ESTIMATION OF A KIND OF JUMP REGRESSION FUNCTION
摘要
Research on jump regression func(?)ons has not been adequate yet According to theinformation about the number of jumps,their positions and jump magnitudes,jump regressionfunctions can be classified into eight types.This paper deals especially with the secondjump regression function.First of all,a concept of trimmed spline estimate is proposed andwith it an L~2-consistent estimate of the smoothing part of the jump regression function isobtained.This along with the L~2-consistent estimate of jump magnitude constitutes an estimateof the second jump regression function.This paper discusses also the case that the jumppositions have some indeterminacy.A new criterion is suggested and its unique solutionderived.In the end,a few numerical results are given.