Nonparametric multiple change-point estimators

Estimating a Changed Segment in a Sample

“…In the case where N n is non random, (11) reduces to N n (Q n − P n ) ≥ γ −1 n for n large enough (one can put γ −1 n = N n (Q n − P n )). If moreover P n = P and Q n = Q do not depend on n, this in turn, reduces to N n (Q − P ) ≥ c 0 with a constant c 0 > 0.…”

“…This is the most simple type of the multiple change models which have attracted big attention and are well studied in the literature, e.g. Yao [16] (estimates a number of jumps in the mean), Schechtman and Wolfe [14] (propose sequential algorithm for estimating the number and the location of change points), Lavielle and Moulines [9] (estimates unknown number of shifts in time series) Lavielle [8] (derives asymptotic results for location and the number of changed segments), Lee [11] (gives asymptotic results for the location of segments, following Dümbgen [6])) to name a few. We also refer to Brodsky and Darkhovsky [2] and Csörgő and Horváth [4] for state-of-the art of change point problems.…”

Automatic Identification of Change Points for the System Testing Process

“…A maximum likelihood based procedure is proposed in [8]. However, especially in the case of unknown distributions, the naive maximum likelihood scheme is likely to return a change at every point, unless restrictions are enforced on the number of change points or the minimum distance ¡ between them [12].…”

A computationally efficient nonparametric approach for changepoint detection

“…Within the sequential changepoint detection literature one can treat the problem as a single changepoint problem which resets every time a changepoint is detected (Ross and Adams 2012). Lee (1996) proposed a weighted empirical measure which is simple to use but has been shown to have unsatisfactory results. Under the multivariate setting Matteson and James (2014) and James and Matteson (2015) proposed methods, E-divisive and e-cp3o, based on clustering and probabilistic pruning respectively.…”