Tests for changing mean with monotonic power

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Structural breaks in time series (2013, background): “Remedies have been offered by Altissimo and Corradi (2003), Juhl and Xiao (2009), and Shao and Zhang (2010).”
Testing for Change Points in Time Series (2010, methodology): “…as in (ii) by replacing ût by ũt, where ũt = ⎧⎪⎪⎪⎪⎪⎨⎪⎪⎪⎪⎪⎩ Xt − k̂−1 k̂∑ t=1 Xt, if t = 1, . . . , k̂ Xt − (n − k̂)−1 n∑ t=k̂+1 Xt, if t = k̂ + 1, . . . ,n. (iv) DDB-JX: Juhl and Xiao (2009) recently proposed to use the residuals from nonparametric regression to calculate the long-run…”