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CONSISTENT SELECTION OF THE NUMBER OF CHANGE-POINTS VIA SAMPLE-SPLITTING.

ABSTRACT: In multiple change-point analysis, one of the major challenges is to estimate the number of change-points. Most existing approaches attempt to minimize a Schwarz information criterion which balances a term quantifying model fit with a penalization term accounting for model complexity that increases with the number of change-points and limits overfitting. However, different penalization terms are required to adapt to different contexts of multiple change-point problems and the optimal penalization magnitude usually varies from the model and error distribution. We propose a data-driven selection criterion that is applicable to most kinds of popular change-point detection methods, including binary segmentation and optimal partitioning algorithms. The key idea is to select the number of change-points that minimizes the squared prediction error, which measures the fit of a specified model for a new sample. We develop a cross-validation estimation scheme based on an order-preserved sample-splitting strategy, and establish its asymptotic selection consistency under some mild conditions. Effectiveness of the proposed selection criterion is demonstrated on a variety of numerical experiments and real-data examples.

SUBMITTER: Zou C

PROVIDER: S-EPMC7397423 | biostudies-literature | 2020 Feb

REPOSITORIES: biostudies-literature

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CONSISTENT SELECTION OF THE NUMBER OF CHANGE-POINTS VIA SAMPLE-SPLITTING.

Zou Changliang C Wang Guanghui G Li Runze R

Annals of statistics 20200217 1

In multiple change-point analysis, one of the major challenges is to estimate the number of change-points. Most existing approaches attempt to minimize a Schwarz information criterion which balances a term quantifying model fit with a penalization term accounting for model complexity that increases with the number of change-points and limits overfitting. However, different penalization terms are required to adapt to different contexts of multiple change-point problems and the optimal penalizatio ...[more]

PMID: 32747841

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Project description:BackgroundThe multivariable fractional polynomial (MFP) approach combines variable selection using backward elimination with a function selection procedure (FSP) for fractional polynomial (FP) functions. It is a relatively simple approach which can be easily understood without advanced training in statistical modeling. For continuous variables, a closed test procedure is used to decide between no effect, linear, FP1, or FP2 functions. Influential points (IPs) and small sample sizes can both have a strong impact on a selected function and MFP model.MethodsWe used simulated data with six continuous and four categorical predictors to illustrate approaches which can help to identify IPs with an influence on function selection and the MFP model. Approaches use leave-one or two-out and two related techniques for a multivariable assessment. In eight subsamples, we also investigated the effects of sample size and model replicability, the latter by using three non-overlapping subsamples with the same sample size. For better illustration, a structured profile was used to provide an overview of all analyses conducted.ResultsThe results showed that one or more IPs can drive the functions and models selected. In addition, with a small sample size, MFP was not able to detect some non-linear functions and the selected model differed substantially from the true underlying model. However, when the sample size was relatively large and regression diagnostics were carefully conducted, MFP selected functions or models that were similar to the underlying true model.ConclusionsFor smaller sample size, IPs and low power are important reasons that the MFP approach may not be able to identify underlying functional relationships for continuous variables and selected models might differ substantially from the true model. However, for larger sample sizes, a carefully conducted MFP analysis is often a suitable way to select a multivariable regression model which includes continuous variables. In such a case, MFP can be the preferred approach to derive a multivariable descriptive model.

Dataset Information

CONSISTENT SELECTION OF THE NUMBER OF CHANGE-POINTS VIA SAMPLE-SPLITTING.

Publications

CONSISTENT SELECTION OF THE NUMBER OF CHANGE-POINTS VIA SAMPLE-SPLITTING.

Similar Datasets

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