Spatial Analysis Using Big Data by Unknown

Author:Unknown
Language: eng
Format: epub
ISBN: 9780128131329
Publisher: Elsevier Ltd.
Published: 2019-11-04T21:39:48+00:00

(5.4.3)

where is a concentrated log-likelihood under the restriction of λ = 0, whereas is that without the restriction. Hypothesis testing uses the fact that LR λ asymptotically follows the χ 2 distribution with degree of freedom equal to 1.

5.4.3. Lagrangean multiplier test

Eq. (5.4.4) provides definition of the LM test statistic:

(5.4.4)

where T = tr[(W′ + W)W]. Also, e, and are the residuals and residual variance of the ML estimate (i.e., e′ e/N) under the restriction λ = 0, and they can be estimated with OLS. 13 Hypothesis testing uses the fact that LM λ asymptotically follows the χ 2 distribution with a degree of freedom equal to 1. The LM test is convenient in that it can be performed using only OLS results. However, note that it cannot determine whether an error term is autoregressive or a moving-average type.

Similarly, in hypothesis testing with SLM, null and alternative hypothesis are given by:

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