arXiv subjects

Rongmao Zhang

Publications and source records attributed to Rongmao Zhang.

5 recordsLinked to original sources

arXiv2026

Feature Screening for High-Dimensional Structural Break Predictive Regression

Predictive regression is a crucial tool for exploring return predictability. In this study, we introduce an efficient procedure for selecting and estimating active predictors and change points in structural break predictive regression. Our approach allows the number of change points to increase with the sample size and accommodates sparse active predictors that may be stationary or cointegrated. We begin by identifying the active predictors using a Sure Independence Canonical Screening (SICS) procedure. Next, we estimate the change points through a Ratio-Controlled Regression Screening (RCRS) method. Finally, we reduce redundancy by eliminating unnecessary breakpoints and predictors using information criteria (IC). This approach allows for consistent estimation and selection of true breakpoints and active predictors. Our simulations and empirical studies demonstrate that the proposed procedure performs effectively.

stat.ME↗

arXiv2018

Krigings Over Space and Time Based on Latent Low-Dimensional Structures

We propose a new approach to represent nonparametrically the linear dependence structure of a spatio-temporal process in terms of latent common factors. Though it is formally similar to the existing reduced rank approximation methods (Section 7.1.3 of Cressie and Wikle, 2011), the fundamental difference is that the low-dimensional structure is completely unknown in our setting, which is learned from the data collected irregularly over space but regularly over time. Furthermore a graph Laplacian is incorporated in the learning in order to take the advantage of the continuity over space, and a new aggregation method via randomly partitioning space is introduced to improve the efficiency. We do not impose any stationarity conditions over space either, as the learning is facilitated by the stationarity in time. Krigings over space and time are carried out based on the learned low-dimensional structure, which is scalable to the cases when the data are taken over a large number of locations and/or over a long time period. Asymptotic properties of the proposed methods are established. Illustration with both simulated and real data sets is also reported.

stat.ME↗

arXiv2018

Identifying Cointegration by Eigenanalysis

We propose a new and easy-to-use method for identifying cointegrated components of nonstationary time series, consisting of an eigenanalysis for a certain non-negative definite matrix. Our setting is model-free, and we allow the integer-valued integration orders of the observable series to be unknown, and to possibly differ. Consistency of estimates of the cointegration space and cointegration rank is established both when the dimension of the observable time series is fixed as sample size increases, and when it diverges slowly. The proposed methodology is also extended and justified in a fractional setting. A Monte Carlo study of finite-sample performance, and a small empirical illustration, are reported.

stat.ME↗

arXiv2013

Marked empirical processes for non-stationary time series

Consider a first-order autoregressive process $X_i=βX_{i-1}+\varepsilon_i,$ where $\varepsilon_i=G(η_i,η_{i-1},\ldots)$ and $η_i,i\in\mathbb{Z}$ are i.i.d. random variables. Motivated by two important issues for the inference of this model, namely, the quantile inference for $H_0: β=1$, and the goodness-of-fit for the unit root model, the notion of the marked empirical process $α_n(x)=\frac{1}{n}\sum_{i=1}^ng(X_i/a_n)I(\varepsilon_i\leq x),x\in\mathbb{R}$ is investigated in this paper. Herein, $g(\cdot)$ is a continuous function on $\mathbb{R}$ and $\{a_n\}$ is a sequence of self-normalizing constants. As the innovation $\{\varepsilon_i\}$ is usually not observable, the residual marked empirical process $\hat α_n(x)=\frac{1}{n}\sum_{i=1}^ng(X_i/a_n)I(\hat{\varepsilon}_iłeq x),x\in\mathbb{R},$ is considered instead, where $\hat{\varepsilon}_i=X_i-\hatβX_{i-1}$ and $\hatβ$ is a consistent estimate of $β.$ In particular, via the martingale decomposition of stationary process and the stochastic integral result of Jakubowski (Ann. Probab. 24 (1996) 2141-2153), the limit distributions of $α_n(x)$ and $\hatα_n(x)$ are established when $\{\varepsilon_i\}$ is a short-memory process. Furthermore, by virtue of the results of Wu (Bernoulli 95 (2003) 809-831) and Ho and Hsing (Ann. Statist. 24 (1996) 992-1024) of empirical process and the integral result of Mikosch and Norvaiša (Bernoulli 6 (2000) 401-434) and Young (Acta Math. 67 (1936) 251-282), the limit distributions of $α_n(x)$ and $\hatα_n(x)$ are also derived when $\{\varepsilon_i\}$ is a long-memory process.

math.ST↗

arXiv2013

Tests for covariance matrix with fixed or divergent dimension

Testing covariance structure is of importance in many areas of statistical analysis, such as microarray analysis and signal processing. Conventional tests for finite-dimensional covariance cannot be applied to high-dimensional data in general, and tests for high-dimensional covariance in the literature usually depend on some special structure of the matrix. In this paper, we propose some empirical likelihood ratio tests for testing whether a covariance matrix equals a given one or has a banded structure. The asymptotic distributions of the new tests are independent of the dimension.

math.ST↗