Statistical function method, researched by Reeds and others, can deal efficiently with a kind of statistics. But an obvious deficiency is that statistical functions don't contain some statistics in common use such...Statistical function method, researched by Reeds and others, can deal efficiently with a kind of statistics. But an obvious deficiency is that statistical functions don't contain some statistics in common use such as U- statistics, kernel density estimates, etc., In this paper, generalized statististical function is proposed and its asymptotical theory is developed, which can remedy the above defect.展开更多
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.Th...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.展开更多
文摘Statistical function method, researched by Reeds and others, can deal efficiently with a kind of statistics. But an obvious deficiency is that statistical functions don't contain some statistics in common use such as U- statistics, kernel density estimates, etc., In this paper, generalized statististical function is proposed and its asymptotical theory is developed, which can remedy the above defect.
文摘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.
