| 1. |
- Bodnar, Rostyslav, et al.
(författare)
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Control charts for high-dimensional time series with estimated in-control parameters
- 2024
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Ingår i: Sequential Analysis. - 0747-4946 .- 1532-4176. ; 43:1, s. 103-129
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Tidskriftsartikel (refereegranskat)abstract
- In this article, we study the effect of misspecification caused by fitting the target process in the Phase I analysis of the monitoring procedure on the behavior of several types of multivariate exponentially weighted moving average (MEWMA) control charts in the high-dimensional setting. In particular, the classical MEWMA control charts, whose control statistics are based on the exact and asymptotic Mahalanobis distance, are considered together with the novel approaches where the Euclidean distance and the diagonalized Euclidean distance are employed in the construction of control statistics. The high-dimensional distributions of the control statistics are deduced at each time. These results are later used to assess the performance of the considered control charts under misspecification. Both theoretical and empirical findings lead to the conclusion that the control charts based on the Euclidean distance and the diagonalized Euclidean distance are robust to misspecification for moderate dimensions of the data-generating model, whereas they tend to overestimate the in-control average run lengths (ARLs) in the case of larger dimensions. On the other hand, the control schemes based on the Mahalanobis distance are considerably affected by the estimation of the parameters of the target process, and their application results in drastically smaller values of the ARLs, especially when the dimension of the data-generating model is large.
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| 2. |
- Christensen, Sören, 1982
(författare)
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An effective method for the explicit solution of sequential problems on the real line
- 2017
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Ingår i: Sequential Analysis. - : Informa UK Limited. - 0747-4946 .- 1532-4176. ; 36:1, s. 2-18
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Tidskriftsartikel (refereegranskat)abstract
- A general method for solving optimal stopping problems for continuous-time Markov processes on the real line is developed. The basic idea is to first study an auxiliary problem for the two-dimensional process consisting of the underlying Markov process and its running maximum. It turns out that this auxiliary problem is much easier to solve using standard methods such as the monotonicity of the problem, and an optimal strategy in the class of threshold times can be found. The optimality of the time carries over to original problem. This two-step procedure gives a unifying approach for solving problems from different fields such as mathematical finance and sequential analysis. © 2017 Taylor & Francis.
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| 3. |
- Christensen, Sören, 1982, et al.
(författare)
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An elementary approach to optimal stopping problems for AR(1) sequences
- 2011
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Ingår i: Sequential Analysis. - : Informa UK Limited. - 0747-4946 .- 1532-4176. ; 30:1, s. 79-93
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Tidskriftsartikel (refereegranskat)abstract
- Optimal stopping problems form a class of stochastic optimization problems that has a wide range of applications in sequential statistics and mathematical finance. Here we consider a general optimal stopping problem with discounting for autoregressive processes. Our strategy for a solution consists of two steps: First we give elementary conditions to ensure that an optimal stopping time is of threshold type. Then the resulting one-dimensional problem of finding the optimal threshold is to be solved explicitly. The second step is carried out for the case of exponentially distributed innovations. © Taylor & Francis Group, LLC.
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| 4. |
- Christensen, Sören, 1982
(författare)
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Discussion on "Sequential Estimation for Time Series Models" by T. N. Sriram and Ross Iaci
- 2014
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Ingår i: Sequential Analysis. - : Informa UK Limited. - 1532-4176 .- 0747-4946. ; 33:2, s. 158-160
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Tidskriftsartikel (refereegranskat)abstract
- Based on the excellent review and numerical study presented by Professor T. N. Sriram and Professor R. Iaci, another sequential problem for autoregressive processes is discussed. © 2014 Copyright Taylor & Francis Group, LLC.
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| 5. |
- Christensen, Sören, 1982, et al.
(författare)
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Optimal Multiple Stopping with Random Waiting Times
- 2013
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Ingår i: Sequential Analysis. - : Informa UK Limited. - 1532-4176 .- 0747-4946. ; 32:3, s. 297-318
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Tidskriftsartikel (refereegranskat)abstract
- In the standard models for optimal multiple stopping problems it is assumed that between two exercises there is always a time period of deterministic length δ, the so-called refraction period. This prevents the optimal exercise times from bunching up together on top of the optimal stopping time for the one-exercise case. In this article we generalize the standard model by considering random refraction times. We develop the theory and reduce the problem to a sequence of ordinary stopping problems, thus extending the results for deterministic times. This requires an extension of the underlying filtrations in general. Furthermore, we consider the Markovian case and treat an example explicitly. © 2013 Copyright Taylor and Francis Group, LLC.
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| 6. |
- Dyrssen, Hannah, et al.
(författare)
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Sequential testing of a Wiener process with costly observations
- 2018
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Ingår i: Sequential Analysis. - : TAYLOR & FRANCIS INC. - 0747-4946 .- 1532-4176. ; 37:1, s. 47-58
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Tidskriftsartikel (refereegranskat)abstract
- We consider the sequential testing of two simple hypotheses for the drift of a Brownian motion when each observation of the underlying process is associated with a positive cost. In this setting where continuous monitoring of the underlying process is not feasible, the question is not only whether to stop or to continue at a given observation time but also, if continuing, how to distribute the next observation time. Adopting a Bayesian methodology, we show that the value function can be characterized as the unique fixed point of an associated operator and that it can be constructed using an iterative scheme. Moreover, the optimal sequential distribution of observation times can be described in terms of the fixed point.
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| 7. |
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| 8. |
- Frisén, Marianne, 1943
(författare)
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Author's Response
- 2009
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Ingår i: Sequential Analysis. - : Informa UK Limited. - 0747-4946 .- 1532-4176. ; 28:3, s. 386-393
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Tidskriftsartikel (refereegranskat)abstract
- The discussants made very interesting contributions to deep theory as well as interesting applications. The many additional references broadened the subject. Evaluation measures had drawn much attention and different views were exposed. The discussants' contributions on multivariate surveillance, robustness, and other specific issues are also commented upon.
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| 9. |
- Frisén, Marianne, 1943
(författare)
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Discussion on “Quickest Detection Problems: Fifty Years Later” by Albert N. Shiryaev
- 2010
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Ingår i: Sequential Analysis: Design Methods and Applications. - : Informa UK Limited. - 0747-4946. ; 29:4, s. 394-397
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Tidskriftsartikel (refereegranskat)abstract
- The comprehensive review and discussion by Professor Shiryaev is inspiring. My remarks will be directed towards questions of optimality and evaluation in situations met in important applications. Bayesian inference and frequentistic inference are suitable for different applications. Complex cases, such as multivariate surveillance, deserve special attention.
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| 10. |
- Frisén, Marianne, 1943
(författare)
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Optimal Sequential Surveillance for Finance, Public Health, and Other Areas
- 2009
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Ingår i: Sequential Analysis. - : Informa UK Limited. - 0747-4946 .- 1532-4176. ; 28:3, s. 310-337
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Tidskriftsartikel (refereegranskat)abstract
- he aim of sequential surveillance is on-line detection of an important change in an underlying process as soon as possible after the change has occurred. Statistical methods suitable for surveillance differ from hypothesis testing methods. In addition, the criteria for optimality differ from those used in hypothesis testing. The need for sequential surveillance in industry, economics, and medicine, and for environmental purposes is described. Even though the methods have been developed under different scientific cultures, inferential similarities can be identified. Applications contain complexities such as autocorrelations, complex distributions, complex types of changes, and spatial as well as other multivariate settings. Approaches to handling these complexities are discussed. Expressing methods for surveillance through likelihood functions makes it possible to link the methods to various optimality criteria. This approach also facilitates the choice of an optimal surveillance method for each specific application and provides some directions for improving earlier suggested methods.
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