arXiv subjects

Jiming Jiang

Publications and source records attributed to Jiming Jiang.

14 recordsLinked to original sources

arXiv2025

Post-2024 U.S. Presidential Election Analysis of Election and Poll Data: Real-life Validation of Prediction via Small Area Estimation and Uncertainty Quantification

We carry out a post-election analysis of the 2024 U.S. Presidential Election (USPE) using a prediction model derived from the Small Area Estimation (SAE) methodology. With pollster data obtained one week prior to the election day, retrospectively, our SAE-based prediction model can perfectly predict the Electoral College election results in all 44 states where polling data were available. In addition to such desirable prediction accuracy, we introduce the probability of incorrect prediction (PoIP) to rigorously analyze prediction uncertainty. Since the standard bootstrap method appears inadequate for estimating PoIP, we propose a conformal inference method that yields reliable uncertainty quantification. We further investigate potential pollster biases by the means of sensitivity analyses and conclude that swing states are particularly vulnerable to polling bias in the prediction of the 2024 USPE.

stat.AP↗

arXiv2024

A Random-Effects Approach to Generalized Linear Mixed Model Analysis of Incomplete Longitudinal Data

We propose a random-effects approach to missing values for generalized linear mixed model (GLMM) analysis. The method converts a GLMM with missing covariates to another GLMM without missing covariates. The standard GLMM analysis tools for longitudinal data then apply. The method applies, in particular, to the cases of linear mixed models and logistic regression. Performance of the method is evaluated empirically, and compared with alternative approaches, including the popular MICE procedure of multiple imputation. Theoretical justification of the method is given, and explained, for the patterns observed in the simulation studies. Two real-data examples from healthcare studies are discussed.

stat.ME↗

arXiv2024

A Random-effects Approach to Regression Involving Many Categorical Predictors and Their Interactions

Linear model prediction with a large number of potential predictors is both statistically and computationally challenging. The traditional approaches are largely based on shrinkage selection/estimation methods, which are applicable even when the number of potential predictors is (much) larger than the sample size. A situation of the latter scenario occurs when the candidate predictors involve many binary indicators corresponding to categories of some categorical predictors as well as their interactions. We propose an alternative approach to the shrinkage prediction methods in such a case based on mixed model prediction, which effectively treats combinations of the categorical effects as random effects. We establish theoretical validity of the proposed method, and demonstrate empirically its advantage over the shrinkage methods. We also develop measures of uncertainty for the proposed method and evaluate their performance empirically. A real-data example is considered.

stat.ME↗

arXiv2024

Precise Asymptotics for Linear Mixed Models with Crossed Random Effects

We obtain an asymptotic normality result that reveals the precise asymptotic behavior of the maximum likelihood estimators of parameters for a very general class of linear mixed models containing cross random effects. In achieving the result, we overcome theoretical difficulties that arise from random effects being crossed as opposed to the simpler nested random effects case. Our new theory is for a class of Gaussian response linear mixed models which includes crossed random slopes that partner arbitrary multivariate predictor effects and does not require the cell counts to be balanced. Statistical utilities include confidence interval construction, Wald hypothesis test and sample size calculations.

math.ST↗

arXiv2023

Building A Theoretical Foundation for Combining Negative Controls and Replicates

Studies using assays to quantify the expression of thousands of genes on tens to thousands of cell samples have been carried out for over 20 years. Such assays are based on microarrays, DNA sequencing or other molecular technologies. All such studies involve unwanted variation, often called batch effects, associated with the cell samples and the assay process. Removing this unwanted variation is essential before the measurements can be used to address the questions that motivated the studies. Combining the results of replicate assays with measurements on negative control genes to estimate the unwanted variation and remove it has proved to be effective at this task. The main goal of this paper is to present asymptotic theory that explains this effectiveness. The approach can be widened by using pseudo-replicate sets of pseudo-samples, for use with studies having no replicate assays. Theory covering this case is also presented. The established theory is supported by results of empirical investigations, including simulation studies and a real-data example.

math.ST↗

arXiv2021

Variance Estimation and Confidence Intervals from High-dimensional Genome-wide Association Studies Through Misspecified Mixed Model Analysis

We study variance estimation and associated confidence intervals for parameters characterizing genetic effects from genome-wide association studies (GWAS) misspecified mixed model analysis. Previous studies have shown that, in spite of the model misspecification, certain quantities of genetic interests are estimable, and consistent estimators of these quantities can be obtained using the restricted maximum likelihood (REML) method under a misspecified linear mixed model. However, the asymptotic variance of such a REML estimator is complicated and not ready to be implemented for practical use. In this paper, we develop practical and computationally convenient methods for estimating such asymptotic variances and constructing the associated confidence intervals. Performance of the proposed methods is evaluated empirically based on Monte-Carlo simulations and real-data application.

stat.ME↗

arXiv2018

Subsampled Optimization: Statistical Guarantees, Mean Squared Error Approximation, and Sampling Method

For optimization on large-scale data, exactly calculating its solution may be computationally difficulty because of the large size of the data. In this paper we consider subsampled optimization for fast approximating the exact solution. In this approach, one gets a surrogate dataset by sampling from the full data, and then obtains an approximate solution by solving the subsampled optimization based on the surrogate. One main theoretical contributions are to provide the asymptotic properties of the approximate solution with respect to the exact solution as statistical guarantees, and to rigorously derive an accurate approximation of the mean squared error (MSE) and an approximately unbiased MSE estimator. These results help us better diagnose the subsampled optimization in the context that a confidence region on the exact solution is provided using the approximate solution. The other consequence of our results is to propose an optimal sampling method, Hessian-based sampling, whose probabilities are proportional to the norms of Newton directions. Numerical experiments with least-squares and logistic regression show promising performance, in line with our results.

stat.ML↗

arXiv2016

A Unified Monte-Carlo Jackknife for Small Area Estimation after Model Selection

We consider estimation of measure of uncertainty in small area estimation (SAE) when a procedure of model selection is involved prior to the estimation. A unified Monte-Carlo jackknife method, called McJack, is proposed for estimating the logarithm of the mean squared prediction error. We prove the second-order unbiasedness of McJack, and demonstrate the performance of McJack in assessing uncertainty in SAE after model selection through empirical investigations that include simulation studies and real-data analyses.

stat.CO↗

arXiv2014

High-dimensional genome-wide association study and misspecified mixed model analysis

We study behavior of the restricted maximum likelihood (REML) estimator under a misspecified linear mixed model (LMM) that has received much attention in recent gnome-wide association studies. The asymptotic analysis establishes consistency of the REML estimator of the variance of the errors in the LMM, and convergence in probability of the REML estimator of the variance of the random effects in the LMM to a certain limit, which is equal to the true variance of the random effects multiplied by the limiting proportion of the nonzero random effects present in the LMM. The aymptotic results also establish convergence rate (in probability) of the REML estimators as well as a result regarding convergence of the asymptotic conditional variance of the REML estimator. The asymptotic results are fully supported by the results of empirical studies, which include extensive simulation studies that compare the performance of the REML estimator (under the misspecified LMM) with other existing methods.

math.ST↗

arXiv2013

The subset argument and consistency of MLE in GLMM: Answer to an open problem and beyond

We give answer to an open problem regarding consistency of the maximum likelihood estimators (MLEs) in generalized linear mixed models (GLMMs) involving crossed random effects. The solution to the open problem introduces an interesting, nonstandard approach to proving consistency of the MLEs in cases of dependent observations. Using the new technique, we extend the results to MLEs under a general GLMM. An example is used to further illustrate the technique.

math.ST↗

arXiv2008

Fence methods for mixed model selection

Many model search strategies involve trading off model fit with model complexity in a penalized goodness of fit measure. Asymptotic properties for these types of procedures in settings like linear regression and ARMA time series have been studied, but these do not naturally extend to nonstandard situations such as mixed effects models, where simple definition of the sample size is not meaningful. This paper introduces a new class of strategies, known as fence methods, for mixed model selection, which includes linear and generalized linear mixed models. The idea involves a procedure to isolate a subgroup of what are known as correct models (of which the optimal model is a member). This is accomplished by constructing a statistical fence, or barrier, to carefully eliminate incorrect models. Once the fence is constructed, the optimal model is selected from among those within the fence according to a criterion which can be made flexible. In addition, we propose two variations of the fence. The first is a stepwise procedure to handle situations of many predictors; the second is an adaptive approach for choosing a tuning constant. We give sufficient conditions for consistency of fence and its variations, a desirable property for a good model selection procedure. The methods are illustrated through simulation studies and real data analysis.

math.ST↗

arXiv2007

Iterative estimating equations: Linear convergence and asymptotic properties

We propose an iterative estimating equations procedure for analysis of longitudinal data. We show that, under very mild conditions, the probability that the procedure converges at an exponential rate tends to one as the sample size increases to infinity. Furthermore, we show that the limiting estimator is consistent and asymptotically efficient, as expected. The method applies to semiparametric regression models with unspecified covariances among the observations. In the special case of linear models, the procedure reduces to iterative reweighted least squares. Finite sample performance of the procedure is studied by simulations, and compared with other methods. A numerical example from a medical study is considered to illustrate the application of the method.

math.ST↗

arXiv2006

Partially observed information and inference about non-Gaussian mixed linear models

In mixed linear models with nonnormal data, the Gaussian Fisher information matrix is called a quasi-information matrix (QUIM). The QUIM plays an important role in evaluating the asymptotic covariance matrix of the estimators of the model parameters, including the variance components. Traditionally, there are two ways to estimate the information matrix: the estimated information matrix and the observed one. Because the analytic form of the QUIM involves parameters other than the variance components, for example, the third and fourth moments of the random effects, the estimated QUIM is not available. On the other hand, because of the dependence and nonnormality of the data, the observed QUIM is inconsistent. We propose an estimator of the QUIM that consists partially of an observed form and partially of an estimated one. We show that this estimator is consistent and computationally very easy to operate. The method is used to derive large sample tests of statistical hypotheses that involve the variance components in a non-Gaussian mixed linear model. Finite sample performance of the test is studied by simulations and compared with the delete-group jackknife method that applies to a special case of non-Gaussian mixed linear models.

math.ST↗

arXiv2004

Mean squared error of empirical predictor

The term ``empirical predictor'' refers to a two-stage predictor of a linear combination of fixed and random effects. In the first stage, a predictor is obtained but it involves unknown parameters; thus, in the second stage, the unknown parameters are replaced by their estimators. In this paper, we consider mean squared errors (MSE) of empirical predictors under a general setup, where ML or REML estimators are used for the second stage. We obtain second-order approximation to the MSE as well as an estimator of the MSE correct to the same order. The general results are applied to mixed linear models to obtain a second-order approximation to the MSE of the empirical best linear unbiased predictor (EBLUP) of a linear mixed effect and an estimator of the MSE of EBLUP whose bias is correct to second order. The general mixed linear model includes the mixed ANOVA model and the longitudinal model as special cases.

math.ST↗