Several Problems On Multiple Change Points Analysis Of Complex Data

Change-point models are widely used in various fields for detecting lack of homo-geneity in a sequence of observations,including seismology,financial,and genetics.The homogeneity means that regression coefficients are grouped and have exactly the same value in each group.Modern statistical applications are faced with complex data of increasing dimension.Detecting the homogeneity of such high dimensional sequences is a challenging but important problem.Compared to single change-point detection,multiple change-points detection is much more challenging.In this paper,multiple change-points detection for complex data is discussed.We focus on the homogeneity detection of regression coefficients under different model settings.We proposed an ef-ficient method for multiple change-points detection by combining the high-dimensional model selection methods,and verified the statistical property of the change point detec-tion.First,this paper considers a general class of high-dimensional linear models,in-cluding balanced panel data dynamic linear models and spatio-temporal linear models.A procedure for simultaneously detecting multiple change-points is developed rigor-ously via the construction of adaptive group Lasso penalty.Consistency of the multiple change-point estimation is established under mild conditions even when the true num-ber of change-points diverges with the sample size,i.e.,the number of time points.The adaptive group Lasso can be substituted by the group Lasso,and other non-convex group selection algorithms including group SCAD,and group MCP,etc.The simula-tion studies show that our procedure is fast and accurate.The wide applicability of the proposed methodology is demonstrated via three completely different but representative empirical examples.Second,the change point detection based on the high-dimensional penalty method depends on the selection of the tuning parameters.This is because only a certain range of the tuning parameter values leads to selection consistency,namely,the oracle esti-mator.Therefore,we proposed an information criteria for tuning parameter selection in adaptive group Lasso regression.We extend the results of the extended regularized information criterion(ERIC)to group selection methods involving concave penalties and then investigate the selection consistency with diverging variables in each group.Moreover,we show that the ERIC-type selector enables one to identify the true model consistently,and the resulting estimator possesses the oracle property,even when the number of group is much larger than the sample size.Numerical studies show that ERIC-type can significantly outperform BIC and cross-validation(CV)in selecting the true grouped variables.Finally,we explore homogeneity of regression coefficients incorporating prior constraint information.A general pairwise fusion approach is proposed to deal with the sparsity and homogeneity detection when combining prior convex constraints.We developed an alternating direction method of multipliers algorithm to obtain the esti-mators and demonstrate its convergence.Our proposed method is further illustrated by simulation studies and analysis of an Ozone dataset.