Two-stage Estimation Procedure Research Articles

Consistent two-stage estimation in heterogeneous network autoregressive model

Obtaining consistent estimates of network effects in the heterogeneous network autoregressive model presents significant challenges. These challenges arise from the large number of target parameters, potential endogeneity, and non-identifiability issues. To overcome these challenges, we reformulate the model into a higher-order version. Our proposed two-stage estimation procedure first reduces parameter complexity by screening out nodes with negligible network effects. Then, we employ the ordinary least squares method and the instrumental variables technique for effective post-screening estimation. We further investigate the consistency and asymptotic normality of the estimators under appropriate assumptions and explore the cases of heteroscedasticity. The finite sample performance of the two-stage method is evaluated by simulation studies and an empirical analysis.

Firm-Level Determinants of Export Performance in Kenya’s Manufacturing Sector

Purpose: This study aimed at investigating the firm-level determinants of export performance (export propensity and export intensity) in Kenya’s manufacturing sector using firm-level panel data obtained from the World Bank Enterprise Surveys for the periods 2007, 2013 and 2018. Methodology: The study adopted a quantitative non-experimental research design. The Heckman Two-Stage estimation procedure was employed to jointly establish the firm-level determinants of export propensity and export intensity in Kenya’s manufacturing sector. Findings: Based on the estimation results, firm-level total factor productivity, firm size, human capital, cost of material, electricity cost and foreign ownership had positive and significant effects on firms’ export propensity while labor productivity negatively influenced export propensity. Firm age, capital intensity and research did not have significant effects on export propensity. On the other hand, export intensity was positively influenced by firm-level total factor productivity, foreign ownership, firm size, firm age, human capital and research. Labor productivity had a negative effect on firms’ export intensity. Whereas the effect of energy cost on export intensity was weakly significant at 10 percent level of significance, there was no significant effect of cost of material on export intensity. Unique Contribution to Theory, Practice and Policy: Employing the new ‘new’ trade theory, the study tested the self-selection hypothesis by analyzing the determinants of export propensity and intensity. According to the self-selection hypothesis, one of the key positive determinants of export propensity and export intensity is firm-level total factor productivity. The study findings validated the self-selection hypothesis since the results revealed firm-level total factor productivity as a positive and significant determinant of both export propensity and export intensity for Kenya’s manufacturing firms. According to the study's conclusions, the government and enterprises must focus on policies that increase firm-level total factor productivity, firm size, human capital, and research in order to improve firms' export performance.

Conditional modeling of panel count data with partly interval-censored failure event.

In longitudinal follow-up studies, panel count data arise from discrete observations on recurrent events. We investigate a more general situation where a partly interval-censored failure event is informative to recurrent events. The existing methods for the informative failure event are based on the latent variable model, which provides indirect interpretation for the effect of failure event. To solve this problem, we propose a failure-time-dependent proportional mean model with panel count data through an unspecified link function. For estimation of model parameters, we consider a conditional expectation of least squares function to overcome the challenges from partly interval-censoring, and develop a two-stage estimation procedure by treating the distribution function of the failure time as a functional nuisance parameter and using the B-spline functions to approximate unknown baseline mean and link functions. Furthermore, we derive the overall convergence rate of the proposed estimators and establish the asymptotic normality of finite-dimensional estimator and functionals of infinite-dimensional estimator. The proposed estimation procedure is evaluated by extensive simulation studies, in which the finite-sample performances coincide with the theoretical results. We further illustrate our method with a longitudinal healthy longevity study and draw some insightful conclusions.

Estimation and bootstrapping under spatiotemporal models with unobserved heterogeneity

Proposed herein is a novel spatiotemporal model to characterize the unobserved heterogeneity across individuals using quantile-function-based correlated random effects and heteroscedastic innovations in a general framework. This model can be used to explore the influence of space-specific factors on latent effects at different quantile levels by controlling for spatiotemporal effects. A two-stage estimation procedure is introduced in which (i) the method of moments is used to estimate spatiotemporal effects then (ii) quantile regression is used for individual effects. A hybrid double bootstrapping procedure is then proposed to approximate the asymptotic distributions of coefficient estimators. The validity of the estimation and bootstrapping is established theoretically and then confirmed by simulation studies, and the usefulness of the proposed model is demonstrated with a real example involving city air quality.

Analysis of secondary failure time responses in studies with response-dependent sampling schemes.

Response-dependent sampling is routinely used as an enrichment strategy in the design of family studies investigating the heritable nature of disease. In addition to the response of primary interest, investigators often wish to investigate the association between biomarkers and secondary responses related to possible comorbidities. Statistical analysis regarding genetic biomarkers and their association with the secondary outcome must address the biased sampling scheme involving the primary response. In this article, we develop composite likelihoods and two-stage estimation procedures for such secondary analyses in which the within-family dependence structure for the primary and secondary outcomes is modeled via a Gaussian copula. The dependence among responses within family members is modeled based on kinship coefficients. Auxiliary data from independent individuals are exploited by augmenting the composite likelihoods to increase precision of marginal parameter estimates and enhance the efficiency of estimators of the dependence parameters. Simulation studies are carried out to evaluate the finite sample performance of the proposed method, and an application to a motivating family study in psoriatic arthritis is given for illustration.

Dynamic Market Timing in Mutual Funds

We use the dynamic conditional correlation (DCC) model to estimate daily frequency mutual fund betas. Compared with traditional estimates, daily betas better capture changes in fund risk stemming from daily fund trading activity. Based on these beta estimates and a two-stage estimation procedure, we find significant evidence of market timing ability among actively managed U.S. equity funds that is not apparent via standard approaches. Unlike traditional measures, our timing estimates correlate positively with fund performance. Market timing is especially evident during down markets, with successful timers exhibiting low downside risk. Timing ability persists across time and attracts investor flows. This paper was accepted by David Sraer, finance. Funding: This work was supported by the National Natural Science Foundation of China [Grants 72173127 and 72121001] and by the Institute for Industrial Innovation and Finance at Tsinghua University. Supplemental Material: The data files and online appendix are available at https://doi.org/10.1287/mnsc.2023.4857 .

Does prescribing apixaban or rivaroxaban versus warfarin for patients diagnosed with atrial fibrillation save health system costs? A multivalued treatment effects analysis.

Non-valvular atrial fibrillation (AF) is a common heart arrhythmia in the elderly population. AF patients are at high-risk of ischemic strokes, but oral anticoagulant (OAC) therapy reduces such risks. Warfarin had been the standard OAC for AF patients, however its effectiveness is highly variable and dependent on close monitoring of the anticoagulant response. Newer OACs such as rivaroxaban and apixaban address these drawbacks but are more costly. It is uncertain which OAC therapy for AF is cost-saving from the healthcare system perspective. We followed a cohort of patients in Ontario, Canada, aged ≥ 66 who were newly diagnosed with AF and prescribed OACs between 2012 and 2017. We used a two-stage estimation procedure. First, we account for the patient selection into OACs using a multinomial logit regression model and estimated propensity scores. Second, we used an inverse probability weighted regression adjustment approach to determine cost-saving OAC options. We also examined component-specific costs (i.e., drug, hospitalization, emergency department and physician) to understand the drivers of cost-saving OACs. We found that compared to warfarin, rivaroxaban and apixaban treatments were cost-saving options, with per-patient 1-year healthcare cost savings at $2436 and $1764, respectively. These savings were driven by cost-savings in hospitalization, emergency department visits, and physician visits, outweighing higher drug costs. These results were robust to alternative model specifications and estimation procedures. Treating AF patients with rivaroxaban and apixaban than warfarin reduces healthcare costs. OAC reimbursement policies for AF patients should consider rivaroxaban or apixaban over warfarin as the first-line treatment.

The sparse estimation of the semiparametric linear transformation model with dependent current status data

In this paper, we study the sparse estimation under the semiparametric linear transformation models for the current status data, also called type I interval-censored data. For the problem, the failure time of interest may be dependent on the censoring time and the association parameter between them is left unspecified. To address this, we employ the copula model to describe the dependence between them and a two-stage estimation procedure to estimate both the association parameter and the regression parameter. In addition, we propose a penalized maximum likelihood estimation procedure based on the broken adaptive ridge regression, and Bernstein polynomials are used to approximate the nonparametric functions involved. The oracle property of the proposed method is established and the numerical studies suggest that the method works well for practical situations. Finally, the method is applied to an Alzheimer's disease study that motivated this investigation.

A Truncated Spline and Local Linear Mixed Estimator in Nonparametric Regression for Longitudinal Data and Its Application

Longitudinal data modeling is widely carried out using parametric methods. However, when the parametric model is misspecified, the obtained estimator might be severely biased and lead to erroneous conclusions. In this study, we propose a new estimation method for longitudinal data modeling using a mixed estimator in nonparametric regression. The objective of this study was to estimate the nonparametric regression curve for longitudinal data using two combined estimators: truncated spline and local linear. The weighted least square method with a two-stage estimation procedure was used to obtain the regression curve estimation of the proposed model. To account for within-subject correlations in the longitudinal data, a symmetric weight matrix was given in the regression curve estimation. The best model was determined by minimizing the generalized cross-validation value. Furthermore, an application to a longitudinal dataset of the poverty gap index in Bengkulu Province, Indonesia, was conducted to illustrate the performance of the proposed mixed estimator. Compared to the single estimator, the truncated spline and local linear mixed estimator had better performance in longitudinal data modeling based on the GCV value. Additionally, the empirical results of the best model indicated that the proposed model could explain the data variation exceptionally well.

Spatial dependence modeling of latent susceptibility and time to joint damage in psoriatic arthritis.

Important scientific insights into chronic diseases affecting several organ systems can be gained from modeling spatial dependence of sites experiencing damage progression. We describe models and methods for studying spatial dependence of joint damage in psoriatic arthritis (PsA). Since a large number of joints may remain unaffected even among individuals with a long disease history, spatial dependence is first modeled in latent joint-specific indicators of susceptibility. Among susceptible joints, a Gaussian copula is adopted for dependence modeling of times to damage. Likelihood and composite likelihoods are developed for settings, where individuals are under intermittent observation and progression times are subject to type K interval censoring. Two-stage estimation procedures help mitigate the computational burden arising when a large number of processes (i.e., joints) are under consideration. Simulation studies confirm that the proposed methods provide valid inference, and an application to the motivating data from the University of Toronto Psoriatic Arthritis Clinic yields important insights which can help physicians distinguish PsA from arthritic conditions with different dependencepatterns.

Smoothed tensor quantile regression estimation for longitudinal data

As extensions of vector and matrix data with ultrahigh dimensionality and complex structures, tensor data are fast emerging in a large variety of scientific applications. In this paper, a two-stage estimation procedure for linear tensor quantile regression (QR) with longitudinal data is proposed. In the first stage, we account for within-subject correlations by using the generalized estimating equations and then impose a low-rank assumption on tensor coefficients to reduce the number of parameters by a canonical polyadic decomposition. To avoid the asymptotic analysis and computation problems caused by the non-smooth QR score function, kernel smoothing method is applied in the second stage to construct the smoothed tensor QR estimator. When the number of rank is given, a block-relaxation algorithm is proposed to estimate the regression coefficients. A modified BIC is applied to estimate the number of rank in practice and show the rank selection consistency. Further, a regularized estimator and its algorithm are investigated for better interpretation and efficiency. The asymptotic properties of the proposed estimators are established. Simulation studies and a real example on Beijing Air Quality data set are provided to show the performance of the proposed estimators.

GPU accelerated estimation of a shared random effect joint model for dynamic prediction

In longitudinal cohort studies, it is often of interest to predict the risk of a terminal clinical event using longitudinal predictor data among subjects at risk by the time of the prediction. The at-risk population changes over time; so does the association between predictors and the outcome, as well as the accumulating longitudinal predictor history. The dynamic nature of this prediction problem has received increasing interest in the literature, but computation often poses a challenge. The widely used joint model of longitudinal and survival data often comes with intensive computation and excessive model fitting time, due to numerical optimization and the analytically intractable high-dimensional integral in the likelihood function. This problem is exacerbated when the model is fit to a large dataset or the model involves multiple longitudinal predictors with nonlinear trajectories. This challenge can be addressed from an algorithmic perspective, by a novel two-stage estimation procedure, and from a computing perspective, by Graphics Processing Unit (GPU) programming. The latter is implemented through PyTorch, an emerging deep learning framework. The numerical studies demonstrate that the proposed algorithm and software can substantially speed up the estimation of the joint model, particularly with large datasets. The numerical studies also concluded that accounting for nonlinearity in longitudinal predictor trajectories can improve the prediction accuracy in comparison to joint modeling that ignore nonlinearity.

Generalised regression estimators for average treatment effect with multicollinearity in high-dimensional covariates

In this paper, a two-stage estimation procedure is proposed to obtain an efficient propensity score (PS) based estimator for the average treatment effect (ATE) with multicollinearity in high-dimensional covariates. In the first stage, we adjust the usual Horvitz–Thompson estimator of the ATE by incorporating instrumental variables in parametric PS models to avoid model misspecification and then propose the generalised regression estimator by utilising the auxiliary information from covariates related to the potential outcomes. In the second stage, we adapt the Elastic-net method to solve the multicollinearity issue and further improve the estimation efficiency based on the selected important covariates. The finite-sample performance of the proposed estimator is studied through simulation, and two applications to HER2 breast cancer and employees' weekly wages are also presented.

Two-Stage Shrinkage Bayesian Estimators For The Shape Parameter of Pareto Distribution Dependent on Katti’s Regions

This study proposes a two-stage shrinkage Bayesian estimation of the shape parameter of Pareto distribution. Additional information from the past and considered presently in new estimation processes has been receiving considerable attention in the last few decades, especially when a sample unit is costly or difficult to obtain. The proposed two-stage pooling estimation procedure assumes that the prior knowledge of θ can take the form of an initial estimate θ0 of θ. The expressions for bias, bias ratio, mean square error, expected sample size, and relative efficiency are derived based on the two regions of R1 and R2. Certain values of the constants are considered, and the R language is used for statistical programming. The numerical results and conclusion suggest that the proposed estimators have higher relative efficiency compared with the classical Bayesian estimator with respect to a guess value. The effective region of the estimator dependent on R2 is better than that of the estimator dependent dependent on R1.

The Willingness to Pay for Cider Products: Results of a Survey on Habits and Consumption Behavior

Purpose The objective of the paper is to investigate the impact of habits and consumption behavior on the willingness to pay (WTP) for cider by surveying young consumers. Method The analysis is based on a questionnaire distributed to a group of 433 French business students from December 2017 to January 2018. Specifically, the questionnaire is designed to test whether young consumers would pay a premium price or not for quality ciders with respect to a traditional sweet cider with similar characteristics. We are modelling the premium that consumers are willing to pay for an organic cider, a farmer cider and rosé cider. To accommodate the feature of a significant proportion of zero or negative premiums in dependent variables, the Heckman two-stage estimation procedure is performed. Results Results show that the young generation consider cider as a cheap, festive and non-organic beverage and is willing to pay a premium for quality ciders like specifically rosé and farmer ciders. Conclusion The results from this research have useful implications not only for the cider market but also in the understanding of the characteristics of competitive beverages that young consumers may prefer and value.

Semiparametric additive time-varying coefficients model for longitudinal data with censored time origin.

Statistical analysis of longitudinal data often involves modeling treatment effects on clinically relevant longitudinal biomarkers since an initial event (the time origin). In some studies including preventive HIV vaccine efficacy trials, some participants have biomarkers measured starting at the time origin, whereas others have biomarkers measured starting later with the time origin unknown. The semiparametric additive time-varying coefficient model is investigated where the effects of some covariates vary nonparametrically with time while the effects of others remain constant. Weighted profile least squares estimators coupled with kernel smoothing are developed. The method uses the expectation maximization approach to deal with the censored time origin. The Kaplan-Meier estimator and other failure time regression models such as the Cox model can be utilized to estimate the distribution and the conditional distribution of left censored event time related to the censored time origin. Asymptotic properties of the parametric and nonparametric estimators and consistent asymptotic variance estimators are derived. A two-stage estimation procedure for choosing weight is proposed to improve estimation efficiency. Numerical simulations are conducted to examine finite sample properties of the proposed estimators. The simulation results show that the theory and methods work well. The efficiency gain of the two-stage estimation procedure depends on the distribution of the longitudinal error processes. The method is applied to analyze data from the Merck 023/HVTN 502 Step HIV vaccinestudy.

Using Bayesian Kriging for spatial smoothing of trends in non-normal yield densities

PurposeThe purpose of this paper is to estimate crop yield densities considering time trends in the first three moments and spatially varying coefficients.Design/methodology/approachYield density parameters are assumed to be spatially correlated, through a Gaussian spatial process. This study spatially smooth multiple parameters using Bayesian Kriging.FindingsAssuming that county yields follow skew normal distributions, the location parameter increased faster in the eastern and northwestern counties of Iowa, while the scale increased faster in southern counties and the shape parameter increased more (implying less left skewness) in southwestern counties. Over time, the mean has increased sharply, while the variance and left skewness increased modestly.Originality/valueBayesian Kriging can smooth time-varying yield distributions, handle unbalanced panel data and provide estimates when data are missing. Most past models used a two-stage estimation procedure, while our procedure estimates parameters jointly.

Nonlinear degradation modeling and prognostics: A Box-Cox transformation perspective

Transforming nonlinear degradation paths into nearly linear ones has been widely used for nonlinear degradation modeling and prognostics. However, types of the current transformation functions are difficult to determine. This paper addresses issues in nonlinear stochastic degradation modeling and prognostics from a Box-Cox transformation (BCT) perspective. Specifically, the BCT is first used to transform the nonlinear degradation data into nearly linear data, and then the Wiener process with random drift is utilized to model the evolving process of the transformed data. To determine the model parameters, a two-stage estimation procedure is developed including offline stage and online stage. In the offline stage, the parameters are determined via maximum likelihood estimation method based on the historical degradation data and such estimated values are used to initialize the online stage. During the online stage, the Bayesian method is adopted to update the model parameters using the data of the degrading system in service, in which the hyperparameters are updated by the expectation maximization algorithm. A closed-form solution to remaining useful life with updated model parameters is further derived for prognostics. Finally, case studies for lithium-ion batteries and liquid coupling devices are provided to demonstrate the proposed approach.

Estimating monthly PM2.5 concentrations from satellite remote sensing data, meteorological variables, and land use data using ensemble statistical modeling and a random forest approach

Fine particulate matter (PM2.5) is associated with various adverse health outcomes and poses serious concerns for public health. However, ground monitoring stations for PM2.5 measurements are mostly installed in population-dense or urban areas. Thus, satellite retrieved aerosol optical depth (AOD) data, which provide spatial and temporal surrogates of exposure, have become an important tool for PM2.5 estimates in a study area. In this study, we used AOD estimates of surface PM2.5 together with meteorological and land use variables to estimate monthly PM2.5 concentrations at a spatial resolution of 3 km2 over Taiwan Island from 2015 to 2019. An ensemble two-stage estimation procedure was proposed, with a generalized additive model (GAM) for temporal-trend removal in the first stage and a random forest model used to assess residual spatiotemporal variations in the second stage. We obtained a model-fitting R2 of 0.98 with a root mean square error (RMSE) of 1.40 μg/m3. The leave-one-out cross-validation (LOOCV) R2 with seasonal stratification was 0.82, and the RMSE was 3.85 μg/m3, whereas the R2 and RMSE obtained by using the pure random forest approach produced R2 and RMSE values of 0.74 and 4.60 μg/m3, respectively. The results indicated that the ensemble modeling approach had a higher predictive ability than the pure machine learning method and could provide reliable PM2.5 estimates over the entire island, which has complex terrain in terms of land use and topography.

Recycled two-stage estimation in nonlinear mixed effects regression models

We consider a re-sampling scheme for estimation of the population parameters in the mixed-effects nonlinear regression models of the type used, for example, in clinical pharmacokinetics. We provide a two-stage estimation procedure which resamples (or recycles), via random weightings, the various parameter's estimates to construct consistent estimates of their respective sampling distributions. In particular, we establish under rather general distribution-free assumptions, the asymptotic normality and consistency of the standard two-stage estimates and of their resampled version and demonstrate the applicability of our proposed resampling methodology in a small simulation study. A detailed example based on real clinical pharmacokinetic data is also provided.