Closed-form estimators are useful when parametric models are repeatedly refitted but likelihood maximization is iterative. We study a likelihood-derived construction of auxiliary estimating equations obtained by differentiating a positive auxiliary function and centering the derivatives under a baseline model. The resulting estimators are just-identified Z-estimators, or equivalently GMM estimators; the contribution is a constructive route to explicitly invertible equations rather than a replacement for general estimating-equation theory. We establish local existence, uniqueness and asymptotic normality of the selected root, characterize optimal linear combinations through Godambe information, and give constrained variants and influence-function diagnostics. Transformed exponential families, Beta, Weibull AFT regression, Wishart covariance estimation, zero-inflated counts, tail modelling and copula dependence illustrate the construction. Simulations and survival-tree split screening quantify the statistical-computational trade-off.
The density ratio model (DRM) provides a flexible and useful platform for combining information from multiple sources. In this paper, we consider statistical inference under two-sample DRMs with additional parameters defined through and/or additional auxiliary information expressed as estimating equations. We examine the asymptotic properties of the maximum empirical likelihood estimators (MELEs) of the unknown parameters in the DRMs and/or defined through estimating equations, and establish the chi-square limiting distributions for the empirical likelihood ratio (ELR) statistics. We show that…
Marginal model is a popular instrument for studying longitudinal data and cluster data. This paper investigates the estimator of marginal model with subgroup auxiliary information. To marginal model, we propose a new type of auxiliary information, and combine them with the traditional estimating equations of the quadratic inference function (QIF) method based on the generalized method of moments (GMM). Thus obtaining a more efficient estimator. The asymptotic normality and the test statistics of the proposed estimator are established. The theoretical result shows that the estimator with subgro…
In this paper, we propose a transformed naïve ratio and product based estimators using the characterizing scalar in presence of auxiliary information of the study variable for estimating the population mode following simple random sampling without replacement. The bias, mean square errors, relative efficiency, ratios of the exact values of mean square errors to the simulated mean square errors and confidence interval are studied for the performance of the proposed transformed naïve ratio type estimator with the certain natural population as well as artificially generated data sets. We have sho…
We establish a general framework for statistical inferences with non-probability survey samples when relevant auxiliary information is available from a probability survey sample. We develop a rigorous procedure for estimating the propensity scores for units in the non-probability sample, and construct doubly robust estimators for the finite population mean. Variance estimation is discussed under the proposed framework. Results from simulation studies show the robustness and the efficiency of our proposed estimators as compared to existing methods. The proposed method is used to analyze a non-p…
Missing data is a common challenge in biomedical research. This fact, along with growing dataset volumes of the modern era, make the issue of computationally-efficient analysis with missing data of crucial practical importance. A general computationally-efficient estimation framework for dealing with missing data is the pseudo-expected estimating equations (PEEE) approach. The method is applicable with any parametric model for which estimation involves the solution of a set of estimating equations, such as likelihood score equations. A key limitation of the PEEE approach is that there is curre…
This paper focuses on drawing statistical inference based on a novel variant of maxima or minima nomination sampling (NS) designs. These sampling designs are useful for obtaining more representative sample units from the tails of the population distribution using the available auxiliary ranking information. However, one common difficulty in performing NS in practice is that the researcher cannot obtain a nominated sample unless he/she uniquely determines the sample unit with the highest or the lowest rank in each set. To overcome this problem, a variant of NS which is called partial nomination…
It has recently become popular to define treatment effects for subsets of the target population characterized by variables not observable at the time a treatment decision is made. Characterizing and estimating such treatment effects is tricky; the most popular but naive approach inappropriately adjusts for variables affected by treatment and so is biased. We consider several appropriate ways to formalize the effects: principal stratification, stratification on a single potential auxiliary variable, stratification on an observed auxiliary variable and stratification on expected levels of auxili…
Transfer learning for high-dimensional Gaussian graphical models (GGMs) is studied with the goal of estimating the target GGM by utilizing the data from similar and related auxiliary studies. The similarity between the target graph and each auxiliary graph is characterized by the sparsity of a divergence matrix. An estimation algorithm, Trans-CLIME, is proposed and shown to attain a faster convergence rate than the minimax rate in the single study setting. Furthermore, a debiased Trans-CLIME estimator is introduced and shown to be element-wise asymptotically normal. It is used to construct a m…
Currently, the high-precision estimation of nonlinear parameters such as Gini indices, low-income proportions or other measures of inequality is particularly crucial. In the present paper, we propose a general class of estimators for such parameters that take into account univariate auxiliary information assumed to be known for every unit in the population. Through a nonparametric model-assisted approach, we construct a unique system of survey weights that can be used to estimate any nonlinear parameter associated with any study variable of the survey, using a plug-in principle. Based on a rig…
The Current Population Survey is the gold-standard data source for studying who turns out to vote in elections. However, it suffers from potentially nonignorable unit and item nonresponse. Fortunately, after elections, the total number of voters is known from administrative sources and can be used to adjust for potential nonresponse bias. We present a model-based approach to utilize this known voter turnout rate, as well as other population marginal distributions of demographic variables, in multiple imputation for unit and item nonresponse. In doing so, we ensure that the imputations produce …
We study nonparametric estimation of an unknown density function $f$ based on the ranked-based observations obtained from a partially rank-ordered set (PROS) sampling design. PROS sampling design has many applications in environmental, ecological and medical studies where the exact measurement of the variable of interest is costly but a small number of sampling units can be ordered with respect to the variable of interest by any means other than actual measurements and this can be done at low cost. PROS observations involve independent order statistics which are not identically distributed and…
Transfer learning has drawn growing attention with the target of improving statistical efficiency of one study (dataset) by digging information from similar and related auxiliary studies (datasets). In the article, we consider transfer learning problem in estimating undirected semi-parametric graphical model. We propose an algorithm called Trans-Copula-CLIME for estimating undirected graphical model while digging information from similar auxiliary studies, characterizing the similarity between the target graph and each auxiliary graph by the sparsity of a divergence matrix. The proposed method…
A model-assisted semiparametric method of estimating finite population totals is investigated to improve the precision of survey estimators by incorporating multivariate auxiliary information. The proposed superpopulation model is a single-index model which has proven to be a simple and efficient semiparametric tool in multivariate regression. A class of estimators based on polynomial spline regression is proposed. These estimators are robust against deviation from single-index models. Under standard design conditions, the proposed estimators are asymptotically design-unbiased, consistent and …
Indirect inference (II) is a methodology for estimating the parameters of an intractable (generative) model on the basis of an alternative parametric (auxiliary) model that is both analytically and computationally easier to deal with. Such an approach has been well explored in the classical literature but has received substantially less attention in the Bayesian paradigm. The purpose of this paper is to compare and contrast a collection of what we call parametric Bayesian indirect inference (pBII) methods. One class of pBII methods uses approximate Bayesian computation (referred to here as ABC…
We propose, implement, and evaluate a method to estimate the daily number of new symptomatic COVID-19 infections, at the level of individual U.S. counties, by deconvolving daily reported COVID-19 case counts using an estimated symptom-onset-to-case-report delay distribution. Importantly, we focus on estimating infections in real-time (rather than retrospectively), which poses numerous challenges. To address these, we develop new methodology for both the distribution estimation and deconvolution steps, and we employ a sensor fusion layer (which fuses together predictions from models that are tr…
RWTH Aachen University（亚琛工业大学）；University of Edinburgh（爱丁堡大学）
Many parametric statistical models are not properly normalised and only specified up to an intractable partition function, which renders parameter estimation difficult. Examples of unnormalised models are Gibbs distributions, Markov random fields, and neural network models in unsupervised deep learning. In previous work, the estimation principle called noise-contrastive estimation (NCE) was introduced where unnormalised models are estimated by learning to distinguish between data and auxiliary noise. An open question is how to best choose the auxiliary noise distribution. We here propose a new…
Correlated outcomes are common in many practical problems. In some settings, one outcome is of particular interest, and others are auxiliary. To leverage information shared by all the outcomes, traditional multi-task learning (MTL) minimizes an averaged loss function over all the outcomes, which may lead to biased estimation for the target outcome, especially when the MTL model is mis-specified. In this work, based on a decomposition of estimation bias into two types, within-subspace and against-subspace, we develop a robust transfer learning approach to estimating a high-dimensional linear de…
The article considers the problem of estimating a high-dimensional sparse parameter in the presence of side information that encodes the sparsity structure. We develop a general framework that involves first using an auxiliary sequence to capture the side information, and then incorporating the auxiliary sequence in inference to reduce the estimation risk. The proposed method, which carries out adaptive SURE-thresholding using side information (ASUS), is shown to have robust performance and enjoy optimality properties. We develop new theories to characterize regimes in which ASUS far outperfor…
We present a method for estimating causal effects in time series data when fine-grained information about the outcome of interest is available. Specifically, we examine what we call the split-door setting, where the outcome variable can be split into two parts: one that is potentially affected by the cause being studied and another that is independent of it, with both parts sharing the same (unobserved) confounders. We show that under these conditions, the problem of identification reduces to that of testing for independence among observed variables, and present a method that uses this approac…
In surveys, the interest lies in estimating finite population parameters such as population totals and means. In most surveys, some auxiliary information is available at the estimation stage. This information may be incorporated in the estimation procedures to increase their precision. In this article, we use random forests to estimate the functional relationship between the survey variable and the auxiliary variables. In recent years, random forests have become attractive as National Statistical Offices have now access to a variety of data sources, potentially exhibiting a large number of obs…
The present paper discusses the problem of estimating the finite population mean of study variable in simple random sampling in the presence of non response and response error together. The estimators in this article use auxiliary information to improve efficiency and we suppose that non response and measurement error are present in both the study and auxiliary variables. A class of estimators has been proposed and its properties are studied in the simultaneous presence of non-response and response errors. It has been shown that proposed class of estimators is more efficient than the usual unb…
We consider the problem of estimating parameters of stochastic differential equations (SDEs) with discrete-time observations that are either completely or partially observed. The transition density between two observations is generally unknown. We propose an importance sampling approach with an auxiliary parameter when the transition density is unknown. We embed the auxiliary importance sampler in a penalized maximum likelihood framework which produces more accurate and computationally efficient parameter estimates. Simulation studies in three different models illustrate promising improvements…
In observational studies, instrumental variable (IV) methods are commonly applied when there exists some unmeasured covariates. In Mendelian Randomization (MR), constructing an allele score by using many single nucleotide polymorphisms (SNPs) is often implemented; however, there are risks estimating biased causal effects by including some invalid IVs. Invalid IVs are candidates of IVs associated with some unobserved variables. To solve this problem, we propose a novel strategy in this paper: using Negative Control Outcomes (NCOs) as auxiliary variables. By using NCOs, we can essentialy select …
This paper introduces an alternative procedure for estimating the prevalence of international migration at the municipal level in Colombia. The new methodology uses the empirical best linear unbiased predictor based on a Fay-Herriot model with target and auxiliary variables available from census studies and from the Demographic and Health Survey. The proposed alternative produces prevalence estimates which are consistent with sample sizes and demographic dynamics in Colombia. Additionally, the estimated coefficients of variation are lower than 20% for municipalities and large demographically-r…
