Advanced Econometrics Takeshi Amemiya

Akaike Information Criterion

The Akaike information criterion in the context of the linear regression model was mentioned in Section 2.1.5. Here we shall consider it in a more general setting. Suppose we want to test the hypothesis (4.5.2) on the basis of the likelihood ratio test (4.5.3). It means that we choose L(0) over Да) if

LRT > d, (4.5.28)

where d is determined so that P[LRT > dL{a)] — c, a certain prescribed constant such as 5%. However, if we must choose one model out of many competing models Да,), Да2),. . . , this classical testing procedure is at best time consuming and at worst inconclusive. Akaike (1973) proposed a simple procedure that enables us to solve this kind of model-selection prob­lem. Here we shall give only a brief account; for the full details the reader is referred to Akaike’s original article or to Amemiya (1980a).

We can write a typical member of the many competing models Цаі), Ца2),... as Да). Akaike proposed the loss function

Щвo, a)----- у J [log Д0O) dx, (4.5.29)

where a is treated as a constant in the integration. Because W(Q0, а) ё W(0o, 0O) = 0, (4.5.29) can serve as a reasonable loss function that is to be minimized among the competing models. However, because W depends on the unknown parameters 0O, a predictor of W must be used instead. After rather complicated algebraic manipulation, Akaike arrived at the following simple predictor of W, which he called the Akaike Information Criterion (AIC):

AIC---- -- у log Ца) + Ц, (4.5.30)

where p is the dimension of the vector a. The idea is to choose the model for which AIC is smallest. Akaike’s explanation regarding why AIC (plus a certain omitted term that does not depend on a or p) may be regarded as a good predictor of W is not entirely convincing. Nevertheless, many empirical re­searchers think that AIC serves as a satisfactory guideline for selecting a model.

Добавить комментарий

Advanced Econometrics Takeshi Amemiya

Nonlinear Limited Information Maximum Likelihood Estimator

In the preceding section we assumed the model (8.1.1) without specifying the model for Y( or assuming the normality of u, and derived the asymptotic distribution of the class of …

Results of Cosslett: Part II

Cosslett (1981b) summarized results obtained elsewhere, especially from his earlier papers (Cosslett, 1978, 1981a). He also included a numerical evalua­tion of the asymptotic bias and variance of various estimators. We …

Other Examples of Type 3 Tobit Models

Roberts, Maddala, and Enholm (1978) estimated two types of simultaneous equations Tobit models to explain how utility rates are determined. One of their models has a reduced form that is …

Как с нами связаться:

Украина:
г.Александрия
тел./факс +38 05235  77193 Бухгалтерия

+38 050 457 13 30 — Рашид - продажи новинок
e-mail: msd@msd.com.ua
Схема проезда к производственному офису:
Схема проезда к МСД

Партнеры МСД

Контакты для заказов оборудования:

Внимание! На этом сайте большинство материалов - техническая литература в помощь предпринимателю. Так же большинство производственного оборудования сегодня не актуально. Уточнить можно по почте: Эл. почта: msd@msd.com.ua

+38 050 512 1194 Александр
- телефон для консультаций и заказов спец.оборудования, дробилок, уловителей, дражираторов, гереторных насосов и инженерных решений.