Wavelet Analysis of Change Points in Nonparametric Hazard Rate Models Under Random Censorship

In this article, we consider detection and estimation of change points in nonparametric hazard rate models. Wavelet methods are utilized to develop a testing procedure for change points detection. The asymptotic properties of the test statistic are explored. When there exist change points in hazard function, we also propose estimators for the number, the locations, and the jump sizes of the change points. The asymptotic properties of these estimators are systematically derived. Some simulation examples are conducted to assess the finite sample performance of the proposed approach and to make comparisons with some existing methods. A real data analysis is provided to illustrate the new approach.     

A Bayesian model for multiple change point to extremes,with application to environmental and financial data

Abrupt changes often occur for environmental and financial time series. Most often, these changes are due to human intervention. Change point analysis is a statistical tool used to analyze sudden changes in observations along the time series. In this paper, we propose a Bayesian model for extreme values for environmental and economic datasets that present a typical change point behavior. The model proposed in this paper addresses the situation in which more than one change point can occur in a time series. By analyzing maxima, the distribution of each regime is a generalized extreme value distribution. In this model, the change points are unknown and considered parameters to be estimated. Simulations of extremes with two change points showed that the proposed algorithm can recover the true values of the parameters, in addition to detecting the true change points in different configurations. Also, the number of change points was a problem to be considered, and the Bayesian estimation can correctly identify the correct number of change points for each application. Environmental and financial data were analyzed and results showed the importance of considering the change point in the data and revealed that this change of regime brought about an increase in the return levels, increasing the number of floods in cities around the rivers. Stock market levels showed the necessity of a model with three different regimes.     

Stochastic approximation Monte Carlo EM for change-point analysis

In the expectation–maximization (EM) algorithm for maximum likelihood estimation from incomplete data, Markov chain Monte Carlo (MCMC) methods have been used in change-point inference for a long time when the expectation step is intractable. However, the conventional MCMC algorithms tend to get trapped in local mode in simulating from the posterior distribution of change points. To overcome this problem, in this paper we propose a stochastic approximation Monte Carlo version of EM (SAMCEM), which is a combination of adaptive Markov chain Monte Carlo and EM utilizing a maximum likelihood method. SAMCEM is compared with the stochastic approximation version of EM and reversible jump Markov chain Monte Carlo version of EM on simulated and real datasets. The numerical results indicate that SAMCEM can outperform among the three methods by producing much more accurate parameter estimates and the ability to achieve change-point positions and estimates simultaneously.     

Subgroup Analysis with Time‐to‐Event Data Under a Logistic‐Cox Mixture Model

Subgroup detection has received increasing attention recently in different fields such as clinical trials, public management and market segmentation analysis. In these fields, people often face time‐to‐event data, which are commonly subject to right censoring. This paper proposes a semiparametric Logistic‐Cox mixture model for subgroup analysis when the interested outcome is event time with right censoring. The proposed method mainly consists of a likelihood ratio‐based testing procedure for testing the existence of subgroups. The expectation–maximization iteration is applied to improve the testing power, and a model‐based bootstrap approach is developed to implement the testing procedure. When there exist subgroups, one can also use the proposed model to estimate the subgroup effect and construct predictive scores for the subgroup membership. The large sample properties of the proposed method are studied. The finite sample performance of the proposed method is assessed by simulation studies. A real data example is also provided for illustration.     

The performance of diagnostic-robust generalized potentials for the identification of multiple high leverage points in linear regression

Leverage values are being used in regression diagnostics as measures of influential observations in the $X$-space. Detection of high leverage values is crucial because of their responsibility for misleading conclusion about the fitting of a regression model, causing multicollinearity problems, masking and/or swamping of outliers, etc. Much work has been done on the identification of single high leverage points and it is generally believed that the problem of detection of a single high leverage point has been largely resolved. But there is no general agreement among the statisticians about the detection of multiple high leverage points. When a group of high leverage points is present in a data set, mainly because of the masking and/or swamping effects the commonly used diagnostic methods fail to identify them correctly. On the other hand, the robust alternative methods can identify the high leverage points correctly but they have a tendency to identify too many low leverage points to be points of high leverages which is not also desired. An attempt has been made to make a compromise between these two approaches. We propose an adaptive method where the suspected high leverage points are identified by robust methods and then the low leverage points (if any) are put back into the estimation data set after diagnostic checking. The usefulness of our newly proposed method for the detection of multiple high leverage points is studied by some well-known data sets and Monte Carlo simulations.     

航班动态定价机制下的机票价格序列变点估计

文章旨在研究受航空业动态定价机制影响下的机票价格序列变点估计模型,文中分析了机票价格u8序列数据的结构特点,提出了可用于高噪声数据环境下、阶梯状、带明显多变点的多阶段序列变点估计框架,该框架中级联组合了DBSCAN算法、EM-高斯混合模型聚类、凝聚层次聚类算法和基于乘积划分模型的变点估计方法等多种成熟的数据分析方法,通过对“北京-昆明”航线航班的实证分析,验证了数据分析框架的有效性和普遍适用性。     

Estimation of parameterized spatio-temporal dynamic models

Spatio-temporal processes are often high-dimensional, exhibiting complicated variability across space and time. Traditional state-space model approaches to such processes in the presence of uncertain data have been shown to be useful. However, estimation of state-space models in this context is often problematic since parameter vectors and matrices are of high dimension and can have complicated dependence structures. We propose a spatio-temporal dynamic model formulation with parameter matrices restricted based on prior scientific knowledge and/or common spatial models. Estimation is carried out via the expectation–maximization (EM) algorithm or general EM algorithm. Several parameterization strategies are proposed and analytical or computational closed form EM update equations are derived for each. We apply the methodology to a model based on an advection–diffusion partial differential equation in a simulation study and also to a dimension-reduced model for a Palmer Drought Severity Index (PDSI) data set.     

Reliability analysis of masked data in adaptive step-stress partially accelerated lifetime tests with progressive removal

By combining the progressive hybrid censoring with the step-stress partially accelerated lifetime test, we propose an adaptive step-stress partially accelerated lifetime test, which allows random changing of the number of step-stress levels according to the pre-fixed censoring number and time points. Thus, the time expenditure and economic cost of the test will be reduced greatly. Based on the Lindley-distributed tampered failure rate (TFR) model with masked system lifetime data, the BFGS method is introduced in the expectation maximization (EM) algorithm to obtain the maximum likelihood estimation (MLE), which overcomes the difficulties of the vague maximization procedure in the M-step. Asymptotic confidence intervals of components' distribution parameters are also investigated according to the missing information principle. As comparison, the Bayesian estimation and the highest probability density (HPD) credible intervals are obtained by using adaptive rejection sampling. Furthermore, the reliability of the system and components are estimated at a specified time under usual and severe operating conditions. Finally, a numerical simulation example is presented to illustrate the performance of our proposed method.     

Detection of structurally homogeneous subsets in graphs

The analysis of complex networks is a rapidly growing topic with many applications in different domains. The analysis of large graphs is often made via unsupervised classification of vertices of the graph. Community detection is the main way to divide a large graph into smaller ones that can be studied separately. However another definition of a cluster is possible, which is based on the structural distance between vertices. This definition includes the case of community clusters but is more general in the sense that two vertices may be in the same group even if they are not connected. Methods for detecting communities in undirected graphs have been recently reviewed by Fortunato. In this paper we expand Fortunato’s work and make a review of methods and algorithms for detecting essentially structurally homogeneous subsets of vertices in binary or weighted and directed and undirected graphs.     

Bayesian inference of multiple structural change models with asymmetric GARCH errors

Structural change in any time series is practically unavoidable, and thus correctly detecting breakpoints plays a pivotal role in statistical modelling. This research considers segmented autoregressive models with exogenous variables and asymmetric GARCH errors, GJR-GARCH and exponential-GARCH specifications, which utilize the leverage phenomenon to demonstrate asymmetry in response to positive and negative shocks. The proposed models incorporate skew Student-t distribution and prove the advantages of the fat-tailed skew Student-t distribution versus other distributions when structural changes appear in financial time series. We employ Bayesian Markov Chain Monte Carlo methods in order to make inferences about the locations of structural change points and model parameters and utilize deviance information criterion to determine the optimal number of breakpoints via a sequential approach. Our models can accurately detect the number and locations of structural change points in simulation studies. For real data analysis, we examine the impacts of daily gold returns and VIX on S&P 500 returns during 2007–2019. The proposed methods are able to integrate structural changes through the model parameters and to capture the variability of a financial market more efficiently.

     

A Kernel Smooth Approach for Joint Modeling of Accelerated Failure Time and Longitudinal Data

Joint likelihood approaches have been widely used to handle survival data with time-dependent covariates. In construction of the joint likelihood function for the accelerated failure time (AFT) model, the unspecified baseline hazard function is assumed to be a piecewise constant function in the literature. However, there are usually no close form formulas for the regression parameters, which require numerical methods in the EM iterations. The nonsmooth step function assumption leads to very spiky likelihood function which is very hard to find the globe maximum. Besides, due to nonsmoothness of the likelihood function, direct search methods are conducted for the maximization which are very inefficient and time consuming. To overcome the two disadvantages, we propose a kernel smooth pseudo-likelihood function to replace the nonsmooth step function assumption. The performance of the proposed method is evaluated by simulation studies. A case study of reproductive egg-laying data is provided to demonstrate the usefulness of the new approach.     

Nonparametric change point detection for periodic time series

We consider detection of multiple changes in the distribution of periodic and autocorrelated data with known period. To account for periodicity we transform the sequence of vector observations by arranging them in matrices and thereby producing a sequence of independently and identically distributed matrix observations. We propose methods of testing the equality of matrix distributions and present methods that can be applied to matrix observations using the E-divisive algorithm. We show that periodicity and autocorrelation degrade existing change detection methods because they blur the changes that these procedures aim to discover. Methods that ignore the periodicity have low power to detect changes in the mean and the variance of periodic time series when the periodic effects overwhelm the true changes, while the proposed methods detect such changes with high power. We illustrate the proposed methods by detecting changes in the water quality of Lake Kasumigaura in Japan. The Canadian Journal of Statistics 48: 518–534; 2020 © 2020 Statistical Society of Canada     

BAYESIAN DETECTION AND ANALYSIS OF CHANGING TRANSITION MATRICES OF STATIONARY MARKOV CHAINS

This paper considers the detection of abrupt changes in the transition matrix of a Markov chain from a Bayesian viewpoint. It derives Bayes factors and posterior probabilities for unknown numbers of change‐points, as well as the positions of the change‐points, assuming non‐informative but proper priors on the parameters and fixed upper bound. The Markov chain Monte Carlo approach proposed by Chib in 1998 for estimating multiple change‐points models is adapted for the Markov chain model. It is especially useful when there are many possible change‐points. The method can be applied in a wide variety of disciplines and is particularly relevant in the social and behavioural sciences, for analysing the effects of events on the attitudes of people.     

Nonparametric estimation of the sojourn time distributions for a multipath model

Summary. We use a multipath (multistate) model to describe data with multiple end points. Statistical inference based on the intermediate end point is challenging because of the problems of nonidentifiability and dependent censoring. We study nonparametric estimation for the path probability and the sojourn time distributions between the states. The methodology proposed can be applied to analyse cure models which account for the competing risk of death. Asymptotic properties of the estimators proposed are derived. Simulation shows that the methods proposed have good finite sample performance. The methodology is applied to two data sets.     

Functional and dynamic magnetic resonance imaging using vector adaptive weights smoothing

We consider the problem of statistical inference for functional and dynamic magnetic resonance imaging (MRI). A new approach is proposed which extends the adaptive weights smoothing procedure of Polzehl and Spokoiny that was originally designed for image denoising. We demonstrate how the adaptive weights smoothing method can be applied to time series of images, which typically occur in functional and dynamic MRI. It is shown how signal detection in functional MRI and the analysis of dynamic MRI can benefit from spatially adaptive smoothing. The performance of the procedure is illustrated by using real and simulated data.     

Rapid penalized likelihood-based outlier detection via heteroskedasticity test

Outlier detection is fundamental to statistical modelling. When there are multiple outliers, many traditional approaches in use are stepwise detection procedures, which can be computationally expensive and ignore stochastic error in the outlier detection process. Outlier detection can be performed by a heteroskedasticity test. In this article, a rapid outlier detection method via multiple heteroskedasticity test based on penalized likelihood approaches is proposed to handle these kinds of problems. The proposed method detects the heteroskedasticity of all data only by one step and estimate coefficients simultaneously. The proposed approach is distinguished from others in that a rapid modelling approach uses a weighted least squares formulation coupled with nonconvex sparsity-including penalization. Furthermore, the proposed approach does not need to construct test statistics and calculate their distributions. A new algorithm is proposed for optimizing penalized likelihood functions. Favourable theoretical properties of the proposed approach are obtained. Our simulation studies and real data analysis show that the newly proposed methods compare favourably with other traditional outlier detection techniques.     

Sufficient Reduction in Multivariate Surveillance

The relation between change points in multivariate surveillance is important but seldom considered. The sufficiency principle is here used to clarify the structure of some problems, to find efficient methods, and to determine appropriate evaluation metrics. We study processes where the changes occur simultaneously or with known time lags. The surveillance of spatial data is one example where known time lags can be of interest. A general version of a theorem for the sufficient reduction of processes that change with known time lags is given. A simulation study illustrates the benefits or the methods based on the sufficient statistics.     

Maximum Likelihood Inference for Multivariate Frailty Models Using an Automated Monte Carlo EM Algorithm

We present a maximum likelihood estimation procedure for the multivariate frailty model. The estimation is based on a Monte Carlo EM algorithm. The expectation step is approximated by averaging over random samples drawn from the posterior distribution of the frailties using rejection sampling. The maximization step reduces to a standard partial likelihood maximization. We also propose a simple rule based on the relative change in the parameter estimates to decide on sample size in each iteration and a stopping time for the algorithm. An important new concept is acquiring absolute convergence of the algorithm through sample size determination and an efficient sampling technique. The method is illustrated using a rat carcinogenesis dataset and data on vase lifetimes of cut roses. The estimation results are compared with approximate inference based on penalized partial likelihood using these two examples. Unlike the penalized partial likelihood estimation, the proposed full maximum likelihood estimation method accounts for all the uncertainty while estimating standard errors for the parameters.     

A comparison of estimators for regression models with change points

We consider two problems concerning locating change points in a linear regression model. One involves jump discontinuities (change-point) in a regression model and the other involves regression lines connected at unknown points. We compare four methods for estimating single or multiple change points in a regression model, when both the error variance and regression coefficients change simultaneously at the unknown point(s): Bayesian, Julious, grid search, and the segmented methods. The proposed methods are evaluated via a simulation study and compared via some standard measures of estimation bias and precision. Finally, the methods are illustrated and compared using three real data sets. The simulation and empirical results overall favor both the segmented and Bayesian methods of estimation, which simultaneously estimate the change point and the other model parameters, though only the Bayesian method is able to handle both continuous and dis-continuous change point problems successfully. If it is known that regression lines are continuous then the segmented method ranked first among methods.     

A refined parameter estimating approach for HIV dynamic model

HIV dynamic models, a set of ordinary differential equations (ODEs), have provided new understanding of the pathogenesis of HIV infection and the treatment effects of antiviral therapies. However, to estimate parameters for ODEs is very challenging due to the complexity of this nonlinear system. In this article, we propose a comprehensive procedure to deal with this issue. In the proposed procedure, a series of cutting-edge statistical methods and techniques are employed, including nonparametric mixed-effects smoothing-based methods for ODE models and stochastic approximation expectation–maximization (EM) approach for mixed-effects ODE models. A simulation study is performed to validate the proposed approach. An application example from a real HIV clinical trial study is used to illustrate the usefulness of the proposed method.