arXiv subjects

Yukun Liu

Publications and source records attributed to Yukun Liu.

69 records · Page 4Linked to original sources

arXiv2022

Nearly optimal capture-recapture sampling and empirical likelihood weighting estimation for M-estimation with big data

Subsampling techniques can reduce the computational costs of processing big data. Practical subsampling plans typically involve initial uniform sampling and refined sampling. With a subsample, big data inferences are generally built on the inverse probability weighting (IPW), which becomes unstable when the probability weights are close to zero and cannot incorporate auxiliary information. First, we consider capture-recapture sampling, which combines an initial uniform sampling with a second Poisson sampling. Under this sampling plan, we propose an empirical likelihood weighting (ELW) estimation approach to an M-estimation parameter. Second, based on the ELW method, we construct a nearly optimal capture-recapture sampling plan that balances estimation efficiency and computational costs. Third, we derive methods for determining the smallest sample sizes with which the proposed sampling-and-estimation method produces estimators of guaranteed precision. Our ELW method overcomes the instability of IPW by circumventing the use of inverse probabilities, and utilizes auxiliary information including the size and certain sample moments of big data. We show that the proposed ELW method produces more efficient estimators than IPW, leading to more efficient optimal sampling plans and more economical sample sizes for a prespecified estimation precision. These advantages are confirmed through simulation studies and real data analyses.

stat.ME↗

arXiv2022

Penalized empirical likelihood estimation and EM algorithms for closed-population capture-recapture models

Capture-recapture experiments are widely used to estimate the abundance of a finite population. Based on capture-recapture data, the empirical likelihood (EL) method has been shown to outperform the conventional conditional likelihood (CL) method. However, the current literature on EL abundance estimation ignores behavioral effects, and the EL estimates may not be stable, especially when the capture probability is low. We make three contributions in this paper. First, we extend the EL method to capture-recapture models that account for behavioral effects. Second, to overcome the instability of the EL method, we propose a penalized EL (PEL) estimation method that penalizes large abundance values. We then investigate the asymptotics of the maximum PEL estimator and the PEL ratio statistic. Third, we develop standard expectation-maximization (EM) algorithms for PEL to improve its practical performance. The EM algorithm is also applicable to EL and CL with slight modifications. Our simulation and a real-world data analysis demonstrate that the PEL method successfully overcomes the instability of the EL method and the proposed EM algorithm produces more reliable results than existing optimization algorithms.

stat.ME↗

arXiv2022

Tuning-parameter-free optimal propensity score matching approach for causal inference

Propensity score matching (PSM) is a pseudo-experimental method that uses statistical techniques to construct an artificial control group by matching each treated unit with one or more untreated units of similar characteristics. To date, the problem of determining the optimal number of matches per unit, which plays an important role in PSM, has not been adequately addressed. We propose a tuning-parameter-free PSM method based on the nonparametric maximum-likelihood estimation of the propensity score under the monotonicity constraint. The estimated propensity score is piecewise constant, and therefore automatically groups data. Hence, our proposal is free of tuning parameters. The proposed estimator is asymptotically semiparametric efficient for the univariate case, and achieves this level of efficiency in the multivariate case when the outcome and the propensity score depend on the covariate in the same direction. We conclude that matching methods based on the propensity score alone cannot, in general, be efficient.

math.ST↗

arXiv2022

Weighted-average quantile regression

In this paper, we introduce the weighted-average quantile regression framework, $\int_0^1 q_{Y|X}(u)ψ(u)du = X'β$, where $Y$ is a dependent variable, $X$ is a vector of covariates, $q_{Y|X}$ is the quantile function of the conditional distribution of $Y$ given $X$, $ψ$ is a weighting function, and $β$ is a vector of parameters. We argue that this framework is of interest in many applied settings and develop an estimator of the vector of parameters $β$. We show that our estimator is $\sqrt T$-consistent and asymptotically normal with mean zero and easily estimable covariance matrix, where $T$ is the size of available sample. We demonstrate the usefulness of our estimator by applying it in two empirical settings. In the first setting, we focus on financial data and study the factor structures of the expected shortfalls of the industry portfolios. In the second setting, we focus on wage data and study inequality and social welfare dependence on commonly used individual characteristics.

econ.EM↗

arXiv2021

Biased-sample empirical likelihood weighting: an alternative to inverse probability weighting

Inverse probability weighting (IPW) is widely used in many areas when data are subject to unrepresentativeness, missingness, or selection bias. An inevitable challenge with the use of IPW is that the IPW estimator can be remarkably unstable if some probabilities are very close to zero. To overcome this problem, at least three remedies have been developed in the literature: stabilizing, thresholding, and trimming. However the final estimators are still IPW type estimators, and inevitably inherit certain weaknesses of the naive IPW estimator: they may still be unstable or biased. We propose a biased-sample empirical likelihood weighting (ELW) method to serve the same general purpose as IPW, while completely overcoming the instability of IPW-type estimators by circumventing the use of inverse probabilities. The ELW weights are always well defined and easy to implement. We show theoretically that the ELW estimator is asymptotically normal and more efficient than the IPW estimator and its stabilized version for missing data problems and unequal probability sampling without replacement. Its asymptotic normality is also established under unequal probability sampling with replacement. Our simulation results and a real data analysis indicate that the ELW estimator is shift-equivariant, nearly unbiased, and usually outperforms the IPW-type estimators in terms of mean square error.

stat.ME↗

arXiv2021

Towards hexagonal $C_{2v}$ systems with anisotropic DMI: Characterization of epitaxial Co$(10\bar{1}0)$/Pt$(110)$ multilayer films

Ferromagnet/heavy metal (FM/HM) multilayer thin films with $C_{2v}$ symmetry have the potential to host antiskyrmions and other chiral spin textures via an anisotropic Dzyaloshinkii-Moriya interaction (DMI). Here, we present a candidate material system that also has a strong uniaxial magnetocrystalline anisotropy aligned in the plane of the film. This system is based on a new Co/Pt epitaxial relationship, which is the central focus of this work: hexagonal closed-packed Co$(10\bar{1}0)[0001]$ $\parallel$ face-centered cubic Pt$(110)[001]$. We characterized the crystal structure and magnetic properties of our films using X-ray diffraction techniques and magnetometry respectively, including q-scans to determine stacking fault densities and their correlation with the measured magnetocrystalline anisotropy constant and thickness of Co. In future ultrathin multilayer films, we expect this epitaxial relationship to further enable an anisotropic DMI while supporting interfacial perpendicular magnetic anisotropy. The anticipated confluence of these properties, along with the tunability of multilayer films, make this material system a promising testbed for unveiling new spin configurations in FM/HM films.

cond-mat.mtrl-sci↗

arXiv2021

Score test for missing at random or not

Missing data are frequently encountered in various disciplines and can be divided into three categories: missing completely at random (MCAR), missing at random (MAR) and missing not at random (MNAR). Valid statistical approaches to missing data depend crucially on correct identification of the underlying missingness mechanism. Although the problem of testing whether this mechanism is MCAR or MAR has been extensively studied, there has been very little research on testing MAR versus MNAR.A critical challenge that is faced when dealing with this problem is the issue of model identification under MNAR. In this paper, under a logistic model for the missing probability, we develop two score tests for the problem of whether the missingness mechanism is MAR or MNAR under a parametric model and a semiparametric location model on the regression function. The score tests require only parameter estimation under the null MAR assumption, which completely circumvents the identification issue. Our simulations and analysis of human immunodeficiency virus data show that the score tests have well-controlled type I errors and desirable powers.

stat.ME↗

arXiv2021

Improved Conformer-based End-to-End Speech Recognition Using Neural Architecture Search

Recently neural architecture search(NAS) has been successfully used in image classification, natural language processing, and automatic speech recognition(ASR) tasks for finding the state-of-the-art(SOTA) architectures than those human-designed architectures. NAS can derive a SOTA and data-specific architecture over validation data from a pre-defined search space with a search algorithm. Inspired by the success of NAS in ASR tasks, we propose a NAS-based ASR framework containing one search space and one differentiable search algorithm called Differentiable Architecture Search(DARTS). Our search space follows the convolution-augmented transformer(Conformer) backbone, which is a more expressive ASR architecture than those used in existing NAS-based ASR frameworks. To improve the performance of our method, a regulation method called Dynamic Search Schedule(DSS) is employed. On a widely used Mandarin benchmark AISHELL-1, our best-searched architecture outperforms the baseline Conform model significantly with about 11% CER relative improvement, and our method is proved to be pretty efficient by the search cost comparisons.

eess.AS↗

arXiv2020

A selective review on calibration information from similar studies based on parametric likelihood or empirical likelihood

In multi-center clinical trials, due to various reasons, the individual-level data are strictly restricted to be assessed publicly. Instead, the summarized information is widely available from published results. With the advance of computational technology, it has become very common in data analyses to run on hundreds or thousands of machines simultaneous, with the data distributed across those machines and no longer available in a single central location. How to effectively assemble the summarized clinical data information or information from each machine in parallel computation has become a challenging task for statisticians and computer scientists. In this paper, we selectively review some recently-developed statistical methods, including communication efficient distributed statistical inference, and renewal estimation and incremental inference, which can be regarded as the latest development of calibration information methods in the era of big data. Even though those methods were developed in different fields and in different statistical frameworks, in principle, they are asymptotically equivalent to those well known methods developed in meta analysis. Almost no or little information is lost compared with the case when full data are available. As a general tool to integrate information, we also review the generalized method of moments and estimating equations approach by using empirical likelihood method.

stat.ME↗

arXiv2020

Permutation tests under a rotating sampling plan with clustered data

Consider a population consisting of clusters of sampling units, evolving temporally, spatially, or according to other dynamics. We wish to monitor the evolution of its means, medians, or other parameters. For administrative convenience and informativeness, clustered data are often collected via a rotating plan. Under rotating plans, the observations in the same clusters are correlated, and observations on the same unit collected on different occasions are also correlated. Ignoring this correlation structure may lead to invalid inference procedures. Accommodating cluster structure in parametric models is difficult or will have a high level of misspecification risk. In this paper, we explore exchangeability in clustered data collected via a rotating sampling plan to develop a permutation scheme for testing various hypotheses of interest. We also introduce a semiparametric density ratio model to facilitate the multiple population structure in rotating sampling plans. The combination ensures the validity of the inference methods while extracting maximum information from the sampling plan. A simulation study indicates that the proposed tests firmly control the type I error whether or not the data are clustered. The use of the density ratio model improves the power of the tests.

stat.ME↗

arXiv2019

Full-semiparametric-likelihood-based inference for non-ignorable missing data

During the past few decades, missing-data problems have been studied extensively, with a focus on the ignorable missing case, where the missing probability depends only on observable quantities. By contrast, research into non-ignorable missing data problems is quite limited. The main difficulty in solving such problems is that the missing probability and the regression likelihood function are tangled together in the likelihood presentation, and the model parameters may not be identifiable even under strong parametric model assumptions. In this paper we discuss a semiparametric model for non-ignorable missing data and propose a maximum full semiparametric likelihood estimation method, which is an efficient combination of the parametric conditional likelihood and the marginal nonparametric biased sampling likelihood. The extra marginal likelihood contribution can not only produce efficiency gain but also identify the underlying model parameters without additional assumptions. We further show that the proposed estimators for the underlying parameters and the response mean are semiparametrically efficient. Extensive simulations and a real data analysis demonstrate the advantage of the proposed method over competing methods.

stat.ME↗

arXiv2018

Inference for case-control studies with incident and prevalent cases

We propose and study a fully efficient method to estimate associations of an exposure with disease incidence when both, incident cases and prevalent cases, i.e. individuals who were diagnosed with the disease at some prior time point and are alive at the time of sampling, are included in a case-control study. We extend the exponential tilting model for the relationship between exposure and case status to accommodate two case groups, and correct for the survival bias in the prevalent cases through a tilting term that depends on the parametric distribution of the backward time, i.e. the time from disease diagnosis to study enrollment. We construct an empirical likelihood that also incorporates the observed backward times for prevalent cases, obtain efficient estimates of odds ratio parameters that relate exposure to disease incidence and propose a likelihood ratio test for model parameters that has a standard chi-squared distribution. We quantify the changes in efficiency of association parameters when incident cases are supplemented with, or replaced by, prevalent cases in simulations. We illustrate our methods by estimating associations of single nucleotide polymorphisms (SNPs) with breast cancer incidence in a sample of controls and incident and prevalent cases from the U.S. Radiologic Technologists Health Study.

stat.ME↗

arXiv2017

Small Area Quantile Estimation

Sample surveys are widely used to obtain information about totals, means, medians, and other parameters of finite populations. In many applications, similar information is desired for subpopulations such as individuals in specific geographic areas and socio-demographic groups. When the surveys are conducted at national or similarly high levels, a probability sampling can result in just a few sampling units from many unplanned subpopulations at the design stage. Cost considerations may also lead to low sample sizes from individual small areas. Estimating the parameters of these subpopulations with satisfactory precision and evaluating their accuracy are serious challenges for statisticians. To overcome the difficulties, statisticians resort to pooling information across the small areas via suitable model assumptions, administrative archives, and census data. In this paper, we develop an array of small area quantile estimators. The novelty is the introduction of a semiparametric density ratio model for the error distribution in the unit-level nested error regression model. In contrast, the existing methods are usually most effective when the response values are jointly normal. We also propose a resampling procedure for estimating the mean square errors of these estimators. Simulation results indicate that the new methods have superior performance when the population distributions are skewed and remain competitive otherwise.

stat.ME↗

arXiv2013

Quantile and quantile-function estimations under density ratio model

Population quantiles and their functions are important parameters in many applications. For example, the lower quantiles often serve as crucial quality indices for forestry products. Given several independent samples from populations satisfying the density ratio model, we investigate the properties of empirical likelihood (EL) based inferences. The induced EL quantile estimators are shown to admit a Bahadur representation that leads to asymptotically valid confidence intervals for functions of quantiles. We rigorously prove that EL quantiles based on all the samples are more efficient than empirical quantiles based on individual samples. A simulation study shows that the EL quantiles and their functions have superior performance when the density ratio model assumption is satisfied and when it is mildly violated. An example is used to demonstrate the new method and the potential cost savings.

math.ST↗

arXiv2010

Adjusted empirical likelihood with high-order precision

Empirical likelihood is a popular nonparametric or semi-parametric statistical method with many nice statistical properties. Yet when the sample size is small, or the dimension of the accompanying estimating function is high, the application of the empirical likelihood method can be hindered by low precision of the chi-square approximation and by nonexistence of solutions to the estimating equations. In this paper, we show that the adjusted empirical likelihood is effective at addressing both problems. With a specific level of adjustment, the adjusted empirical likelihood achieves the high-order precision of the Bartlett correction, in addition to the advantage of a guaranteed solution to the estimating equations. Simulation results indicate that the confidence regions constructed by the adjusted empirical likelihood have coverage probabilities comparable to or substantially more accurate than the original empirical likelihood enhanced by the Bartlett correction.

math.ST↗