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基于加权残差的比例风险检验与诊断AI 解读

SUMMARY Nonproportional hazards can often be expressed by extending the Cox model to include time varying coefficients; e.g., for a single covariate, the hazard function for subject i is modelled as exp { fl(t)Zi(t)}. A common example is a treatment effect that decreases with time. We show that the function /3(t) can be directly visualized by smoothing an appropriate residual plot. Also, many tests of proportional hazards, including those of Cox (1972), Gill & Schumacher…

离散时间生存数据的动态建模与惩罚似然估计AI 解读

This paper describes a dynamic or state-space approach for analyzing discrete time or grouped survival data. Simultaneous estimation of baseline hazard functions and of time-varying covariate effects is based on maximization of posterior densities or, equivalently, a penalized likelihood, leading to Kalman-type smoothing algorithms. Data-driven choice of unknown smoothing parameters is possible via an EM-type procedure. The methods are illustrated by applications to real…

时间序列的稳健似然计算AI 解读

SUMMARY We propose a computationally efficient method for calculating the likelihoods of a time series under many submodels, each of which assumes a patch of outliers or level shifts. We assume a state space representation of the time series model with a Bayesian-type treatment of anomalies. The calculations form the basis for an efficient and robust estimation procedure. The method is also applicable to linear regression with correlated errors and is illustrated with two…

具有误报概率界的动态抽样正态均值变化检测AI 解读

We show that when dynamic sampling is feasible, there exist surveillance schemes for which the probability of a false alarm is bounded and which have a bounded expected delay when detecting a (true) change. In the case of detecting a change of a normal mean, we probe optimality and suggest procedures. These procedures compare favorably to those having a fixed sampling rate which have been developed for an expectation constraint on the average run length until a false alarm.

自回归时间序列均值与方差变化的贝叶斯推断及预测AI 解读

This article is concerned with statistical inference and prediction of mean and variance changes in an autoregressive time series. We first extend the analysis of random mean-shift models to random variance-shift models. We then consider a method for predicting when a shift is about to occur. This involves appending to the autoregressive model a probit model for the probability that a shift occurs given a chosen set of explanatory variables. The basic computational tool we…

简单线性回归变化点似然比检验的稳健性AI 解读

This article examines the robustness of the likelihood ratio tests for a change point in simple linear regression. We first summarize the normal theory of Kim and Siegmund, who have considered the likelihood ratio tests for no change in the regression coefficients versus the alternatives with a change in the intercept alone and with a change in the intercept and slope. We then discuss the robustness of these tests. Using the convergence theory of stochastic processes, we…

简单线性回归变化点似然比检验的稳健性AI 解读

This article examines the robustness of the likelihood ratio tests for a change point in simple linear regression. We first summarize the normal theory of Kim and Siegmund, who have considered the likelihood ratio tests for no change in the regression coefficients versus the alternatives with a change in the intercept alone and with a change in the intercept and slope. We then discuss the robustness of these tests. Using the convergence theory of stochastic processes, we…

结构突变与异常值下时变参数及多过程混合模型的蒙特卡洛比较AI 解读

This Monte Carlo study compares the performance of a recently proposed multiprocess mixture model and a more traditional random walk time-varying parameter model in the face of structural shifts and outliers. The mixture model performs well and the latter model performs poorly. This finding is of general interest since investigators often adopt random-walk time-varying parameter models to accommodate potential regime shifts in regression relationships. The findings suggest…

未知变化点下参数不稳定与结构变化的检验AI 解读

This paper considers tests for parameter instability and structural change with unknown change point. The results apply to a wide class of parametric models that are suitable for estimation by generalized method of moments procedures. The asymptotic distributions of the test statistics considered here are nonstandard because the change point parameter only appears under the alternative hypothesis and not under the null. The tests considered here are shown to have nontrivial…

利用后验赔率检测多个方差变点AI 解读

This article uses a Bayesian procedure based on obtaining posterior odds to assess the evidence about the existence of multiple changes of variance in a time series. The approach is developed for sequences of independent observations. An extension to consider autoregressive models is also discussed. The information on the data about the location of the change points and the magnitude of the variances at the different pieces of the series is summarized through posterior…

含马尔可夫转换异方差的不可观测成分时间序列模型：状态变化与通胀不确定性AI 解读

In this article, I first extend the standard unobserved-component time series model to include Hamilton's Markov-switching heteroscedasticity. This will provide an alternative to the unobserved-component model with autoregressive conditional heteroscedasticity, as developed by Harvey, Ruiz, and Sentana and by Evans and Wachtel. I then apply a generalized version of the model to investigate the link between inflation and its uncertainty (U.S. data, gross national product…

均值偏移检测中 EWMA、CUSUM 与 Shiryayev–Roberts 方法的比较AI 解读

Pollak and Siegmund compared the Shiryayev-Roberts procedure with the CUSUM procedure for detecting a change in the drift of a Brownian motion based on the conditional average delay time. In this paper, the exponentially weighted moving average (EWMA) procedure proposed by Roberts is compared with the Shiryayev-Roberts and CUSUM procedures. The comparison is based on the stationary average delay time as advocated by Shiryayev. The optimal design for the EWMA procedure and…

未知变点之前的参数估计AI 解读

Consider the problem of estimating $\mu$, based on the observation of $Y_0, Y_1, \ldots, Y_n$, where it is assumed only that $Y_0, Y_1, \ldots, Y_\kappa \operatorname{iid} N(\mu, \sigma^2)$ for some unknown $\kappa$. Unlike the traditional change-point problem, the focus here is not on estimating $\kappa$, which is now a nuisance parameter. When it is known that $\kappa = k$, the sample mean $\bar{Y}_k = \sum^k_0Y_i/(k + 1)$, provides, in addition to wonderful efficiency…

检验正态观测参数变化的最大似然方法AI 解读

We compute the asymptotic distribution of the maximum likelihood ratio test when we want to check whether the parameters of normal observations have changed at an unknown point. The proof is based on the limit distribution of the largest deviation between a $d$-dimensional Ornstein-Uhlenbeck process and the origin.

多元时间序列均值变化预测：企业失败预测应用AI 解读

A firm in the early stages of financial distress exhibits characteristics different from those of healthy firms. As the economic condition of a firm worsens, its financial characteristics shift toward those of failed firms. Practitioners in the financial sector have long been interested in the early detection of a firm's slide toward insolvency. Several models have been developed with this purpose in mind, but these older models are static in nature. Therefore, a need exists…

序列相关对未知时点参数变化检验的影响AI 解读

It is shown that serial correlation can produce striking effects in distributions of change-point statistics. Failure to account for these effects is shown to invalidate change-point tests, either through increases in the type 1 error rates if low frequency spectral mass predominates in the spectrum of the noise process, or through diminution of the power of the tests when high frequency mass predominates. These effects are characterized by the expression ${2\pi f(0)/\int^\pi_-\pi f(\lambda)d\lambda}$…

变点问题的贝叶斯分析AI 解读

A sequence of observations undergoes sudden changes at unknown times. We model the process by supposing that there is an underlying sequence of parameters partitioned into contiguous blocks of equal parameter values; the beginning of each block is said to be a change point. Observations are then assumed to be independent in different blocks given the sequence of parameters. In a Bayesian analysis it is necessary to give probability distributions to both the change points and…

函数系数自回归模型AI 解读

In this article we propose a new class of models for nonlinear time series analysis, investigate properties of the proposed model, and suggest a modeling procedure for building such a model. The proposed modeling procedure makes use of ideas from both parametric and nonparametric statistics. A consistency result is given to support the procedure. For illustration we apply the proposed model and procedure to several data sets and show that the resulting models substantially…

暂时性均值变化备择下的变点检验AI 解读

The purpose of this paper is to discuss the tests to detect an epidemic alternative in the mean value of a sequence of independent normal variables. Various test statistics, such as the likelihood ratio, the score-like statistic, Levin & Kline's statistic, the semilikelihood ratio, and the recursive residual, are studied. The large deviation approximations to the significance levels and powers are developed by integrating approximations to conditional boundary crossing…

均值与方差发生马尔可夫状态切换的自回归时间序列：Gibbs 抽样贝叶斯推断AI 解读

The authors examine autoregressive time series models subject to regime switching. A Bayesian framework is develope d in which the unobserved.states, one for each time point, are treated as missing data and then analyzed using the Gibbs sampler. This approac h is straightforward because the conditional posterior distribution of the parameters given the states, and the conditional posterior distribution of the states given the parameters, are amenable to simulation. The…

时间序列水平突变的检测AI 解读

This article demonstrates the difficulty that traditional outlier detection methods, such as that of R. S. Tsay, have in identifying level shifts in time series. Initializing the outlier/level-shift search with an estimated autoregressive moving average model lowers the power of the level-shift detection statisti cs. Furthermore, the rule employed by these methods for distinguishing between level shifts and innovation outliers does not work well in t he presence of level…

英镑兑美元汇率高频模型中的新闻效应AI 解读

Abstract This paper uses an extremely high frequency data set on the dollar‐sterllng exchange rate to investigate the impact of news events on the very short‐term movements in exchange rates. The data set is a continuous record of the quoted price for the exchange rate on the Reuters screen. As such it records some 130,000 observations over an 8‐week period. The paper investigates the time‐series properties of the data using orthodox regression models, and then by making…

流行型备择下的变点检验AI 解读

The purpose of this paper is to discuss the tests to detect an epidemic alternative in the mean value of a sequence of independent normal variables. Various test statistics, such as the likelihood ratio, the score-like statistic, Levin & Kline's statistic, the semilikelihood ratio, and the recursive residual, are studied. The large deviation approximations to the significance levels and powers are developed by integrating approximations to conditional boundary crossing…

随机游走与变点备择下的回归系数恒定性检验AI 解读

The locally best invariant statistic to test for the constancy of regression coefficients under a random walk alternative is shown to be the same as a Bayesian-type statistic derived under a change-point alternative. Asymptotic theory for this and more general statistics is discussed.