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An omnibus test for departures from constant mean. (English) Zbl 0706.62046
Summary: Observations \(y_ i\) are made at points \(x_ i\) according to the model \(y_ i=F(x_ i)+e_ i\), where the \(e_ i\) are independent normals with constant variance. In order to decide whether or not F(x) is constant, a likelihood ratio test is constructed, comparing F(x)\(\equiv \mu\) with \(F(x)=\mu +Z(x)\), where Z(x) is a Brownian motion.
The ratio of error variance to Brownian motion variance is chosen to maximize the likelihood, and the resulting maximum likelihood statistic B is used to test departures from constant mean. Its asymptotic distribution is derived and its finite sample size behavior is compared with five other tests. The B-statistic is comparable or superior to each of the tests on the five alternatives considered.

62G10 Nonparametric hypothesis testing
62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
62E20 Asymptotic distribution theory in statistics
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