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对象值时间序列的变点检测AI 解读

This article is concerned with change point detection for object-valued data that reside in a metric space, which has attracted some recent interests in statistics and econometrics literature. The existing methods either focus on independent data or can only detect change in the Fréchet mean or variance. In this article, we propose a self-normalization (SN, hereafter) based statistic for detecting a shift in the marginal distribution of object-valued time series. Our test is…

通过自归一化检验函数型参数假设AI 解读

Testing simple or composite hypothesis on a functional parameter has attracted considerable attention in time series analysis. To accommodate for the unknown temporal dependence, classical nonparametric approaches such as block bootstrapping and subsampling all involve a bandwidth parameter, the choice of which can substantially affect the finite sample performance. The self normalization (SN) method is tuning parameter free when applied to the inference of a…

高维谱密度矩阵的统计推断AI 解读

The spectral density matrix is a fundamental object of interest in time series analysis, and it encodes both contemporary and dynamic linear relationships between component processes of the multivariate system. In this paper we develop novel inference procedures for the spectral density matrix in the high-dimensional setting. Specifically, we introduce a new global testing procedure to test the nullity of the cross-spectral density for a given set of frequencies and across…

不依赖维度区分的变点检测AI 解读

Change point testing for high-dimensional data has attracted a lot of attention in statistics, econometrics and machine learning owing to the emergence of high-dimensional data with structural breaks from many fields. In practice, when the dimension is less than the sample size but is not small, it is often unclear whether a method that is tailored to high-dimensional data or simply a classical method that is developed and justified for low-dimensional data is preferred. In…

对象值时间序列的序列独立性检验AI 解读

Summary We propose a novel method for testing serial independence of object-valued time series in metric spaces, which are more general than Euclidean or Hilbert spaces. The proposed method is fully nonparametric, free of tuning parameters and can capture all nonlinear pairwise dependence. The key concept used in this paper is the distance covariance in metric spaces, which is extended to the autodistance covariance for object-valued time series. Furthermore, we propose a…

重新审视免带宽推断：样本分割方法AI 解读

Abstract The bandwidth-free tests for a multi-dimensional parameter have attracted considerable attention in econometrics and statistics literature. These tests can be conveniently implemented due to their tuning-parameter free nature and possess more accurate size as compared to the traditional heteroskedasticity and autocorrelation consistent-based approaches. However, when sample size is small/medium, these bandwidth-free tests exhibit large size distortion when both the…

高维鞅差假设检验AI 解读

In this paper, we consider testing the martingale difference hypothesis for high-dimensional time series. Our test is built on the sum of squares of the element-wise max-norm of the proposed matrix-valued nonlinear dependence measure at different lags. To conduct the inference, we approximate the null distribution of our test statistic by Gaussian approximation and provide a simulation-based approach to generate critical values. The asymptotic behavior of the test statistic…

高维空间数据的高斯逼近与空间相依野生自助法AI 解读

In this article, we establish a high-dimensional CLT for the sample mean of p-dimensional spatial data observed over irregularly spaced sampling sites in Rd, allowing the dimension p to be much larger than the sample size n. We adopt a stochastic sampling scheme that can generate irregularly spaced sampling sites in a flexible manner and include both pure increasing domain and mixed increasing domain frameworks. To facilitate statistical inference, we develop the spatially…

COVID-19 感染曲线的时间序列分析：变点视角AI 解读

In this paper, we model the trajectory of the cumulative confirmed cases and deaths of COVID-19 (in log scale) via a piecewise linear trend model. The model naturally captures the phase transitions of the epidemic growth rate via change-points and further enjoys great interpretability due to its semiparametric nature. On the methodological front, we advance the nascent self-normalization (SN) technique (Shao, 2010) to testing and estimation of a single change-point in the…

通过自归一化进行时间序列分段AI 解读

Abstract We propose a novel and unified framework for change-point estimation in multivariate time series. The proposed method is fully non-parametric, robust to temporal dependence and avoids the demanding consistent estimation of long-run variance. One salient and distinct feature of the proposed method is its versatility, where it allows change-point detection for a broad class of parameters (such as mean, variance, correlation and quantile) in a unified fashion. At the…

COVID-19 感染轨迹建模：分段线性分位数趋势模型AI 解读

Abstract We propose a piecewise linear quantile trend model to analyse the trajectory of the COVID-19 daily new cases (i.e. the infection curve) simultaneously across multiple quantiles. The model is intuitive, interpretable and naturally captures the phase transitions of the epidemic growth rate via change-points. Unlike the mean trend model and least squares estimation, our quantile-based approach is robust to outliers, captures heteroscedasticity (commonly exhibited by…

高维数据变点的自适应推断AI 解读

In this article, we propose a class of test statistics for a change point in the mean of high-dimensional independent data. Our test integrates the U-statistic based approach in a recent work by Wang et al. and the Lq-norm based high-dimensional test in a recent work by He et al., and inherits several appealing features such as being tuning parameter free and asymptotic independence for test statistics corresponding to even q’s. A simple combination of test statistics…

多变量时间序列模型中的鞅差假设检验AI 解读

This article proposes a general class of tests to examine whether the error term is a martingale difference sequence in a multivariate time series model with parametric conditional mean. These new tests are formed based on recently developed martingale difference divergence matrix (MDDM), and they provide formal tools to test the multivariate martingale difference hypothesis in the literature for the first time. Under suitable conditions, the asymptotic null distributions of…

基于自归一化的高维数据变点推断AI 解读

This article considers change-point testing and estimation for a sequence of high-dimensional data. In the case of testing for a mean shift for high-dimensional independent data, we propose a new test which is based on U-statistic in Chen and Qin (Ann. Statist. 38 (2010) 808–835) and utilizes the self-normalization principle (Shao J. R. Stat. Soc. Ser. B. Stat. Methodol. 72 (2010) 343–366; Shao and Zhang J. Amer. Statist. Assoc. 105 (2010) 1228–1240). Our test targets dense…

基于自归一化的高维时间序列假设检验AI 解读

Self-normalization has attracted considerable attention in the recent literature of time series analysis, but its scope of applicability has been limited to low-/fixed-dimensional parameters for low-dimensional time series. In this article, we propose a new formulation of self-normalization for inference about the mean of high-dimensional stationary processes. Our original test statistic is a U-statistic with a trimming parameter to remove the bias caused by weak dependence.…

分段局部平稳误差下的自助辅助单位根检验AI 解读

In unit root testing, a piecewise locally stationary process is adopted to accommodate nonstationary errors that can have both smooth and abrupt changes in second- or higher-order properties. Under this framework, the limiting null distributions of the conventional unit root test statistics are derived and shown to contain a number of unknown parameters. To circumvent the difficulty of direct consistent estimation, we propose to use the dependent wild bootstrap to…

鞅差散度矩阵及其在平稳多元时间序列降维中的应用AI 解读

In this article, we introduce a new methodology to perform dimension reduction for a stationary multivariate time series. Our method is motivated by the consideration of optimal prediction and focuses on the reduction of the effective dimension in conditional mean of time series given the past information. In particular, we seek a contemporaneous linear transformation such that the transformed time series has two parts with one part being conditionally mean independent of…

面向海量数据的子抽样双重自助法AI 解读

The bootstrap is a popular and powerful method for assessing precision of estimators and inferential methods. However, for massive datasets that are increasingly prevalent, the bootstrap becomes prohibitively costly in computation and its feasibility is questionable even with modern parallel computing platforms. Recently, Kleiner and co-authors proposed a method called BLB (bag of little bootstraps) for massive data, which is more computationally scalable with little…

时间序列经验似然方法的覆盖率上界问题AI 解读

Summary The upper bounds on the coverage probabilities of the confidence regions based on blockwise empirical likelihood and non-standard expansive empirical likelihood methods for time series data are investigated via studying the probability of violating the convex hull constraint. The large sample bounds are derived on the basis of the pivotal limit of the blockwise empirical log-likelihood ratio obtained under fixed b asymptotics, which has recently been shown to provide…

时间序列自归一化：近期进展综述AI 解读

This article reviews some recent developments on the inference of time series data using the self-normalized approach. We aim to provide a detailed discussion about the use of self-normalization in different contexts and highlight distinctive feature associated with each problem and connections among these recent developments. The topics covered include: confidence interval construction for a parameter in a weakly dependent stationary time series setting, change point…

弱依赖与异方差误差下时间序列回归模型的推断AI 解读

Motivated by the need to assess the significance of the trend in some macroeconomic series, this article considers inference of a parameter in parametric trend functions when the errors exhibit certain degrees of nonstationarity with changing unconditional variances. We adopt the recently developed self-normalized approach to avoid the difficulty involved in the estimation of the asymptotic variance of the ordinary least-square estimator. The limiting distribution of the…

时间序列的固定平滑渐近理论AI 解读

In this paper, we derive higher order Edgeworth expansions for the finite sample distributions of the subsampling-based $t$-statistic and the Wald statistic in the Gaussian location model under the so-called fixed-smoothing paradigm. In particular, we show that the error of asymptotic approximation is at the order of the reciprocal of the sample size and obtain explicit forms for the leading error terms in the expansions. The results are used to justify the second-order…

具有相依误差的线性模型推断AI 解读

Summary The paper is concerned with inference for linear models with fixed regressors and weakly dependent stationary time series errors. Theoretically, we obtain asymptotic normality for the M-estimator of the regression parameter under mild conditions and establish a uniform Bahadur representation for recursive M-estimators. Methodologically, we extend the recently proposed self-normalized approach of Shao from stationary time series to the regression set-up, where the…

固定 b 子抽样与区块自助法：基于 p 值校准的改进置信集AI 解读

Summary Subsampling and block-based bootstrap methods have been used in a wide range of inference problems for time series. To accommodate the dependence, these resampling methods involve a bandwidth parameter, such as the subsampling window width and block size in the block-based bootstrap. In empirical work, using different bandwidth parameters could lead to different inference results, but traditional first-order asymptotic theory does not capture the choice of the…