير معلومة. Var 2 ( u i ) u Groupwise

3 Cook and (8) Weisberg,1983) Chatterjee Imon, Imon 12,13, ,2008,2005 and Hadi, White ) (20),

4 and Leroy,1987) BP ([( n p ) / 2] 1) / n P Hampel, n (17) (Rousseeuw and Leroy,1987). LTS يمكن ايجاد مقدراتها من خالل تقهيم دانة انهدف ادناه انى اقم مايمكن min h 2 r() i, i 1 2 r (i) h h [( 1 ) n] [ ( k 1)] n k (17) (Rousseeuw

5 (18) (Rana and et.al, 2008)

6 S-PLUS2000 F ( RMGQ) (18) (Rana MGQ and et.al, 2008)

7 (LTS) c MSR 1/5 Max Min (n c) F (n c)/2 Xi Max F = Min X i

8 F (n c 2k)/2 F F F p MGQ (18) (Rana and et.al, 2008)

9 ,1995 Montgomery, Peck and Vining,2001) (Pindyck and Rubinfeld,1997) Gujarati Pindyck and Rubinfeld Pindyck and Rubinfeld (1997) Pindyck and Rubinfeld التسلسل الدخل االنفاق المنزلي التسلسل الدخل االنفاق المنلي (4.9)

10 residuals residuals Fited Fited Pindyck and Rubinfeld Pindyck and Rubinfeld Gujarati Gujarati (1995)

11 (1,2,3,4,29,30) Gujarati لسلستلا قافنلاا لخدلا لسلستلا قافنلاا ا لخدلا لسلستلا قافنلاا لخدلا (10) 65(10) 70(10) 80(10) (100) 189 (100)

12 residuals residuals Fited Gujarati Fited Gujarati 4

13 Montgomer, Peck and Vining ( Montgomery, Peck and 1,2,3,27,28,30) (2001) Vining Montgomery, Peck and Vining االنفاق الدخل على االعالن االنفاق على الدخل االعالن االنفاق الدخل على االعالن (300000) (300000) (300000) (300000) (21431) (21431) 19350

14 residuals residuals Fited Pindyck and )7331( Rubinfeld Montgomery, Peck 5 and Vining P Classical GQ Fited RMGQ MGQ 6 Montgomery, Peck )7331( Pindyck and Rubinfeld and Vining

15 Pindyck and Rubinfeld :-7 Test بوجود القيم الشاذة بدون قيم شاذة FC= F p value F p value Classical GQ 78172< : ;; MGQ 9< ; RMGQ F P F

16 RMGQ MGQ RMGQ Gujarati MGQ )199.( )733;( Gujarati RMGQ F

17 MGQ Gujarati Test FC=2.978 بوجود القيم الشاذة بدون قيم شاذة F p value F p value Classical GQ : MGQ :8 01:1: RMGQ (2001) Montgomery, Peck and F Vining Montgomery, Peck and Vining

18 P Montgomery, Peck and Vining Test بوجود القيم الشاذة بدون قيم شاذة FC=2.978 F p value F p value Classical GQ MGQ RMGQ

19 RMGQ Gujarati Pindyck and Rubinfeld )7331( (2001) Montgomery, Peck and Vining

20 MGQ MGQ RMGQ Pindyck and Rubinfeld )7331( MGQ

21

22 10. Gujarati, D. (1995). Basic Econometrics, 4rd ed. New York: McGraw-Hill. 11. Hampel, F.R , A general Qualitative Definition of robustness, The Annals Mathematical of Statistics., 42, Imon, A. H. M. R. (2002). On deletion residuals, Calcutta Statistical Association Bulletin, 52, Imon, A.H.M.R. (2005). Identifying multiple influential observations in linear regression, Journal of Applied Statistics, 32, Imon, A.H.M.R. (2008). Deletion residuals in the detection of heterogeneity of variances in linear regression, (Accepted for 6. Chatterjee, S. and Hadi, A.S. (1988). Sensitivity Analysis in Linear Regression, New York.: Wiley. 7.Chatterjee, S. and Hadi, A.S. (2006). Regression Analysis By Examples, 4th ed., New York.: Wiley. 8.Cook, R. D. and Weisberg S. (1983). Diagnostics for heteroscedasticity in regression, Biometrika, 70, Goldfeld, S.M. and Quandt, R.E. (1965). Some tests for homoskedasticity, Journal of the American Statistical Association, 60,

23 Presence of Outliers. Journal of Mathematics and Statistics 4 (4): , Ryan, T. P., (1997). Modern Regression Methods, New York: Wiley. 20. White, H. (1980). Heteroscedasticity-consistent covariance matrix estimator and a direct test for heteroscedasticity, Econometrica, 48, publication), Journal of Applied Statistics. 15. Montgomery, D.C., Peck, E.A. and Vining, G.G. (2001). Introduction to Linear Regression Analysis, 3rd ed., New York: Wiley. 16. Pindyck, S. R and Rubinfeld, L. D. (1997). Econometric Models and Econometric Forecasts, 4th ed., New York: Irwin/McGraw-Hill. 17. Rousseeuw, P.J. and Leroy, A. (1987). Robust Regression and Outlier Detection, New York.: Wiley. 18. Rana;Md. Sohel, Midi;Habshah, Imon;A.H.M. A Robust Modification of the Goldfield-Quandt Test for Detection of Heteroscedasticity in the