combine_stat function

Combine p-values

This function is used to combine the four moment-based p-values as in eq. 17 and 18 of Dufour & Luger 2017.

combine_stat(stats, params, type)

Arguments

• stats: A (l x 4) matrix where l is the number of moment-based test statistics.
• params: A (2 x 4) matrix with parameters to combine test statistics. See approxDistDL.
• type: String determining the type of method used to combine p-values. If set to "min" the min method of combining p-values is used as in Fisher 1932 and Pearson 1933. If set to "prod" the product of p-values is used as in Tippett 1931 and Wilkinson 1951.

Returns

A (N x 1) vector with test statistics. The last element is the test statistic from observed data.

References

Dufour, J. M., & Luger, R. 2017. "Identification-robust moment-based tests for Markov switching in autoregressive models." Econometric Reviews, 36(6-9), 713-727.

Tippett, L. 1931. "The Method of Statistics". London: Williams & Norgate.

Wilkinson, B. 1951. "A statistical consideration in psychological research." Psychology Bulletin 48:156–158.

Pearson, K. 1933. "On a method of determining whether a sample of size n supposed to have been drawn from a parent population having a known probability integral has probably been drawn at random". Biometrika 25:379–410.

Fisher, R. 1932. "Statistical Methods for Research Workers." Edinburgh: Oliver and Boyd.