Change Point Estimation with Independent Observations and Piece-Wise Continuous Variance Function

Grégoire and Hamrouni use locally linear smoothers to find jumps in the mean of a regression function under a set of weak assumptions. This paper extends this work to find jumps in the variance function of a mean zero series of independent observations. We transform this problem into the problem considered by Grégoire and Hamrouni by means of a log transform. We also demonstrate that a bootstrap technique proposed by Gijbels and Goderniaux is valid in this setting.