Inference about the Change-Point in a Sequence of Random Variables: A Selection Approach

By T. Liang, S. Panchapakesan. 1988

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Differentially Private Change-Point Detection (2018, background): “The existing change-point literature works primarily in the asymptotic setting when k ∗ n /n → r for some r ∈ (0 , 1) as n → ∞ (see, e.g., [Hin70, Car88]).”
The Changepoint Model for Statistical Process Control (2003, background): “Though maximum likelihood, these estimators are somewhat biased (see Hinkley (1970, 1971) for a discussion).”
Confidence Sets for the Date of a Single Break in Linear Time Series Regressions (2004, background): “The literature on estimation and construction of confidence sets for break dates back to Hinkley (1970), Hawkins (1977), Worsley (1979), Worsley (1986), Bhattacharya (1987) and others–see the reviews by Zacks (1983), Stock (1994) and Bhattacharya (1995) for additional discussion and references.”
Detecting gradual changes in locally stationary processes (2013, methodology): “For example, several authors investigate broken line regression models with independent normally distributed errors [see for example Hinkley (1970) or Siegmund and Zhang (1994)] and the performance of control charts under a gradual change in the mean [see Bissell (1984b,a) or Gan (1991, 1992) among ”
Consistencies and rates of convergence of jump-penalized least squares estimators (2009, unknown): “The case when the regression function is a step function has been studied ﬁrst by Hinkley (1970) and later by Yao (1988) and Yao and Au (1989).”
Biomanipulation as a restoration tool to combat eutrophication : recent advances and future challenges (2012, background): “Change point analysis (Hinkley, 1970) identified a shift (p 0.01) in phytoplankton biomass trends in July 1993, immediately after the fish biomanipulation (Fig.”
A review of change point detection methods (2018, background): “First introduced in [68] and later in [134, 135], it was then studied under more general assumptions [24–26].”
Dealing with Structural Breaks (2005, background): “An important early treatment of this result for a sequence of i.i.d. random variables is Hinkley (1970).”
Multiple breaks detection in general causal time series using penalized quasi-likelihood (2012, result): “The first important result in this topic was obtained by Page [20] in 1955 and real advances have been done during the seventies, notably with the results of Hinkley (see for instance [12]) and the break detection became a distinct and important area of research in statistic (see the book of Bassevi”
Exact post-selection inference for the generalized lasso path (2018, background): “Hinkley [17], Worsley [42], Bai [2] are some examples, and Jandhyala et al. [20], Horvath and Rice [19] provide nice surveys and extensions.”
Nonparametric estimation of structural change points in volatility models for time series (2005, background): “2 There is a well-developed theory under maximum-likelihood estimation (MLE) for independent and identically distributed observations up to a parametric shift (see Hinkley, 1970; and Bhattacharya, 1987).”
Inference for single and multiple change‐points in time series (2013, methodology): “Even though Hinkley (1970, 1972) pursued the study of asymptotic distribution of the change-point MLE, it is still largely intractable under the classical abrupt changemodelling (Borovkov, 1999; Jandhyala and Fotopoulos, 1999, 2001; Fotopoulos et al., 2010), whereas it ismuchmore tractable under…”