arXiv subjects

Feiyu Jiang

Publications and source records attributed to Feiyu Jiang.

At least 19 recordsLinked to original sources

arXiv2026

On Non-Stationary Dynamic Pricing: Adaptivity and Optimality

We study the contextual dynamic pricing problem under non-stationarity, where a firm sells products to $T$ sequentially arriving consumers that behave according to an unknown demand model that can change over time. The demand model is assumed to be a generalized linear model (GLM), allowing for a feature vector in $\mathbb{R}^d$ that encodes products and consumer information. To achieve optimal revenue (i.e., least regret), the firm needs to learn and exploit the unknown GLMs while monitoring for potential changes. We propose a multiscale change-point detection based algorithm that achieves a regret of order $\widetilde{O}(\sqrt{s_TdT}\wedge\{V_T^{1/3}d^{1/3}T^{2/3}+\sqrt{dT}\})$, where $s_T$ is the number of piecewise stationary segments and $V_T$ is a newly defined notion of design-adjusted variation budget of model parameters. Our algorithm is adaptive and does not require knowing $s_T$ or $V_T$. Moreover, to our knowledge, this is the first dynamic pricing algorithm that is adaptive to the nature of changes and achieves the best-of-both-worlds rate, thus closing a long-standing gap in the literature. We remark that, due to the varying contexts, existing works in the adaptive non-stationary bandit literature cannot be applied to achieve optimality for contextual dynamic pricing. The regret is further accompanied with a newly constructed minimax lower bound, confirming the optimality of our algorithm (up to logarithmic factors). Extensive numerical experiments are conducted to illustrate the efficiency and robustness of the proposed algorithm in non-stationary dynamic pricing.

stat.ML↗

arXiv2026

Generalized Spectral Testing with Sample Splitting

Residual-based goodness-of-fit tests for parametric time-series models are often complicated by parameter-estimation effects, which can alter the limiting behavior of diagnostic statistics. We propose a sample-splitting generalized spectral test (in the spirit of Escanciano(2006)) for assessing conditional mean specification in linear and nonlinear time-series models. The procedure estimates the model parameter on a fitting subsample and constructs a generalized spectral Cramer-von Mises statistic from residuals computed on a checking/testing subsample. The statistic aggregates pairwise conditional mean restrictions over all lags and is therefore bandwidth-free and free of truncation-lag selection. Under mild regularity conditions and a score-alignment condition, the residual-based process has the same limiting null distribution as the infeasible oracle process based on the true errors. Although the resulting limiting law is still non-pivotal, it can be consistently approximated by a simple multiplier bootstrap that does not require generating bootstrap time series or re-estimating parameters. Such an oracle-equivalence property is in sharp contrast to the original full-sample test, for which parameter estimation contributes an additional first-order term to the limiting process, and requires re-estimating parameters in each bootstrapped sample. We further establish consistency of the proposed test against fixed alternatives and nontrivial power against local alternatives. Extensive simulations and real data analyses show that the proposed test controls size well, has comparable power, and delivers substantial computational savings in models where repeated estimation is costly.

econ.EM↗

arXiv2025

Diagnostic Checking for Wasserstein Autoregression

Wasserstein autoregression provides a robust framework for modeling serial dependence among probability distributions, with wide-ranging applications in economics, finance, and climate science. In this paper, we develop portmanteau-type diagnostic tests for assessing the adequacy of Wasserstein autoregressive models. By defining autocorrelation functions for model errors and residuals in the Wasserstein space, we construct two related tests: one analogous to the classical McLeod type test, and the other based on the sample-splitting approach of Davis and Fernandes(2025). We establish that, under mild regularity conditions, the corresponding test statistics converge in distribution to chi-square limits. Simulation studies and empirical applications demonstrate that the proposed tests effectively detect model mis-specification, offering a principled and reliable diagnostic tool for distributional time series analysis.

stat.ME↗

arXiv2025

Model-free Change-point Detection using AUC of a Classifier

In contemporary data analysis, it is increasingly common to work with non-stationary complex data sets. These data sets typically extend beyond the classical low-dimensional Euclidean space, making it challenging to detect shifts in their distribution without relying on strong structural assumptions. This paper proposes a novel offline change-point detection method that leverages classifiers developed in the statistics and machine learning community. With suitable data splitting, the test statistic is constructed through sequential computation of the Area Under the Curve (AUC) of a classifier, which is trained on data segments on both ends of the sequence. It is shown that the resulting AUC process attains its maxima at the true change-point location, which facilitates the change-point estimation. The proposed method is characterized by its complete nonparametric nature, high versatility, considerable flexibility, and absence of stringent assumptions on the underlying data or any distributional shifts. Theoretically, we derive the limiting pivotal distribution of the proposed test statistic under null, as well as the asymptotic behaviors under both local and fixed alternatives. The localization rate of the change-point estimator is also provided. Extensive simulation studies and the analysis of two real-world data sets illustrate the superior performance of our approach compared to existing model-free change-point detection methods.

stat.ME↗

arXiv2025

Contextual Dynamic Pricing: Algorithms, Optimality, and Local Differential Privacy Constraints

We study contextual dynamic pricing problems where a firm sells products to $T$ sequentially-arriving consumers, behaving according to an unknown demand model. The firm aims to minimize its regret over a clairvoyant that knows the model in advance. The demand follows a generalized linear model (GLM), allowing for stochastic feature vectors in $\mathbb R^d$ encoding product and consumer information. We first show the optimal regret is of order $\sqrt{dT}$, up to logarithmic factors, improving existing upper bounds by a $\sqrt{d}$ factor. This optimal rate is materialized by two algorithms: a confidence bound-type algorithm and an explore-then-commit (ETC) algorithm. A key insight is an intrinsic connection between dynamic pricing and contextual multi-armed bandit problems with many arms with a careful discretization. We further study contextual dynamic pricing under local differential privacy (LDP) constraints. We propose a stochastic gradient descent-based ETC algorithm achieving regret upper bounds of order $d\sqrt{T}/ε$, up to logarithmic factors, where $ε>0$ is the privacy parameter. The upper bounds with and without LDP constraints are matched by newly constructed minimax lower bounds, characterizing costs of privacy. Moreover, we extend our study to dynamic pricing under mixed privacy constraints, improving the privacy-utility tradeoff by leveraging public data. This is the first time such setting is studied in the dynamic pricing literature and our theoretical results seamlessly bridge dynamic pricing with and without LDP. Extensive numerical experiments and real data applications are conducted to illustrate the efficiency and practical value of our algorithms.

cs.LG↗

arXiv2025

Locally Private Nonparametric Contextual Multi-armed Bandits

Motivated by privacy concerns in sequential decision-making on sensitive data, we address the challenge of nonparametric contextual multi-armed bandits (MAB) under local differential privacy (LDP). We develop a uniform-confidence-bound-type estimator, showing its minimax optimality supported by a matching minimax lower bound. We further consider the case where auxiliary datasets are available, subject also to (possibly heterogeneous) LDP constraints. Under the widely-used covariate shift framework, we propose a jump-start scheme to effectively utilize the auxiliary data, the minimax optimality of which is further established by a matching lower bound. Comprehensive experiments on both synthetic and real-world datasets validate our theoretical results and underscore the effectiveness of the proposed methods.

stat.ML↗

arXiv2025

Transfer Learning for Nonparametric Contextual Dynamic Pricing

Dynamic pricing strategies are crucial for firms to maximize revenue by adjusting prices based on market conditions and customer characteristics. However, designing optimal pricing strategies becomes challenging when historical data are limited, as is often the case when launching new products or entering new markets. One promising approach to overcome this limitation is to leverage information from related products or markets to inform the focal pricing decisions. In this paper, we explore transfer learning for nonparametric contextual dynamic pricing under a covariate shift model, where the marginal distributions of covariates differ between source and target domains while the reward functions remain the same. We propose a novel Transfer Learning for Dynamic Pricing (TLDP) algorithm that can effectively leverage pre-collected data from a source domain to enhance pricing decisions in the target domain. The regret upper bound of TLDP is established under a simple Lipschitz condition on the reward function. To establish the optimality of TLDP, we further derive a matching minimax lower bound, which includes the target-only scenario as a special case and is presented for the first time in the literature. Extensive numerical experiments validate our approach, demonstrating its superiority over existing methods and highlighting its practical utility in real-world applications.

cs.LG↗

arXiv2024

Estimation for conditional moment models based on martingale difference divergence

We provide a new estimation method for conditional moment models via the martingale difference divergence (MDD).Our MDD-based estimation method is formed in the framework of a continuum of unconditional moment restrictions. Unlike the existing estimation methods in this framework, the MDD-based estimation method adopts a non-integrable weighting function, which could grab more information from unconditional moment restrictions than the integrable weighting function to enhance the estimation efficiency. Due to the nature of shift-invariance in MDD, our MDD-based estimation method can not identify the intercept parameters. To overcome this identification issue, we further provide a two-step estimation procedure for the model with intercept parameters. Under regularity conditions, we establish the asymptotics of the proposed estimators, which are not only easy-to-implement with analytic asymptotic variances, but also applicable to time series data with an unspecified form of conditional heteroskedasticity. Finally, we illustrate the usefulness of the proposed estimators by simulations and two real examples.

econ.EM↗

arXiv2024

SNSeg: An R Package for Time Series Segmentation via Self-Normalization

Time series segmentation aims to identify potential change-points in a sequence of temporally dependent data, so that the original sequence can be partitioned into several homogeneous subsequences. It is useful for modeling and predicting non-stationary time series and is widely applied in natural and social sciences. Existing segmentation methods primarily focus on only one type of parameter changes such as mean and variance, and they typically depend on laborious tuning or smoothing parameters, which can be challenging to choose in practice. The self-normalization based change-point estimation framework SNCP by Zhao et al. (2022), however, offers users more flexibility and convenience as it allows for change-point estimation of different types of parameters (e.g. mean, variance, quantile and autocovariance) in a unified fashion, and requires effortless tuning. In this paper, the R package SNSeg is introduced to implement SNCP for segmentation of univariate and multivariate time series. An extension of SNCP, named SNHD, is also designed and implemented for change-point estimation in the mean vector of high-dimensional time series. The estimated changepoints as well as segmented time series are available with graphical tools. Detailed examples of SNSeg are given in simulations of multivariate autoregressive processes with change-points.

stat.CO↗

arXiv2023

Testing Serial Independence of Object-Valued Time Series

We propose a novel method for testing serial independence of object-valued time series in metric spaces, which is 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 auto distance covariance for object-valued time series. Furthermore, we propose a generalized spectral density function to account for pairwise dependence at all lags and construct a Cramer-von Mises type test statistic. New theoretical arguments are developed to establish the asymptotic behavior of the test statistic. A wild bootstrap is also introduced to obtain the critical values of the non-pivotal limiting null distribution. Extensive numerical simulations and two real data applications are conducted to illustrate the effectiveness and versatility of our proposed method.

stat.ME↗

arXiv2023

Two-Sample and Change-Point Inference for Non-Euclidean Valued Time Series

Data objects taking value in a general metric space have become increasingly common in modern data analysis. In this paper, we study two important statistical inference problems, namely, two-sample testing and change-point detection, for such non-Euclidean data under temporal dependence. Typical examples of non-Euclidean valued time series include yearly mortality distributions, time-varying networks, and covariance matrix time series. To accommodate unknown temporal dependence, we advance the self-normalization (SN) technique (Shao, 2010) to the inference of non-Euclidean time series, which is substantially different from the existing SN-based inference for functional time series that reside in Hilbert space (Zhang et al., 2011). Theoretically, we propose new regularity conditions that could be easier to check than those in the recent literature, and derive the limiting distributions of the proposed test statistics under both null and local alternatives. For change-point detection problem, we also derive the consistency for the change-point location estimator, and combine our proposed change-point test with wild binary segmentation to perform multiple change-point estimation. Numerical simulations demonstrate the effectiveness and robustness of our proposed tests compared with existing methods in the literature. Finally, we apply our tests to two-sample inference in mortality data and change-point detection in cryptocurrency data.

stat.ME↗

arXiv2023

Matrix GARCH Model: Inference and Application

Matrix-variate time series data are largely available in applications. However, no attempt has been made to study their conditional heteroskedasticity that is often observed in economic and financial data. To address this gap, we propose a novel matrix generalized autoregressive conditional heteroskedasticity (GARCH) model to capture the dynamics of conditional row and column covariance matrices of matrix time series. The key innovation of the matrix GARCH model is the use of a univariate GARCH specification for the trace of conditional row or column covariance matrix, which allows for the identification of conditional row and column covariance matrices. Moreover, we introduce a quasi maximum likelihood estimator (QMLE) for model estimation and develop a portmanteau test for model diagnostic checking. Simulation studies are conducted to assess the finite-sample performance of the QMLE and portmanteau test. To handle large dimensional matrix time series, we also propose a matrix factor GARCH model. Finally, we demonstrate the superiority of the matrix GARCH and matrix factor GARCH models over existing multivariate GARCH-type models in volatility forecasting and portfolio allocations using three applications on credit default swap prices, global stock sector indices, and future prices.

stat.ME↗

arXiv2023

High-Dimensional Dynamic Pricing under Non-Stationarity: Learning and Earning with Change-Point Detection

We consider a high-dimensional dynamic pricing problem under non-stationarity, where a firm sells products to $T$ sequentially arriving consumers that behave according to an unknown demand model with potential changes at unknown times. The demand model is assumed to be a high-dimensional generalized linear model (GLM), allowing for a feature vector in $\mathbb R^d$ that encodes products and consumer information. To achieve optimal revenue (i.e., least regret), the firm needs to learn and exploit the unknown GLMs while monitoring for potential change-points. To tackle such a problem, we first design a novel penalized likelihood-based online change-point detection algorithm for high-dimensional GLMs, which is the first algorithm in the change-point literature that achieves optimal minimax localization error rate for high-dimensional GLMs. A change-point detection assisted dynamic pricing (CPDP) policy is further proposed and achieves a near-optimal regret of order $O(s\sqrt{Υ_T T}\log(Td))$, where $s$ is the sparsity level and $Υ_T$ is the number of change-points. This regret is accompanied with a minimax lower bound, demonstrating the optimality of CPDP (up to logarithmic factors). In particular, the optimality with respect to $Υ_T$ is seen for the first time in the dynamic pricing literature, and is achieved via a novel accelerated exploration mechanism. Extensive simulation experiments and a real data application on online lending illustrate the efficiency of the proposed policy and the importance and practical value of handling non-stationarity in dynamic pricing.

stat.ME↗

arXiv2022

Segmenting Time Series via Self-Normalization

We propose a novel and unified framework for change-point estimation in multivariate time series. The proposed method is fully nonparametric, enjoys effortless tuning and is robust to temporal dependence. 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 core of our method, we couple the self-normalization (SN) based tests with a novel nested local-window segmentation algorithm, which seems new in the growing literature of change-point analysis. Due to the presence of an inconsistent long-run variance estimator in the SN test, non-standard theoretical arguments are further developed to derive the consistency and convergence rate of the proposed SN-based change-point detection method. Extensive numerical experiments and relevant real data analysis are conducted to illustrate the effectiveness and broad applicability of our proposed method in comparison with state-of-the-art approaches in the literature.

stat.ME↗

arXiv2022

A Consistent ICM-based $\chi^2$ Specification Test

In spite of the omnibus property of Integrated Conditional Moment (ICM) specification tests, they are not commonly used in empirical practice owing to features such as the non-pivotality of the test and the high computational cost of available bootstrap schemes, especially in large samples. This paper proposes specification and mean independence tests based on ICM metrics. The proposed test exhibits consistency, asymptotic $\chi^2$-distribution under the null hypothesis, and computational efficiency. Moreover, it demonstrates robustness to heteroskedasticity of unknown form and can be adapted to enhance power towards specific alternatives. A power comparison with classical bootstrap-based ICM tests using Bahadur slopes is also provided. Monte Carlo simulations are conducted to showcase the excellent size control and competitive power of the proposed test.

econ.EM↗

arXiv2022

Robust Inference for Change Points in High Dimension

This paper proposes a new test for a change point in the mean of high-dimensional data based on the spatial sign and self-normalization. The test is easy to implement with no tuning parameters, robust to heavy-tailedness and theoretically justified with both fixed-$n$ and sequential asymptotics under both null and alternatives, where $n$ is the sample size. We demonstrate that the fixed-$n$ asymptotics provide a better approximation to the finite sample distribution and thus should be preferred in both testing and testing-based estimation. To estimate the number and locations when multiple change-points are present, we propose to combine the p-value under the fixed-$n$ asymptotics with the seeded binary segmentation (SBS) algorithm. Through numerical experiments, we show that the spatial sign based procedures are robust with respect to the heavy-tailedness and strong coordinate-wise dependence, whereas their non-robust counterparts proposed in Wang et al. (2022) appear to under-perform. A real data example is also provided to illustrate the robustness and broad applicability of the proposed test and its corresponding estimation algorithm.

stat.ME↗

arXiv2020

Adaptive inference for a semiparametric generalized autoregressive conditional heteroskedasticity model

This paper considers a semiparametric generalized autoregressive conditional heteroskedasticity (S-GARCH) model. For this model, we first estimate the time-varying long run component for unconditional variance by the kernel estimator, and then estimate the non-time-varying parameters in GARCH-type short run component by the quasi maximum likelihood estimator (QMLE). We show that the QMLE is asymptotically normal with the parametric convergence rate. Next, we construct a Lagrange multiplier test for linear parameter constraint and a portmanteau test for model checking, and obtain their asymptotic null distributions. Our entire statistical inference procedure works for the non-stationary data with two important features: first, our QMLE and two tests are adaptive to the unknown form of the long run component; second, our QMLE and two tests share the same efficiency and testing power as those in variance targeting method when the S-GARCH model is stationary.

stat.ME↗

arXiv2020

Time series models for realized covariance matrices based on the matrix-F distribution

We propose a new Conditional BEKK matrix-F (CBF) model for the time-varying realized covariance (RCOV) matrices. This CBF model is capable of capturing heavy-tailed RCOV, which is an important stylized fact but could not be handled adequately by the Wishart-based models. To further mimic the long memory feature of the RCOV, a special CBF model with the conditional heterogeneous autoregressive (HAR) structure is introduced. Moreover, we give a systematical study on the probabilistic properties and statistical inferences of the CBF model, including exploring its stationarity, establishing the asymptotics of its maximum likelihood estimator, and giving some new inner-product-based tests for its model checking. In order to handle a large dimensional RCOV matrix, we construct two reduced CBF models -- the variance-target CBF model (for moderate but fixed dimensional RCOV matrix) and the factor CBF model (for high dimensional RCOV matrix). For both reduced models, the asymptotic theory of the estimated parameters is derived. The importance of our entire methodology is illustrated by simulation results and two real examples.

math.ST↗