1. What have the authors contributed in "Nonparametric simultaneous testing for structural breaks" ?
In this paper the authors consider a regression model with errors that are martingale differences.. The aim is to study the appearance of structural breaks in both the mean and the variance functions, assuming that such breaks may occur simultaneously in both the functions.
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2. What future works have the authors mentioned in the paper "Nonparametric simultaneous testing for structural breaks" ?
Further research is needed here for identifying the most appropriate test statistics.. Ac ce pt ed m an us cr ip t Throughout this paper, the authors will simply use f ( x1, · · ·, xl ) to denote the joint density function of ( X1+s1,..., X1+sl ) for simplicity of notation.. For the given 1 < ζ < 2 and T sufficiently large, the authors can show that M ( 1+δ1 ) T11 = E |aikajk|ζ = ( 1 + o ( 1 ) ) E |bijk|ζ = T−2ζ ∫ ∫ ∫ |π ( u ) π ( v ) |ζ ∣∣∣∣L1 ( u − wh ) ∣∣∣∣ζ ∣∣∣∣L1 ( v − wh ) ∣∣∣∣ζ f ( u, v, w ) dudvdw = T−2ζh2d1 ∫ ∫ ∫ |π ( z + xh ) π ( z + yh ) |ζ |L1 ( x ) L1 ( y ) |ζf ( z + xh, z + yh, z ) dxdydz = CpT−2ζh2d1 ( 1 + o ( 1 ) ) ( A. 9 ) using Assumptions A. 2–A. 4, where Cp is a constant and f ( u, v, w ) is the joint density function of ( X1, X1+s1, X1+s2 ).
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3. what is the second method to generate et?
The second method is to use a bootstrap resampling procedure to generate {e∗t} (see Hjellvik, Yao and Tjøstheim 1998; Franke, Kreiss and Mammen 2002 for example).
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4. What is the way to deal with this problem?
One way to deal (partially) with this problem is to construct an adaptive version of a test by taking the maximum of the test over a range of bandwidth values.
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