On Tests for Detecting Change in Mean

doi:10.1214/AOS/1176343001

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On Tests for Detecting Change in Mean

Journal Article•DOI•

On Tests for Detecting Change in Mean

01 Jan 1975-Annals of Statistics (Institute of Mathematical Statistics)-Vol. 3, Iss: 1, pp 98-108

TL;DR: In this article, the means of each variable in a sequence of independent random variables can be taken to be the same, against alternatives that a shift might have occurred after some point $r$.

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Abstract: Procedures are considered for testing whether the means of each variable in a sequence of independent random variables can be taken to be the same, against alternatives that a shift might have occurred after some point $r$. Bayesian test statistics as well as some statistics depending on estimates of $r$ are presented and their powers compared. Exact and asymptotic distribution functions are derived for some of the Bayesian statistics.

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Journal Article•DOI•

Circular binary segmentation for the analysis of array-based DNA copy number data.

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Adam B. Olshen¹, Ennapadam Venkatraman¹, Robert Lucito², Michael Wigler²•Institutions (2)

Memorial Sloan Kettering Cancer Center¹, Cold Spring Harbor Laboratory²

01 Oct 2004-Biostatistics

TL;DR: A modification ofbinary segmentation is developed, which is called circular binary segmentation, to translate noisy intensity measurements into regions of equal copy number in DNA sequence copy number.

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Abstract: DNA sequence copy number is the number of copies of DNA at a region of a genome. Cancer progression often involves alterations in DNA copy number. Newly developed microarray technologies enable simultaneous measurement of copy number at thousands of sites in a genome. We have developed a modification of binary segmentation, which we call circular binary segmentation, to translate noisy intensity measurements into regions of equal copy number. The method is evaluated by simulation and is demonstrated on cell line data with known copy number alterations and on a breast cancer cell line data set.

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2,269 citations

Cites background or methods from "On Tests for Detecting Change in Me..."

...Biostatistics (2004), 5, 4, pp. 557–572 doi: 10.1093/biostatistics/kxh008 Circular binary segmentation for the analysis of array-based DNA copy number data...
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...We propose a modification of binary segmentation (Sen and Srivastava, 1975) that we call circular binary segmentation (CBS) for this purpose....
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...…1), the likelihood ratio statistic for testing the null hypothesis that there is no change against the alternative that there is exactly one change at an unknown location i (Sen and Srivastava, 1975) is given by Z B = max1 i n |Zi |, where Zi = {1/ i + 1/(n − i)}−1/2{Si/ i − (Sn − Si )/(n − i)}....
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Journal Article•DOI•

Optimal Detection of Changepoints With a Linear Computational Cost

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Rebecca Killick¹, Paul Fearnhead¹, Idris A. Eckley¹•Institutions (1)

Lancaster University¹

17 Oct 2012-Journal of the American Statistical Association

TL;DR: This work considers the problem of detecting multiple changepoints in large data sets and introduces a new method for finding the minimum of such cost functions and hence the optimal number and location of changepoints that has a computational cost which is linear in the number of observations.

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Abstract: In this article, we consider the problem of detecting multiple changepoints in large datasets. Our focus is on applications where the number of changepoints will increase as we collect more data: for example, in genetics as we analyze larger regions of the genome, or in finance as we observe time series over longer periods. We consider the common approach of detecting changepoints through minimizing a cost function over possible numbers and locations of changepoints. This includes several established procedures for detecting changing points, such as penalized likelihood and minimum description length. We introduce a new method for finding the minimum of such cost functions and hence the optimal number and location of changepoints that has a computational cost, which, under mild conditions, is linear in the number of observations. This compares favorably with existing methods for the same problem whose computational cost can be quadratic or even cubic. In simulation studies, we show that our new method can...

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1,647 citations

Cites background from "On Tests for Detecting Change in Me..."

...Early applications include Scott and Knott (1974) and Sen and Srivastava (1975)....
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Journal Article•DOI•

changepoint: An R Package for Changepoint Analysis

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Rebecca Killick, Idris A. Eckley

25 Jun 2014-Journal of Statistical Software

TL;DR: The changepoint package has been developed to provide users with a choice of multiple changepoint search methods to use in conjunction with a given changepoint method and in particular provides an implementation of the recently proposed PELT algorithm.

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Abstract: One of the key challenges in changepoint analysis is the ability to detect multiple changes within a given time series or sequence. The changepoint package has been developed to provide users with a choice of multiple changepoint search methods to use in conjunction with a given changepoint method and in particular provides an implementation of the recently proposed PELT algorithm. This article describes the search methods which are implemented in the package as well as some of the available test statistics whilst highlighting their application with simulated and practical examples. Particular emphasis is placed on the PELT algorithm and how results differ from the binary segmentation approach.

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1,068 citations

Cites methods from "On Tests for Detecting Change in Me..."

...…changepoint search algorithms have been proposed to overcome this challenge, most notably the binary segmentation algorithm (Scott and Knott, 1974; Sen and Srivastava, 1975); the Segment Neighbourhood algorithm (Auger and Lawrence, 1989; Bai and Perron, 1998) and more recently the PELT algorithm…...
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...At the time of writing Binary Segmentation is arguably the most widely used multiple changepoint search method and originates from the work of Edwards and Cavalli-Sforza (1965), Scott and Knott (1974) and Sen and Srivastava (1975)....
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...Over the years several multiple changepoint search algorithms have been proposed to overcome this challenge, most notably the binary segmentation algorithm (Scott and Knott, 1974; Sen and Srivastava, 1975); the Segment Neighbourhood algorithm (Auger and Lawrence, 1989; Bai and Perron, 1998) and more recently the PELT algorithm (Killick et al....
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Journal Article•DOI•

Some methods for testing the homogeneity of rainfall records

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T.A. Buishand¹•Institutions (1)

Royal Netherlands Meteorological Institute¹

01 Aug 1982-Journal of Hydrology

TL;DR: In this paper, five tests on cumulative deviations from the mean are discussed, including the classical von Neumann ratio, and they are applied to the annual amounts of 30-yr. rainfall records in The Netherlands.

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968 citations

A Non-parametric Approach to the Change-point Problem

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A. N. PETTrrr

01 Jan 1979

TL;DR: In this paper, non-parametric techniques are introduced for the change-point problem and exact and approximate results are obtained for testing the null hypothesis of no change for zero-one observations, Binomial observations and continuous observations.

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Abstract: SUMMARY Non-parametric techniques are introduced for the change-point problem. Exact and approximate results are obtained for testing the null hypothesis of no change. The methods are illustrated by the analysis of three sets of data illustrating the techniques for zero-one observations, Binomial observations and continuous observations. Some comparisons are made with methods based on CUSUMS.

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768 citations

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References

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Journal Article•DOI•

Asymptotic Theory of Certain "Goodness of Fit" Criteria Based on Stochastic Processes

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01 Jan 1952-Annals of Mathematical Statistics

TL;DR: In this article, a general method for calculating the limiting distributions of these criteria is developed by reducing them to corresponding problems in stochastic processes, which in turn lead to more or less classical eigenvalue and boundary value problems for special classes of differential equations.

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Abstract: The statistical problem treated is that of testing the hypothesis that $n$ independent, identically distributed random variables have a specified continuous distribution function $F(x)$. If $F_n(x)$ is the empirical cumulative distribution function and $\psi(t)$ is some nonnegative weight function $(0 \leqq t \leqq 1)$, we consider $n^{\frac{1}{2}} \sup_{-\infty

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Book•

A course in probability theory

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TL;DR: This edition of A Course in Probability Theory includes an introduction to measure theory that expands the market, as this treatment is more consistent with current courses.

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Abstract: Since the publication of the first edition of this classic textbook over thirty years ago, tens of thousands of students have used A Course in Probability Theory. New in this edition is an introduction to measure theory that expands the market, as this treatment is more consistent with current courses. While there are several books on probability, Chung's book is considered a classic, original work in probability theory due to its elite level of sophistication.

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2,647 citations

Journal Article•DOI•

Goodness of Fit

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Hans Riedwyl¹•Institutions (1)

University of Bern¹

01 Jun 1967-Journal of the American Statistical Association

TL;DR: In this paper, the authors define a class of distribution free measures of goodness of fit; their exact distribution for small samples can be calculated by means of a computer and two of them have the same asymptotic distribution as the Kolmogorov-Smirnov statistic.

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Abstract: This Paper defines a class of distribution free measures of goodness of fit; their exact distribution for small samples can be calculated by means of a computer. Two of them have the same asymptotic distribution as the Kolmogorov-Smirnov statistic.

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999 citations