arXiv subjects

Yuan Liao

Publications and source records attributed to Yuan Liao.

At least 55 records · Page 3Linked to original sources

arXiv2022

Energy and Age Pareto Optimal Trajectories in UAV-assisted Wireless Data Collection

This paper studies an unmanned aerial vehicle (UAV)-assisted wireless network, where a UAV is dispatched to gather information from ground sensor nodes (SN) and transfer the collected data to the depot. The information freshness is captured by the age of information (AoI) metric, whilst the energy consumption of the UAV is seen as another performance criterion. Most importantly, the AoI and energy efficiency are inherently competing metrics, since decreasing the AoI requires the UAV returning to the depot more frequently, leading to a higher energy consumption. To this end, we design UAV paths that optimize these two competing metrics and reveal the Pareto frontier. To formulate this problem, a multi-objective mixed integer linear programming (MILP) is proposed with a flow-based constraint set and we apply Bender's decomposition on the proposed formulation. The overall outcome shows that the proposed method allows deriving non-dominated solutions for decision making for UAV based wireless data collection. Numerical results are provided to corroborate our study by presenting the Pareto front of the two objectives and the effect on the UAV trajectory.

cs.NI↗

arXiv2022

Max-min Rate Deployment Optimization for Backhaul-limited Robotic Aerial 6G Small Cells

To overcome the limited on-board battery issue of nominal airborne base stations (ABSs), we are exploring the use of robotic airborne base station (RABS) with energy neutral grasping end-effectors that are able to autonomously perch at tall urban landforms. Specifically, this paper studies a heterogeneous network (HetNet) assisted by a movable RABS as a small cell which connects to a macro base station (MBS) through a limited-capacity wireless backhaul link, which can be deemed as another major challenge. To exploit the potential gains that the mobility of RABS can bring in the system, the minimum rate among all users is maximized by jointly optimizing the RABS deployment, user association and subcarrier allocation. This problem is initially formulated as a binary polynomial optimization (BPO) problem. After reformulating it as a nonconvex quadratically constrained quadratic programming (QCQP), we propose a semidefinite relaxation (SDR) based heuristic method to capture a high-quality solution in polynomial time. Numerical results reveal that deploying a RABS as the small cell can improve the minimum data rate by 95.43% at most and 33.97% on average, and the developed SDR heuristic algorithm significantly outperforms the linear relaxation (LR) baseline method.

cs.NI↗

arXiv2022

Scattered Image Reconstruction at Near-infrared Based on Spatial Modulation Instability

We present a method of near-infrared image reconstruction based on spatial modulation instability in a photorefractive strontium barium niobate crystal. The conditions that lead to the formation of modulation instability at near-infrared are discussed depending on the theory of modulation instability gain. Experimental results of scattered image reconstruction at the 1064 nm wavelength show the maximum cross-correlation coefficient and cross-correlation gain are 0.57 and 2.09 respectively. This method is expected to be an aid for near-infrared imaging technologies.

physics.optics↗

arXiv2022

Optimal Deployment and Operation of Robotic Aerial 6G Small Cells with Grasping End Effectors

Although airborne base stations (ABSs) mounted on drones show a significant potential to enhance network capacity and coverage due to their flexible deployment, the system performance is severely limited by the endurance of the on-board battery. To overcome this key shortcoming, we are exploring robotic airborne base station (RABS) with energy neutral grasping end-effectors able to autonomously perch at tall urban landforms. This paper studies the optimal deployment (fly to another grasping location or remain in the same one) and operation (active or sleep at an epoch) of RABS based on the spatio-temporal characteristics of underlying traffic demand from end-users. Specifically, an integer linear programming (ILP) is formulated by exploiting the coupling between these two decisions, that is, the RABS only needs to visit the locations where it is active. A Lagrangian heuristic algorithm is then proposed by exploiting the totally unimodular structure of the ILP formulation. A wide set of numerical investigations reveal that thanks to its mobility, a single robotic aerial small cell is able to outperform five (5) fixed small cells in terms of served user generated traffic within a 16 to 41 hours period.

cs.NI↗

arXiv2021

Fast and Robust Online Inference with Stochastic Gradient Descent via Random Scaling

We develop a new method of online inference for a vector of parameters estimated by the Polyak-Ruppert averaging procedure of stochastic gradient descent (SGD) algorithms. We leverage insights from time series regression in econometrics and construct asymptotically pivotal statistics via random scaling. Our approach is fully operational with online data and is rigorously underpinned by a functional central limit theorem. Our proposed inference method has a couple of key advantages over the existing methods. First, the test statistic is computed in an online fashion with only SGD iterates and the critical values can be obtained without any resampling methods, thereby allowing for efficient implementation suitable for massive online data. Second, there is no need to estimate the asymptotic variance and our inference method is shown to be robust to changes in the tuning parameters for SGD algorithms in simulation experiments with synthetic data.

stat.ML↗

arXiv2021

Trajectory Design in Rechargeable UAV Aided Wireless Networks: A Unified Framework for Energy Efficiency and Flight Time Minimization

This paper studies a rechargeable unmanned aerial vehicle (UAV) assisted wireless network, where a UAV is dispatched to disseminate information to a group of ground terminals (GTs) and returns to a recharging station (RS) before the on-board battery is depleted. The central aim is to design a UAV trajectory with the minimum total time duration, including the flight and recharging time, by optimizing the flying velocity, transmit power and hovering positions jointly. A flow-based mathematical programming formulation is proposed to provide optimal for joint optimization of flying and recharging time. Furthermore, to attack the curse of dimensionality for optimal decision making, a two-step method is proposed. In the first step, the UAV hovering positions is fixed and initialize a feasible trajectory design by solving a travelling salesman problem with energy constraints (TSPE) problem. In the second step, for the given initial trajectory, the time consumption for each sub-tour is minimized by optimizing the flying velocity, transmit power and hovering positions jointly. Numerical results show that the proposed method outperforms state of art techniques and reduces the aggregate time duration in an efficient way.

cs.NI↗

arXiv2020

Recent Developments on Factor Models and its Applications in Econometric Learning

This paper makes a selective survey on the recent development of the factor model and its application on statistical learnings. We focus on the perspective of the low-rank structure of factor models, and particularly draws attentions to estimating the model from the low-rank recovery point of view. The survey mainly consists of three parts: the first part is a review on new factor estimations based on modern techniques on recovering low-rank structures of high-dimensional models. The second part discusses statistical inferences of several factor-augmented models and applications in econometric learning models. The final part summarizes new developments dealing with unbalanced panels from the matrix completion perspective.

econ.EM↗

arXiv2020

Factor-Driven Two-Regime Regression

We propose a novel two-regime regression model where regime switching is driven by a vector of possibly unobservable factors. When the factors are latent, we estimate them by the principal component analysis of a panel data set. We show that the optimization problem can be reformulated as mixed integer optimization, and we present two alternative computational algorithms. We derive the asymptotic distribution of the resulting estimator under the scheme that the threshold effect shrinks to zero. In particular, we establish a phase transition that describes the effect of first-stage factor estimation as the cross-sectional dimension of panel data increases relative to the time-series dimension. Moreover, we develop bootstrap inference and illustrate our methods via numerical studies.

econ.EM↗

arXiv2020

Feasible Generalized Least Squares for Panel Data with Cross-sectional and Serial Correlations

This paper considers generalized least squares (GLS) estimation for linear panel data models. By estimating the large error covariance matrix consistently, the proposed feasible GLS (FGLS) estimator is more efficient than the ordinary least squares (OLS) in the presence of heteroskedasticity, serial, and cross-sectional correlations. To take into account the serial correlations, we employ the banding method. To take into account the cross-sectional correlations, we suggest to use the thresholding method. We establish the limiting distribution of the proposed estimator. A Monte Carlo study is considered. The proposed method is applied to an empirical application.

econ.EM↗

arXiv2020

Sparse HP Filter: Finding Kinks in the COVID-19 Contact Rate

In this paper, we estimate the time-varying COVID-19 contact rate of a Susceptible-Infected-Recovered (SIR) model. Our measurement of the contact rate is constructed using data on actively infected, recovered and deceased cases. We propose a new trend filtering method that is a variant of the Hodrick-Prescott (HP) filter, constrained by the number of possible kinks. We term it the $\textit{sparse HP filter}$ and apply it to daily data from five countries: Canada, China, South Korea, the UK and the US. Our new method yields the kinks that are well aligned with actual events in each country. We find that the sparse HP filter provides a fewer kinks than the $\ell_1$ trend filter, while both methods fitting data equally well. Theoretically, we establish risk consistency of both the sparse HP and $\ell_1$ trend filters. Ultimately, we propose to use time-varying $\textit{contact growth rates}$ to document and monitor outbreaks of COVID-19.

econ.EM↗

arXiv2020

Learning Latent Factors from Diversified Projections and its Applications to Over-Estimated and Weak Factors

Estimations and applications of factor models often rely on the crucial condition that the number of latent factors is consistently estimated, which in turn also requires that factors be relatively strong, data are stationary and weak serial dependence, and the sample size be fairly large, although in practical applications, one or several of these conditions may fail. In these cases it is difficult to analyze the eigenvectors of the data matrix. To address this issue, we propose simple estimators of the latent factors using cross-sectional projections of the panel data, by weighted averages with pre-determined weights. These weights are chosen to diversify away the idiosyncratic components, resulting in "diversified factors". Because the projections are conducted cross-sectionally, they are robust to serial conditions, easy to analyze and work even for finite length of time series. We formally prove that this procedure is robust to over-estimating the number of factors, and illustrate it in several applications, including post-selection inference, big data forecasts, large covariance estimation and factor specification tests. We also recommend several choices for the diversified weights.

math.ST↗

arXiv2020

Desperate times call for desperate measures: government spending multipliers in hard times

We investigate state-dependent effects of fiscal multipliers and allow for endogenous sample splitting to determine whether the US economy is in a slack state. When the endogenized slack state is estimated as the period of the unemployment rate higher than about 12 percent, the estimated cumulative multipliers are significantly larger during slack periods than non-slack periods and are above unity. We also examine the possibility of time-varying regimes of slackness and find that our empirical results are robust under a more flexible framework. Our estimation results point out the importance of the heterogenous effects of fiscal policy and shed light on the prospect of fiscal policy in response to economic shocks from the current COVID-19 pandemic.

econ.GN↗

arXiv2020

Standard Errors for Panel Data Models with Unknown Clusters

This paper develops a new standard-error estimator for linear panel data models. The proposed estimator is robust to heteroskedasticity, serial correlation, and cross-sectional correlation of unknown forms. The serial correlation is controlled by the Newey-West method. To control for cross-sectional correlations, we propose to use the thresholding method, without assuming the clusters to be known. We establish the consistency of the proposed estimator. Monte Carlo simulations show the method works well. An empirical application is considered.

econ.EM↗

arXiv2019

Inference for Heterogeneous Effects using Low-Rank Estimation of Factor Slopes

We study a panel data model with general heterogeneous effects where slopes are allowed to vary across both individuals and over time. The key dimension reduction assumption we employ is that the heterogeneous slopes can be expressed as having a factor structure so that the high-dimensional slope matrix is low-rank and can thus be estimated using low-rank regularized regression. We provide a simple multi-step estimation procedure for the heterogeneous effects. The procedure makes use of sample-splitting and orthogonalization to accommodate inference following the use of penalized low-rank estimation. We formally verify that the resulting estimator is asymptotically normal allowing simple construction of inferential statements for {the individual-time-specific effects and for cross-sectional averages of these effects}. We illustrate the proposed method in simulation experiments and by estimating the effect of the minimum wage on employment.

math.ST↗

arXiv2018

Uniform Inference for Characteristic Effects of Large Continuous-Time Linear Models

We consider continuous-time models with a large panel of moment conditions, where the structural parameter depends on a set of characteristics, whose effects are of interest. The leading example is the linear factor model in financial economics where factor betas depend on observed characteristics such as firm specific instruments and macroeconomic variables, and their effects pick up long-run time-varying beta fluctuations. We specify the factor betas as the sum of characteristic effects and an orthogonal idiosyncratic parameter that captures high-frequency movements. It is often the case that researchers do not know whether or not the latter exists, or its strengths, and thus the inference about the characteristic effects should be valid uniformly over a broad class of data generating processes for idiosyncratic parameters. We construct our estimation and inference in a two-step continuous-time GMM framework. It is found that the limiting distribution of the estimated characteristic effects has a discontinuity when the variance of the idiosyncratic parameter is near the boundary (zero), which makes the usual "plug-in" method using the estimated asymptotic variance only valid pointwise and may produce either over- or under- coveraging probabilities. We show that the uniformity can be achieved by cross-sectional bootstrap. Our procedure allows both known and estimated factors, and also features a bias correction for the effect of estimating unknown factors.

econ.EM↗

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↗

arXiv2016

Oracle Estimation of a Change Point in High Dimensional Quantile Regression

In this paper, we consider a high-dimensional quantile regression model where the sparsity structure may differ between two sub-populations. We develop $\ell_1$-penalized estimators of both regression coefficients and the threshold parameter. Our penalized estimators not only select covariates but also discriminate between a model with homogeneous sparsity and a model with a change point. As a result, it is not necessary to know or pretest whether the change point is present, or where it occurs. Our estimator of the change point achieves an oracle property in the sense that its asymptotic distribution is the same as if the unknown active sets of regression coefficients were known. Importantly, we establish this oracle property without a perfect covariate selection, thereby avoiding the need for the minimum level condition on the signals of active covariates. Dealing with high-dimensional quantile regression with an unknown change point calls for a new proof technique since the quantile loss function is non-smooth and furthermore the corresponding objective function is non-convex with respect to the change point. The technique developed in this paper is applicable to a general M-estimation framework with a change point, which may be of independent interest. The proposed methods are then illustrated via Monte Carlo experiments and an application to tipping in the dynamics of racial segregation.

stat.ME↗

arXiv2016

The Factor-Lasso and K-Step Bootstrap Approach for Inference in High-Dimensional Economic Applications

We consider inference about coefficients on a small number of variables of interest in a linear panel data model with additive unobserved individual and time specific effects and a large number of additional time-varying confounding variables. We allow the number of these additional confounding variables to be larger than the sample size, and suppose that, in addition to unrestricted time and individual specific effects, these confounding variables are generated by a small number of common factors and high-dimensional weakly-dependent disturbances. We allow that both the factors and the disturbances are related to the outcome variable and other variables of interest. To make informative inference feasible, we impose that the contribution of the part of the confounding variables not captured by time specific effects, individual specific effects, or the common factors can be captured by a relatively small number of terms whose identities are unknown. Within this framework, we provide a convenient computational algorithm based on factor extraction followed by lasso regression for inference about parameters of interest and show that the resulting procedure has good asymptotic properties. We also provide a simple k-step bootstrap procedure that may be used to construct inferential statements about parameters of interest and prove its asymptotic validity. The proposed bootstrap may be of substantive independent interest outside of the present context as the proposed bootstrap may readily be adapted to other contexts involving inference after lasso variable selection and the proof of its validity requires some new technical arguments. We also provide simulation evidence about performance of our procedure and illustrate its use in two empirical applications.

stat.ME↗