On the distribution of the maximum of Brownian bridges with application to regression with correlated errors. (English) Zbl 0726.62151
Summary: A Brownian bridge of order q is the weak limit of a residual partial sum obtained from regression fitting. When \(q=0\), the process is the usual Brownian bridge, and the distribution of the maximum is known analytically. For \(q\geq 1\), the supremum distributions are approximated by a Monte Carlo technique. The theoretical results are then applied in two examples involving polynomial regression. Tables are given that allow a determination of the degree of regression fitting in the case of polynomial regression with autoregressive errors. This procedure is also a graphical procedure.
MSC:
| 62M10 | Time series, auto-correlation, regression, etc. in statistics (GARCH) |
| 65C05 | Monte Carlo methods |
| 60G15 | Gaussian processes |
| 62M99 | Inference from stochastic processes |
References:
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| [4] | DOI: 10.1214/aoms/1177706645 · Zbl 0085.13720 · doi:10.1214/aoms/1177706645 |
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