arXiv subjects

Yuan Ke

Publications and source records attributed to Yuan Ke.

11 recordsLinked to original sources

arXiv2026

On tail-robust autocovariance matrix estimation for high-dimensional and potentially nonstationary time series

In this paper, we study the autocovariance matrix estimation and inference problems under heavy-tailedness, high-dimensionality, general nonlinear temporal dependence, and potentially nonstationarity of time series. We consider two types of tail-robust autocovariance matrix estimation methods: the element-wise Huber's $M$-estimator and a computationally more efficient element-wise truncated estimator. Both estimators are designed to achieve sharp error bounds in matrix max-norm. The nonasymptotic properties of these estimators are proved based on new variants of Bernstein-type inequalities under functional dependence for the potentially nonstationary processes which may be of independent interest. Moreover, we prove a high-dimensional Gaussian approximation result, as a limiting distribution, for our element-wise truncated autocovariance estimator. A Gaussian multiplier bootstrap result is also given to facilitate the practicality. Our theoretical results are nonasymptotic, which gives explicit error bounds in terms of the sample size, dimensionality, moments, and the strength of temporal dependence. Numerical evidence is provided to support our theoretical results. Finally, we illustrate the benefits of the proposed methodology for detecting change points in monthly macroeconomic data.

stat.ME↗

arXiv2022

A Generalized Knockoff Procedure for FDR Control in Structural Change Detection

Controlling false discovery rate (FDR) is crucial for variable selection, multiple testing, among other signal detection problems. In literature, there is certainly no shortage of FDR control strategies when selecting individual features, but the relevant works for structural change detection, such as profile analysis for piecewise constant coefficients and integration analysis with multiple data sources, are limited. In this paper, we propose a generalized knockoff procedure (GKnockoff) for FDR control under such problem settings. We prove that the GKnockoff possesses pairwise exchangeability, and is capable of controlling the exact FDR under finite sample sizes. We further explore GKnockoff under high dimensionality, by first introducing a new screening method to filter the high-dimensional potential structural changes. We adopt a data splitting technique to first reduce the dimensionality via screening and then conduct GKnockoff on the refined selection set. Furthermore, the powers of proposed methods are systematically studied. Numerical comparisons with other methods show the superior performance of GKnockoff, in terms of both FDR control and power. We also implement the proposed methods to analyze a macroeconomic dataset for detecting changes of driven effects of economic development on the secondary industry.

stat.ME↗

arXiv2021

Improving COVID-19 Forecasting using eXogenous Variables

In this work, we study the pandemic course in the United States by considering national and state levels data. We propose and compare multiple time-series prediction techniques which incorporate auxiliary variables. One type of approach is based on spatio-temporal graph neural networks which forecast the pandemic course by utilizing a hybrid deep learning architecture and human mobility data. Nodes in this graph represent the state-level deaths due to COVID-19, edges represent the human mobility trend and temporal edges correspond to node attributes across time. The second approach is based on a statistical technique for COVID-19 mortality prediction in the United States that uses the SARIMA model and eXogenous variables. We evaluate these techniques on both state and national levels COVID-19 data in the United States and claim that the SARIMA and MCP models generated forecast values by the eXogenous variables can enrich the underlying model to capture complexity in respectively national and state levels data. We demonstrate significant enhancement in the forecasting accuracy for a COVID-19 dataset, with a maximum improvement in forecasting accuracy by 64.58% and 59.18% (on average) over the GCN-LSTM model in the national level data, and 58.79% and 52.40% (on average) over the GCN-LSTM model in the state level data. Additionally, our proposed model outperforms a parallel study (AUG-NN) by 27.35% improvement of accuracy on average.

cs.LG↗

arXiv2021

Best Subset Selection: Statistical Computing Meets Quantum Computing

With the rapid development of quantum computers, quantum algorithms have been studied extensively. However, quantum algorithms tackling statistical problems are still lacking. In this paper, we propose a novel non-oracular quantum adaptive search (QAS) method for the best subset selection problems. QAS performs almost identically to the naive best subset selection method but reduces its computational complexity from $O(D)$ to $O(\sqrt{D}\log_2D)$, where $D=2^p$ is the total number of subsets over $p$ covariates. Unlike existing quantum search algorithms, QAS does not require the oracle information of the true solution state and hence is applicable to various statistical learning problems with random observations. Theoretically, we prove QAS attains any arbitrary success probability $q \in (0.5, 1)$ within $O(\log_2D)$ iterations. When the underlying regression model is linear, we propose a quantum linear prediction method that is faster than its classical counterpart. We further introduce a hybrid quantum-classical strategy to avoid the capacity bottleneck of existing quantum computing systems and boost the success probability of QAS by majority voting. The effectiveness of this strategy is justified by both theoretical analysis and extensive empirical experiments on quantum and classical computers.

stat.ME↗

arXiv2021

Large-scale optimal transport map estimation using projection pursuit

This paper studies the estimation of large-scale optimal transport maps (OTM), which is a well-known challenging problem owing to the curse of dimensionality. Existing literature approximates the large-scale OTM by a series of one-dimensional OTM problems through iterative random projection. Such methods, however, suffer from slow or none convergence in practice due to the nature of randomly selected projection directions. Instead, we propose an estimation method of large-scale OTM by combining the idea of projection pursuit regression and sufficient dimension reduction. The proposed method, named projection pursuit Monge map (PPMM), adaptively selects the most ``informative'' projection direction in each iteration. We theoretically show the proposed dimension reduction method can consistently estimate the most ``informative'' projection direction in each iteration. Furthermore, the PPMM algorithm weakly convergences to the target large-scale OTM in a reasonable number of steps. Empirically, PPMM is computationally easy and converges fast. We assess its finite sample performance through the applications of Wasserstein distance estimation and generative models.

stat.ML↗

arXiv2021

Model-free Feature Screening and FDR Control with Knockoff Features

This paper proposes a model-free and data-adaptive feature screening method for ultra-high dimensional datasets. The proposed method is based on the projection correlation which measures the dependence between two random vectors. This projection correlation based method does not require specifying a regression model and applies to the data in the presence of heavy-tailed errors and multivariate response. It enjoys both sure screening and rank consistency properties under weak assumptions. Further, a two-step approach is proposed to control the false discovery rate (FDR) in feature screening with the help of knockoff features. It can be shown that the proposed two-step approach enjoys both sure screening and FDR control if the pre-specified FDR level $α$ is greater or equal to $1/s$, where $s$ is the number of active features. The superior empirical performance of the proposed methods is justified by various numerical experiments and real data applications.

stat.ME↗

arXiv2019

User-Friendly Covariance Estimation for Heavy-Tailed Distributions

We offer a survey of recent results on covariance estimation for heavy-tailed distributions. By unifying ideas scattered in the literature, we propose user-friendly methods that facilitate practical implementation. Specifically, we introduce element-wise and spectrum-wise truncation operators, as well as their $M$-estimator counterparts, to robustify the sample covariance matrix. Different from the classical notion of robustness that is characterized by the breakdown property, we focus on the tail robustness which is evidenced by the connection between nonasymptotic deviation and confidence level. The key observation is that the estimators needs to adapt to the sample size, dimensionality of the data and the noise level to achieve optimal tradeoff between bias and robustness. Furthermore, to facilitate their practical use, we propose data-driven procedures that automatically calibrate the tuning parameters. We demonstrate their applications to a series of structured models in high dimensions, including the bandable and low-rank covariance matrices and sparse precision matrices. Numerical studies lend strong support to the proposed methods.

stat.ME↗

arXiv2018

FarmTest: Factor-Adjusted Robust Multiple Testing with Approximate False Discovery Control

Large-scale multiple testing with correlated and heavy-tailed data arises in a wide range of research areas from genomics, medical imaging to finance. Conventional methods for estimating the false discovery proportion (FDP) often ignore the effect of heavy-tailedness and the dependence structure among test statistics, and thus may lead to inefficient or even inconsistent estimation. Also, the commonly imposed joint normality assumption is arguably too stringent for many applications. To address these challenges, in this paper we propose a Factor-Adjusted Robust Multiple Testing (FarmTest) procedure for large-scale simultaneous inference with control of the false discovery proportion. We demonstrate that robust factor adjustments are extremely important in both controlling the FDP and improving the power. We identify general conditions under which the proposed method produces consistent estimate of the FDP. As a byproduct that is of independent interest, we establish an exponential-type deviation inequality for a robust $U$-type covariance estimator under the spectral norm. Extensive numerical experiments demonstrate the advantage of the proposed method over several state-of-the-art methods especially when the data are generated from heavy-tailed distributions. The proposed procedures are implemented in the R-package FarmTest.

stat.ME↗

arXiv2018

Augmented Factor Models with Applications to Validating Market Risk Factors and Forecasting Bond Risk Premia

We study factor models augmented by observed covariates that have explanatory powers on the unknown factors. In financial factor models, the unknown factors can be reasonably well explained by a few observable proxies, such as the Fama-French factors. In diffusion index forecasts, identified factors are strongly related to several directly measurable economic variables such as consumption-wealth variable, financial ratios, and term spread. With those covariates, both the factors and loadings are identifiable up to a rotation matrix even only with a finite dimension. To incorporate the explanatory power of these covariates, we propose a smoothed principal component analysis (PCA): (i) regress the data onto the observed covariates, and (ii) take the principal components of the fitted data to estimate the loadings and factors. This allows us to accurately estimate the percentage of both explained and unexplained components in factors and thus to assess the explanatory power of covariates. We show that both the estimated factors and loadings can be estimated with improved rates of convergence compared to the benchmark method. The degree of improvement depends on the strength of the signals, representing the explanatory power of the covariates on the factors. The proposed estimator is robust to possibly heavy-tailed distributions. We apply the model to forecast US bond risk premia, and find that the observed macroeconomic characteristics contain strong explanatory powers of the factors. The gain of forecast is more substantial when the characteristics are incorporated to estimate the common factors than directly used for forecasts.

stat.ME↗

arXiv2018

Factor-Adjusted Regularized Model Selection

This paper studies model selection consistency for high dimensional sparse regression when data exhibits both cross-sectional and serial dependency. Most commonly-used model selection methods fail to consistently recover the true model when the covariates are highly correlated. Motivated by econometric studies, we consider the case where covariate dependence can be reduced through factor model, and propose a consistent strategy named Factor-Adjusted Regularized Model Selection (FarmSelect). By separating the latent factors from idiosyncratic components, we transform the problem from model selection with highly correlated covariates to that with weakly correlated variables. Model selection consistency as well as optimal rates of convergence are obtained under mild conditions. Numerical studies demonstrate the nice finite sample performance in terms of both model selection and out-of-sample prediction. Moreover, our method is flexible in a sense that it pays no price for weakly correlated and uncorrelated cases. Our method is applicable to a wide range of high dimensional sparse regression problems. An R-package FarmSelect is also provided for implementation.

stat.ME↗

arXiv2015

Model selection and structure specification in ultra-high dimensional generalised semi-varying coefficient models

In this paper, we study the model selection and structure specification for the generalised semi-varying coefficient models (GSVCMs), where the number of potential covariates is allowed to be larger than the sample size. We first propose a penalised likelihood method with the LASSO penalty function to obtain the preliminary estimates of the functional coefficients. Then, using the quadratic approximation for the local log-likelihood function and the adaptive group LASSO penalty (or the local linear approximation of the group SCAD penalty) with the help of the preliminary estimation of the functional coefficients, we introduce a novel penalised weighted least squares procedure to select the significant covariates and identify the constant coefficients among the coefficients of the selected covariates, which could thus specify the semiparametric modelling structure. The developed model selection and structure specification approach not only inherits many nice statistical properties from the local maximum likelihood estimation and nonconcave penalised likelihood method, but also computationally attractive thanks to the computational algorithm that is proposed to implement our method. Under some mild conditions, we establish the asymptotic properties for the proposed model selection and estimation procedure such as the sparsity and oracle property. We also conduct simulation studies to examine the finite sample performance of the proposed method, and finally apply the method to analyse a real data set, which leads to some interesting findings.

math.ST↗