By K. O. Bowman

Ebook by way of Bowman, ok. O., Shenton, L. R.

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We specify the relation as CO2 = α1 (GNP)α2 . 1. In general, when a relation between two variables x and y is expressed as y = f (x), the elasticity of y relative to x is defined by elasticity = lim →0 = f (x + ) − f (x) f (x) f (x)x . 1 CO2 emission data of Japan. Year GNP Volume of CO2 Emission Year GNP Volume of CO2 Emission 1970 1971 1972 1973 1974 1975 1976 1977 1978 1979 1980 1981 1982 1983 187 196 213 230 227 234 244 254 268 283 290 299 309 316 Trillion yen 739 765 822 916 892 854 875 919 916 951 920 903 879 866 Million ton 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 329 344 354 370 393 412 433 449 455 456 459 466 485 934 909 907 897 984 1013 1071 1093 1105 1080 1131 1137 1168 Trillion yen Million ton Source: Nawata (2001) with permission.

2, we define a general linear regression model in a general setup. We also introduce several typical models for applications such as an AR(1) error model, Anderson model, equi-correlated model, heteroscedastic model and SUR model. 3, the GLSE is defined on the basis of the Gauss–Markov theorem. The relation between the GLSEs and some other estimators derived from different principles including linear unbiased estimators, location-equivariant estimators and the maximum likelihood estimator is also discussed.

Then we have ej = yj − Xj (X X)−1 X y p = yj − Xj (X X)−1 Xi yi i=1 GENERALIZED LEAST SQUARES ESTIMATORS 47 p = (Mj + Nj )yj − Xj (X X)−1 Xi (Mi + Ni )yi i=1 p = (Xj βˆj + εˆ j ) − Xj (X X)−1 Xi Xi βˆi i=1 p Xi Xi (βˆi − βˆj ) , = εˆ j − Xj (X X)−1 i=1 where the last equality is due to p Xj βˆj = Xj (X X)−1 Xi Xi βˆj . 8. 7 readily follows since εˆ j = Nj ej . 4, which is described as y = Xβ + ε with y1 0 X1 .. y = ... : n × 1, X = : n × k, . yp β1 .. β = . : k × 1, βp 0 Xp ε1 ..