Estimation and Inference of Discontinuity in Density
Estimation and Inference of Discontinuity in Density
Estimation and Inference of Discontinuity in Density
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AMathematical AppendixHereafter “w.p.a.1”means “with probability approach<strong>in</strong>g one”. De…ne f = f (c),log f; lim = (a l ; b l ; b r ) 0 d log f (x); 0 =x"c dx^ = arg m<strong>in</strong> ` (a l; log ( 0 + e a l) ; b l ; b r ) ; = A l B l B r ;2Xi cg i () = g i (a l ; b l ; b r ) ; A i = (1 I i ) ; (1 I i )hZZK lj1 j 2= u j 1K j 2(u) du; K rj1 j 2= u j 1K j 2(u) du;ku
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