Bias–variance and breadth–depth tradeoffs in respondent-driven sampling

Respondent-driven sampling (RDS) is a link-tracing network sampling strategy for collecting data from hard-to-reach populations, such as injection drug users or individuals at high risk of being infected with HIV. The mechanism is to find initial participants (seeds), and give each of them a fixed number of coupons allowing them to recruit people they know from the population of interest, with a mutual financial incentive. The new participants are again given coupons and the process repeats. Currently, the standard RDS estimator used in practice is known as the Volz–Heckathorn (VH) estimator. It relies on strong assumptions about the underlying social network and the RDS process. Via simulation, we study the relative performance of the plain mean and VH estimators when assumptions of the latter are not satisfied, under different network types (including homophily and rich-get-richer networks), participant referral patterns, and varying number of coupons. The analysis demonstrates that the plain mean outperforms the VH estimator in many but not all of the simulated settings, including homophily networks. Also, we highlight the implications of multiple recruitment and varying referral patterns on the depth of RDS process. We develop interactive visualizations of the findings and RDS process to further build insight into the various factors contributing to the performance of current RDS estimation techniques.     

Inference in Approximately Sparse Correlated Random Effects Probit Models With Panel Data

Abstract

We propose a simple procedure based on an existing “debiased” l₁-regularized method for inference of the average partial effects (APEs) in approximately sparse probit and fractional probit models with panel data, where the number of time periods is fixed and small relative to the number of cross-sectional observations. Our method is computationally simple and does not suffer from the incidental parameters problems that come from attempting to estimate as a parameter the unobserved heterogeneity for each cross-sectional unit. Furthermore, it is robust to arbitrary serial dependence in underlying idiosyncratic errors. Our theoretical results illustrate that inference concerning APEs is more challenging than inference about fixed and low-dimensional parameters, as the former concerns deriving the asymptotic normality for sample averages of linear functions of a potentially large set of components in our estimator when a series approximation for the conditional mean of the unobserved heterogeneity is considered. Insights on the applicability and implications of other existing Lasso-based inference procedures for our problem are provided. We apply the debiasing method to estimate the effects of spending on test pass rates. Our results show that spending has a positive and statistically significant average partial effect; moreover, the effect is comparable to found using standard parametric methods.     

Unified Inference for Sparse and Dense Longitudinal Data in Time‐varying Coefficient Models

Time‐varying coefficient models are widely used in longitudinal data analysis. These models allow the effects of predictors on response to vary over time. In this article, we consider a mixed‐effects time‐varying coefficient model to account for the within subject correlation for longitudinal data. We show that when kernel smoothing is used to estimate the smooth functions in time‐varying coefficient models for sparse or dense longitudinal data, the asymptotic results of these two situations are essentially different. Therefore, a subjective choice between the sparse and dense cases might lead to erroneous conclusions for statistical inference. In order to solve this problem, we establish a unified self‐normalized central limit theorem, based on which a unified inference is proposed without deciding whether the data are sparse or dense. The effectiveness of the proposed unified inference is demonstrated through a simulation study and an analysis of Baltimore MACS data.     

A two-stage estimation for panel data models with grouped fixed effects

ABSTRACT

This paper considers panel data models with fixed effects which have grouped patterns with unknown group membership. A two-stage estimation (TSE) procedure is developed to improve the properties of the GFE estimators of common parameters when the time span is small. Firstly, the common parameters are estimated. Subsequently, the optimal group assignment and the estimators of group effects are obtained by the K-means algorithm. Monte Carlo results reveal that the TSE estimator has a much smaller bias than the GFE estimator when the values of difference between effects are moderately small or at high variance of the idiosyncratic error.     

Parameter estimation by minimizing a probability generating function-based power divergence

Abstract

Generating function-based statistical inference is an attractive approach if the probability (density) function is complicated when compared with the generating function. Here, we propose a parameter estimation method that minimizes a probability generating function (pgf)-based power divergence with a tuning parameter to mitigate the impact of data contamination. The proposed estimator is linked to the M-estimators and hence possesses the properties of consistency and asymptotic normality. In terms of parameter biases and mean squared errors from simulations, the proposed estimation method performs better for smaller value of the tuning parameter as data contamination percentage increases.     

固定效应部分线性变系数面板模型的快速有效估计

本文将最小二乘支持向量机(LSSVM) 和二次推断函数法(QIF) 相结合，为个体内具有相关结构的固定效应部分线性变系数面板模型提供了一种新的快速估计方法；在一定的正则条件下，论证了参数估计量的渐近正态性和非参数估计量的收敛速度；采用Monte Carlo模拟考察了估计方法在有限样本下的表现并将估计技术应用于现实数据分析。该方法不仅保证了估计的有效性和统计推断力，而且程序运行速度得到较大幅度提升。     

Oracally efficient spline-backfitted kernel smoothing of additive partial linear measurement error model

Abstract

We consider statistical inference for additive partial linear models when the linear covariate is measured with error. A bias-corrected spline-backfitted kernel smoothing method is proposed. Under mild assumptions, the proposed component function and parameter estimator are oracally efficient and fast to compute. The nonparametric function estimator’s pointwise distribution is asymptotically equivalent to an function estimator in partial linear model. Finite-sample performance of the proposed estimators is assessed by simulation experiments. The proposed methods are applied to Boston house data set.     

Modified Profile Likelihood for Fixed-Effects Panel Data Models

We show how modified profile likelihood methods, developed in the statistical literature, may be effectively applied to estimate the structural parameters of econometric models for panel data, with a remarkable reduction of bias with respect to ordinary likelihood methods. Initially, the implementation of these methods is illustrated for general models for panel data including individual-specific fixed effects and then, in more detail, for the truncated linear regression model and dynamic regression models for binary data formulated along with different specifications. Simulation studies show the good behavior of the inference based on the modified profile likelihood, even when compared to an ideal, although infeasible, procedure (in which the fixed effects are known) and also to alternative estimators existing in the econometric literature. The proposed estimation methods are implemented in an R package that we make available to the reader.     

Estimation and Inference for Linear Panel Data Models Under Misspecification When Both n and T are Large

This article considers fixed effects (FE) estimation for linear panel data models under possible model misspecification when both the number of individuals, n, and the number of time periods, T, are large. We first clarify the probability limit of the FE estimator and argue that this probability limit can be regarded as a pseudo-true parameter. We then establish the asymptotic distributional properties of the FE estimator around the pseudo-true parameter when n and T jointly go to infinity. Notably, we show that the FE estimator suffers from the incidental parameters bias of which the top order is O(T^{? 1}), and even after the incidental parameters bias is completely removed, the rate of convergence of the FE estimator depends on the degree of model misspecification and is either (nT)^{? 1/2} or n^{? 1/2}. Second, we establish asymptotically valid inference on the (pseudo-true) parameter. Specifically, we derive the asymptotic properties of the clustered covariance matrix (CCM) estimator and the cross-section bootstrap, and show that they are robust to model misspecification. This establishes a rigorous theoretical ground for the use of the CCM estimator and the cross-section bootstrap when model misspecification and the incidental parameters bias (in the coefficient estimate) are present. We conduct Monte Carlo simulations to evaluate the finite sample performance of the estimators and inference methods, together with a simple application to the unemployment dynamics in the U.S.     

On bias reduction estimators of skew-normal and skew-t distributions

A particular concerns of researchers in statistical inference is bias in parameters estimation. Maximum likelihood estimators are often biased and for small sample size, the first order bias of them can be large and so it may influence the efficiency of the estimator. There are different methods for reduction of this bias. In this paper, we proposed a modified maximum likelihood estimator for the shape parameter of two popular skew distributions, namely skew-normal and skew-t, by offering a new method. We show that this estimator has lower asymptotic bias than the maximum likelihood estimator and is more efficient than those based on the existing methods.     

A Novel Bayesian Parameter Mapping Method for Estimating the Parameters of an Underlying Scientific Model

Population-parameter mapping (PPM) is a method for estimating the parameters of latent scientific models that describe the statistical likelihood function. The PPM method involves a Bayesian inference in terms of the statistical parameters and the mapping from the statistical parameter space to the parameter space of the latent scientific parameters, and obtains a model coherence estimate, P(coh). The P(coh) statistic can be valuable for designing experiments, comparing competing models, and can be helpful in redesigning flawed models. Examples are provided where greater estimation precision was found for small sample sizes for the PPM point estimates relative to the maximum likelihood estimator (MLE).     

A powerful test for Balaam's design

The crossover trial design (AB/BA design) is often used to compare the effects of two treatments in medical science because it performs within‐subject comparisons, which increase the precision of a treatment effect (i.e., a between‐treatment difference). However, the AB/BA design cannot be applied in the presence of carryover effects and/or treatments‐by‐period interaction. In such cases, Balaam's design is a more suitable choice. Unlike the AB/BA design, Balaam's design inflates the variance of an estimate of the treatment effect, thereby reducing the statistical power of tests. This is a serious drawback of the design. Although the variance of parameter estimators in Balaam's design has been extensively studied, the estimators of the treatment effect to improve the inference have received little attention. If the estimate of the treatment effect is obtained by solving the mixed model equations, the AA and BB sequences are excluded from the estimation process. In this study, we develop a new estimator of the treatment effect and a new test statistic using the estimator. The aim is to improve the statistical inference in Balaam's design. Simulation studies indicate that the type I error of the proposed test is well controlled, and that the test is more powerful and has more suitable characteristics than other existing tests when interactions are substantial. The proposed test is also applied to analyze a real dataset. Copyright © 2015 John Wiley & Sons, Ltd.     

Asymptotic theory and inference of predictive mean matching imputation using a superpopulation model framework

Predictive mean matching imputation is popular for handling item nonresponse in survey sampling. In this article, we study the asymptotic properties of the predictive mean matching estimator for finite-population inference using a superpopulation model framework. We also clarify conditions for its robustness. For variance estimation, the conventional bootstrap inference is invalid for matching estimators with a fixed number of matches due to the nonsmoothness nature of the matching estimator. We propose a new replication variance estimator, which is asymptotically valid. The key strategy is to construct replicates directly based on the linear terms of the martingale representation for the matching estimator, instead of individual records of variables. Simulation studies confirm that the proposed method provides valid inference.     

Statistical inference for generalized case-cohort design under the proportional hazards model with parameter constraints

ABSTRACT

The generalized case-cohort design is widely used in large cohort studies to reduce the cost and improve the efficiency. Taking prior information of parameters into consideration in modeling process can further raise the inference efficiency. In this paper, we consider fitting proportional hazards model with constraints for generalized case-cohort studies. We establish a working likelihood function for the estimation of model parameters. The asymptotic properties of the proposed estimator are derived via the Karush-Kuhn-Tucker conditions, and their finite properties are assessed by simulation studies. A modified minorization-maximization algorithm is developed for the numerical calculation of the constrained estimator. An application to a Wilms tumor study demonstrates the utility of the proposed method in practice.     

Testing for Slope Heterogeneity Bias in Panel Data Models

ABSTRACT

Standard econometric methods can overlook individual heterogeneity in empirical work, generating inconsistent parameter estimates in panel data models. We propose the use of methods that allow researchers to easily identify, quantify, and address estimation issues arising from individual slope heterogeneity. We first characterize the bias in the standard fixed effects estimator when the true econometric model allows for heterogeneous slope coefficients. We then introduce a new test to check whether the fixed effects estimation is subject to heterogeneity bias. The procedure tests the population moment conditions required for fixed effects to consistently estimate the relevant parameters in the model. We establish the limiting distribution of the test and show that it is very simple to implement in practice. Examining firm investment models to showcase our approach, we show that heterogeneity bias-robust methods identify cash flow as a more important driver of investment than previously reported. Our study demonstrates analytically, via simulations, and empirically the importance of carefully accounting for individual specific slope heterogeneity in drawing conclusions about economic behavior.     

Econometric Reviews

This paper considers the problem of estimating a nonlinear statistical model subject to stochastic linear constraints among unknown parameters. These constraints represent prior information which originates from a previous estimation of the same model using an alternative database. One feature of this specification allows for the disign matrix of stochastic linear restrictions to be estimated. The mixed regression technique and the maximum likelihood approach are used to derive the estimator for both the model coefficients and the unknown elements of this design matrix. The proposed estimator whose asymptotic properties are studied, contains as a special case the conventional mixed regression estimator based on a fixed design matrix. A new test of compatibility between prior and sample information is also introduced. Thesuggested estimator is tested empirically with both simulated and actual marketing data.     

Generalized mixed estimator for nonlinear models: a maximum likelihood approach

This paper considers the problem of estimating a nonlinear statistical model subject to stochastic linear constraints among unknown parameters. These constraints represent prior information which originates from a previous estimation of the same model using an alternative database. One feature of this specification allows for the disign matrix of stochastic linear restrictions to be estimated. The mixed regression technique and the maximum likelihood approach are used to derive the estimator for both the model coefficients and the unknown elements of this design matrix. The proposed estimator whose asymptotic properties are studied, contains as a special case the conventional mixed regression estimator based on a fixed design matrix. A new test of compatibility between prior and sample information is also introduced. Thesuggested estimator is tested empirically with both simulated and actual marketing data.     

Central limit theorems of range-based estimators for diffusion models

Abstract

In this article, we consider non parametric range-based estimation procedure for diffusion processes and propose a instantaneous volatility estimator. Under some weak conditions, we certify that the proposed estimator has convergence in probability. Adding some necessary conditions, we prove a central limit theorem. By inference, we reach a conclusion that, with high frequency data in hand, the proposed estimator is more precise than those pure realized instantaneous volatility ones. Numerical simulation illustrates the finite sample properties of the proposed estimator.     

Estimation and Confidence Intervals for Clock Offset in Networks with Bivariate Exponential Delays

There is a large and increasing literature on statistical modeling-based estimation of the offset between two clocks. Recent work has focused on the construction of confidence intervals for offset. However, in most of this work it has been assumed that the network delays that occur during the synchronization process are independent. The network delays are often modeled as independent exponential random variables. Thus, we introduce the use of a bivariate exponential distribution to capture the anticipated correlation between the network delays and derive a maximum likelihood estimator and a confidence interval procedure for the offset parameter. We then illustrate how use of the independent model for network delays can lead to improper inference about the offset parameter.