The Research on Sampling Estimation of Seasonal Index Based on Stratified Random Sampling

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5 7 008 7 Statistical Research Vol. 5, No7 Jul.

1 Statistical Research Vol. 5, No7 Jul. 008 :,,, : ; ; ; :O :A : (008) The Research on Sapling Estiation of Seasonal Index Based on Stratified Rando Sapling Deng Ming Abstract :As the traditional ethod of seasonal index is just a descriptive statistic, this paper puts forward a seasonal index estiator based on stratified rando sapling, and gives the bias and the ean square errors of the estiator, also gives the estiation of the ean square errors, analyses the hypothesis test of the seasonal index and the optiization of the saple quantity. Key words :Stratified rando sapling ; Seasonal index ; Saple survey ; Hypothesis test,, (, 003 ;Anderson, 998) :,,,,,;,,,,,,, Y ijl ( i =,,, ; j =,,, ; l =,,, ) i j l, i j = i =, = i = j = () j ( ) ( ) : gy ij = Y ijl, S ij = l = l = ( Y ijl gy ij )

2 5 7 : 7 gy j = Y ijl = gy ij = i = gy = N i = l = i = i = ij gy ij Y ijl = N gy j = j = l = j = j S j = gy j gy j S j j = = j = j gy j () (3), j ( ) : = i = y ijl ( i =,,, ; j =,,, ; l =,,, ) i j l : gy ij = y ijl, s ij = l = gy j = i gy ij = ij gy ij i = i = gy j s j = N gy j = j gy j j = j = = gy j gy j s j j = l = ( y ijl gy ij ) (4) = s j S j, S j s j = gy i () gy = S j + gy igy gygy j gy E( s j ) = S j E (gy j gy gygy j ) (gy gy) ( gy j gy gygy j ) ( gy gy) gygy gygy (5) Y ijl > 0,Y 0 = in { Y ijl }, i, j, l E( s j ) S j Y 0 gy E ( gy jgy gygy j ) ( gy gy) Y 0 gy E( gy j gy gygy j ) E( gy gy), E( gy j gy gygy j ) = gy E ( gy j gy j ) + gy j E ( gy gy) gy j gye( gy j gy j ) ( gy gy),( Π = Π ) (, 994 ;, 996), E( gy j gy j ) = ij = i = = O S ij i = E( gy gy) = j E( gy j gy j ) j = = j j = i = = O n 0 (6) E( gy j gy j ) ( gy gy) = j E( gy j gy j ) = O, n 0 = in j { } E(s j ) S j Y 0 gy O n 0 O n 0 = O n 0 E( s j ) = S j + O n 0 (7) (7) s j S j, n 0 () (5) ( s j S j ) = gy jgy gygy j gy (6) E( gy j gy gygy j ) = gy ( gy j gy gygy j ) ( gy gy) gygy ( gy j gy gygy j ) ( gy j gy gygy j ) ( gy gy) = + gy ( gy jgy gygy j ) ( gy gy) i = gy + gy j j j =

3 ij S ij gy j gy j i = = h gy h h j + gy j h h j i = i = ih S ih (8) i = E( gy j gy gygy j ) ( gy gy) = gy E( gy j gy j ) ( gy gy) + gy j E( gy gy) 4 gy j gye( gy j gy j ) ( gy gy) 3 (, 98) E( gy ij gy ij ) 4 = E( gy ij gy ij ) 3 = O n ij E( gy ij gy ij ) = O (9) E( gy j gy j ) 4 = 4 ij E( gy ij gy ij ) i = gy ij ) hj E( gy hj gy hj ) O n j i h E( gy gy) 4 = 4 j E( gy j gy j ) j = gy j ) h E( gy h gy h ) O n j E j h, ij E( gy ij j E( gy j E( gy j gy j ) ( gy gy) 3 = 3 j E( gy j gy j ) 4 O n j ( gy j gy gygy j ) ( gy gy) gy gy) = O n 0 Y 0 E( gy jgy gygy j ) ( gy E( gy j gy gygy j ) ( gy gy) = gy E( gy j gy j ) ( gy gy) + gy j E( gy gy) 3 gy j gye( gy j gy j ) ( gy gy) (9) E( gy j gy j ) ( gy gy) = j E( gy ij gy ij ) 3 O n j E( gy gy) 3 = 3 j E( gy j gy j ) 3 O j = n 0 E( gy j gy j ) ( gy gy) = j E( gy j gy j ) 3 O n j (0) E ( gy j gy gygy j ) ( gy gy) gy gy) = O n 0 (8) (0) () MS E( s j ) = E( s j S j ) = h gy h h j + gy j () : h h j Y 0 E( gy jgy gygy j ) ( gy i = () ih S ih + O i = n 0 MS E( s j ) = gy j gy j gy E( gy j gy) + gy gy) + O n 0 () E( gy j gy) E( gy gy) + gy j () (), MS E( s j ) : se ( s j ) = h gy h h j h h j j () E( gy ij s ij i = ih s ih (3) i = (3),:, h gy h = h j gy + jgy j = ( gy + gy) ( gy gy) gy gy gy gy jgy j gy 3 = ( gy + gy ) ( gy + gy) ( gy gy) = ( gy + gygy + gy ) ( gy gy) gy 3 gy 3 gy 3 gy 3 E( s ij) = S ij E ( gy gy) ij s ij i = = O n 0

4 5 7 : 73 E h gy h h j = h gy h n h j j = h gy h n h j j (3), : E gy j = gy j h h j h h j (4) (5),: ij s ij i = ih s ih i = + O i = n 0 + O i = n 0 ih S ih + O i = n 0 E[ se ( s j ) ] = h gy h h j + gy j h h j ih S ih + O i = n 0 (4) (5) i =, (Cochran, 977) n 0, S j : s j z se ( s j ), s j + z se ( s j ) (6), z S j (), S j S h, : H 0 S h = S j H S h S j (3), H 0 gy h = gy j H gy h gy j (7) E( gy j ) = gy j Var( gy j ) = E( gy j gy j ) = n 0 ( gy h gy j ) ( gy h gy j ) Var( gy h ) + Var( gy j ) N (0,), i = z = gy h gy j Var( gy h ) + Var( gy j ) > z (8) H 0, h j,s h S j H 0, h j,s h = S j : Var( gy j ) = ij s ij ; i = E[ Var( gy j ) ] = Var( gy j ) (9) () n 0, MS E( s j ) : V ( s j ) = h gy h h j + gy j h h j ih S ih i =,n = V ( s j ) i =, j = n = j = f = V ( s j ) + n j = 5f 5 = n j j =,,, 5f 5 = = n h j n = 0 j = i = j = i = h gy h i = + = 0,, j =,, (0) i =, ( i =,,, ) (,(4) (5),

5 Statistical Research Vol. 5, No7 Jul. 008 : 3 :, ( ) 987, : (TFP) ;; (CE), :;; :F3 :A : (008) The Copilation and Update of Multiregional InputOutput Table Inter Province : Evidence fro Jiangsu Zhang Min Fan Jin Zhou Yingheng Abstract : It has becoe the research trend of current regional econoics to apply MultiRegional InputOutput (MRIO) odel to illustrate the spatial linage characteristics and dynaic transforation rules, but it still had no reports that MRIO odel has been copiled and used in a provincial level in China. This paper has copiled and updated Jiangsu Province s InputOutput table of threeregions and thirtysections in 00 and 987. The ey techniques include calculating IO coefficients by TFP, calculating Interregional coodity flows through gravitation odel, and updating IO coefficients by CE ethod which can iniize the inforation loss. Key words :MRIO Model in province ;Copilation and Update ;TFP 3 ( ) ), = n S ij i = S ij j = i = = S ij S ij i = = n, j =,, () = S 0,, j =,,, (),,, ;,,,,

6 5 7 ::, :,,,,,,,,,,,,,, (Rose and Casler,996), Isard (95) Polense (980) MRIO ,, ( ICSEAD) , ( IDE) ,(00) (004),, Oaoto and Ihara (004) (00) 997, :, ;,, ,.. Leontief (953), Studies in the Structure of the Aerican Econoy, Oxford University Press, pp (004),997 (006) 75 [ ]. [M]. :, 003. [ ]David R. Anderson, Dennis J. Sweeney, Thoas A. illias. Statistics for Business and Econoic (6 th ed. ) [M]. :, 998. [ 3 ],. [ M]. :, 994. [ 4 ],. [M]. :, 996. [ 5 ]illia G. Cochran, Sapling Techniques (3rd ed. ) [M]. New Yor : John iley & Sons inc, 977. [ 6 ]. [M]. :, 98.,,5,,, ( :)

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