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Abstract:
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Simple, accurate approximations exist for the scan statistic with a fixed-width window for a constant-rate null background. For a nonconstant background, or for the case of simultaneously testing with multiple window sizes, approximations were lacking and simulations used. Recently, Naus and Wallenstein, in Methodology and Computing in Applied Probability 6 (2004), provide a simple formula for the scan test with multiple width windows for the constant background null case. Naus and Wallenstein, in Statistics in Medicine (2006), use a simple formula to determine critical cluster sizes for a fixed window scan, given non-constant-rate null background. The present paper derives approximations that can handle multiple window widths in the nonconstant null background temporal case simultaneously.
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