STRONG CONSISTENT ESTIMATES OF TWO KINDS OF JUMP REGRESSIVE FUNCTION

This paper will research the estimate problem of two kinds of jump regressive function, which number of jumps is known, the jump locations are unknown and the jump magnitudes are known or unknown. The author puts forwards an idea of difference kernel estimate and demonstrates that it is a.s. and L² consistent under some mild conditions. This estimate can be used in the case when there are many jumps. It has the character of direct form, good properties and flexibility in comparison with other estimate methods.