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Measures of dependence and tests of independence. (English) Zbl 0876.62040
Summary: Measures of dependence and resulting tests of independence are surveyed. Measures arising both from linear and nonlinear modeling are examined. Tests based on chaos theory are briefly discussed. The main emphasis, however, is on some recently developed nonparametric tests using estimated distribution and density functions. Most of the paper is phrased in terms of serial dependence for a univariaty stationary time series, but it is indicated how more general situations can be analysed. The bootstrap is an essential tool for determining the critical value of the new tests.

MSC:
62G10 Nonparametric hypothesis testing
62H20 Measures of association (correlation, canonical correlation, etc.)
62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
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