Semiparametric Estimation Research Articles

A Stratified Penalized Kernel Method for Semiparametric Variable Labeling and Estimation of Multi-Output Time-Varying Coefficient Models for Nonstationary Time Series

A Stratified Penalized Kernel Method for Semiparametric Variable Labeling and Estimation of Multi-Output Time-Varying Coefficient Models for Nonstationary Time Series

How responsive are nutrients in India? Some recent evidence

The relationship between nutrient intake and income is an issue of huge policy relevance, especially in the developing world. Using large-scale household-level data from India, this paper analyzes how macronutrient and micronutrient intakes respond to changes in income in both rural and urban areas. It also investigates how food consumption patterns change over time. In a first, this paper employs different estimation approaches i.e., parametric, semi-parametric and non-parametric estimation models to obtain more recent and robust nutrient-income elasticity estimates for three macronutrients and four essential micronutrients. The parametric (OLS) calorie-expenditure elasticities were lower than those estimated for protein and fat. Micronutrients also yielded positive and statistically significant elasticities. In terms of the parametric (IV) estimation, elasticities also declined over time and had lower magnitudes than the parametric (OLS) estimates. Relative to protein, fat and micronutrient intakes, caloric intakes are less sensitive to changes in income. According to parametric (OLS and IV) estimation, calcium is the most income-responsive micronutrient, while zinc is the least. The preferred semi-parametric estimation strategy provides full flexibility to income effects while also simultaneously controlling for additional covariates parametrically, assisting in determining the true relationship between nutrient intake and income. Consistent with the parametric estimation, elasticities were positive and statistically significant. The augmented semi-parametric elasticities, which address endogeneity concerns, were lower than the non-augmented ones. The semi-parametric elasticity curves depict that the relationship between demand for nutrients and income is indeed non-linear and non-monotonic. The findings from this research demonstrate that it is critical to evaluate the effect of income across the entire income distribution, and not just at the means. Even when the elasticities are low, they are always more pronounced for the poor, who are the most vulnerable to malnutrition. The study conducts a battery of checks that further lend credence to the robustness of the main findings. Given the current landscape of India’s nutrition economy, the findings of this study would serve to be useful for designing apt future nutritional interventions and public health policies.

How the EU Cohesion Policy targeted at R&D and innovation impacts the productivity, employment and exports of SMEs in Estonia

The aim of this empirical investigation is to assess how the support targeted at R&D and innovation in the European Union Cohesion Policy Programme 2014–2020 affects the labour productivity, employment and exports of small and medium-sized companies. We estimate the treatment effects of two R&D financial support activities using a semiparametric efficient estimator with over-identified moment conditions and inverse probability weighting. The impact assessment uses population data on small and medium-sized enterprises in Estonia, the European Union member state that benefits most per capita from Cohesion Fund allocations. We found that support for R&D and innovation from the Cohesion Policy had a positive short-term effect on labour productivity and employment over the estimation period 2014–2018, and that the size and robustness of the effect were strongest for labour productivity. The short-term effect on exporting was ambiguous.

Yet another look at the omitted variable bias

When conducting regression analysis, econometricians often face the situation where some relevant regressors are unavailable in the data set at hand. This article shows how to construct a new class of nonparametric proxies by combining the original data set with one containing the missing regressors. Imputation of the missing values is done using a nonstandard kernel adapted to mixed data. We derive the asymptotic distribution of the resulting semiparametric two-sample estimator of the parameters of interest and show, using Monte Carlo simulations, that it dominates the solutions involving instrumental variables and other parametric alternatives. An application to the PSID and NLS data illustrates the importance of our estimation approach for empirical research.

Penalty and Shrinkage Strategies Based on Local Polynomials for Right-Censored Partially Linear Regression.

This study aims to propose modified semiparametric estimators based on six different penalty and shrinkage strategies for the estimation of a right-censored semiparametric regression model. In this context, the methods used to obtain the estimators are ridge, lasso, adaptive lasso, SCAD, MCP, and elasticnet penalty functions. The most important contribution that distinguishes this article from its peers is that it uses the local polynomial method as a smoothing method. The theoretical estimation procedures for the obtained estimators are explained. In addition, a simulation study is performed to see the behavior of the estimators and make a detailed comparison, and hepatocellular carcinoma data are estimated as a real data example. As a result of the study, the estimators based on adaptive lasso and SCAD were more resistant to censorship and outperformed the other four estimators.

Semiparametric modeling of multiple quantiles

We develop a semiparametric model to track a large number of quantiles of a time series. The model satisfies the condition of non-crossing quantiles and the defining property of fixed quantiles. A key feature of the specification is that the updating scheme for time-varying quantiles at each probability level is based on the gradient of the check loss function. Theoretical properties of the proposed model are derived such as weak stationarity of the quantile process and consistency of the estimators of the fixed parameters. The model can be applied for filtering and prediction. We also illustrate a number of possible applications such as: (i) semiparametric estimation of dynamic moments of the observables, (ii) density prediction, and (iii) quantile predictions.

Doubly robust estimators for generalizing treatment effects on survival outcomes from randomized controlled trials to a target population.

In the presence of heterogeneity between the randomized controlled trial (RCT) participants and the target population, evaluating the treatment effect solely based on the RCT often leads to biased quantification of the real-world treatment effect. To address the problem of lack of generalizability for the treatment effect estimated by the RCT sample, we leverage observational studies with large samples that are representative of the target population. This article concerns evaluating treatment effects on survival outcomes for a target population and considers a broad class of estimands that are functionals of treatment-specific survival functions, including differences in survival probability and restricted mean survival times. Motivated by two intuitive but distinct approaches, i.e., imputation based on survival outcome regression and weighting based on inverse probability of sampling, censoring, and treatment assignment, we propose a semiparametric estimator through the guidance of the efficient influence function. The proposed estimator is doubly robust in the sense that it is consistent for the target population estimands if either the survival model or the weighting model is correctly specified and is locally efficient when both are correct. In addition, as an alternative to parametric estimation, we employ the nonparametric method of sieves for flexible and robust estimation of the nuisance functions and show that the resulting estimator retains the root-n consistency and efficiency, the so-called rate-double robustness. Simulation studies confirm the theoretical properties of the proposed estimator and show that it outperforms competitors. We apply the proposed method to estimate the effect of adjuvant chemotherapy on survival in patients with early-stage resected non-small cell lung cancer.

Causal Inference for Social Network Data

We describe semiparametric estimation and inference for causal effects using observational data from a single social network. Our asymptotic results are the first to allow for dependence of each observation on a growing number of other units as sample size increases. In addition, while previous methods have implicitly permitted only one of two possible sources of dependence among social network observations, we allow for both dependence due to transmission of information across network ties and for dependence due to latent similarities among nodes sharing ties. We propose new causal effects that are specifically of interest in social network settings, such as interventions on network ties and network structure. We use our methods to reanalyze an influential and controversial study that estimated causal peer effects of obesity using social network data from the Framingham Heart Study; after accounting for network structure we find no evidence for causal peer effects. Supplementary materials for this article are available online.

Semiparametric estimation of the high-dimensional elliptical distribution

This paper investigates semiparametric estimation of the multivariate elliptical distribution in case dimensionality increases with the sample size. We prove the almost sure convergence and derive the convergence rates of the estimator, depending on the sample size, dimensionality, and the bandwidth of the kernel. As an important by-product, we show almost sure convergence with the corresponding convergence rates for the sample covariance matrix under the Frobenius norm. An extensive simulation study has supported the theory.

Asymptotic properties of semiparametric [formula omitted]-estimators with multiple change points

Statistical models with multiple change points are used in many fields; however, the theoretical properties of semiparametric M-estimators of such models have received relatively little attention. The main purpose of the present work is to investigate the asymptotic properties of semiparametric M-estimators with non-smooth criterion functions of the parameters of a multiple change-point model for a general class of models in which the form of the distribution can change from segment to segment and in which, possibly, there are parameters that are common to all segments. Consistency of the semiparametric M-estimators of the change points is established and the rate of convergence is determined. The asymptotic normality of the semiparametric M-estimators of the parameters of the within-segment distributions is established under quite general conditions. These results, together with a generic paradigm for studying semiparametric M-estimators with multiple change points, provide a valuable extension to previous related research on (semi)parametric maximum-likelihood estimators. For illustration, the classification with missing data in the model is investigated in detail and a short simulation result is provided.

Sparse semiparametric efficient estimation in high-dimensional linear regression models

Linear regression estimation 问题 with high-dimensional covariates has been extensively studied in the literature. However, how to integrate the efficiency consideration into the high-dimensional estimation with the unknown error density is still an unsolved but challenging 问题. Parametric estimators such as ordinary least squares estimators will suffer efficiency loss with non-Gaussian error density, while the maximum likelihood estimation cannot be directly applied due to the unknown error density. In this paper, we propose a novel sparse semiparametric efficient estimation method for the high-dimensional linear regression with the unknown error density via penalized estimating equations. We prove that the new estimator is asymptotically as efficient as the oracle MLE (maximum likelihood estimator) in the ultra-high-dimensional setting with the unknown error density and thus is more efficient than the traditional penalized least squares estimator for non-Gaussian error densities. In addition, we demonstrate that several popularly used high-dimensional regression estimators are special cases of ours. Extensive simulation studies and the empirical analysis of a real data set are conducted which demonstrate the effectiveness of the proposed procedure and its superior performance compared with least squares based methods.

Semiparametric current status regression model using kernel smoothing with application to HIV study

In current status regression analysis, the responses are indirectly observed and the regression coefficients can not be estimated using the commonly used least squares estimate, instead semiparametric maximum likelihood estimate is used. As the nonparametric component estimate is a non-smooth step function, the regression coefficients are bundled inside it, so the asymptotic distribution of the estimated coefficients is an open problem. To overcome this issue, smoothed versions are proposed in the literature; however, in these versions the score equation for the regression coefficients is still not continuous, the estimate is not an exact solution of the score equation, and zero-crossing is used instead. Here we propose a modified smoothed version to make the score equation a continuous function of the regression coefficients, and thus the estimator is the exact solution of the score equation. Asymptotic distribution of the resulting estimators can be shown as in our related papers. Simulation studies are conducted to evaluate the performance of the method, and it demonstrates superior finite sample behavior. For illustration, we applied the method to the analysis of a real data set from a HIV study.

Semiparametric estimation of expected shortfall and its application in finance

AbstractMeasuring risk effectively is crucial for managing risk in financial markets. The expected shortfall has become an increasingly popular metric for risk in recent years. How to estimate it is important in statistics and financial econometrics. Based on the single index quantile regression, we introduce a new semiparametric approach, namely, weighted single index quantile regression. We assess the performance of the proposed expected shortfall estimator with backtesting. Our simulation results indicate that the estimator has a good finite sample performance and often outperforms existing methods. By applying the new method to both a market index and individual stocks, we show that it not only exhibits the best performance but also reveals an insight about the effect of the COVID pandemic, that is, the pandemic increases the market risk.

AN AVERAGING ESTIMATOR FOR TWO-STEP M-ESTIMATION IN SEMIPARAMETRIC MODELS

In a two-step extremum estimation (M-estimation) framework with a finite-dimensional parameter of interest and a potentially infinite-dimensional first-step nuisance parameter, this paper proposes an averaging estimator that combines a semiparametric estimator based on a nonparametric first step and a parametric estimator which imposes parametric restrictions on the first step. The averaging weight is an easy-to-compute sample analog of an infeasible optimal weight that minimizes the asymptotic quadratic risk. Under Stein-type conditions, the asymptotic lower bound of the truncated quadratic risk difference between the averaging estimator and the semiparametric estimator is strictly less than zero for a class of data generating processes that includes both correct specification and varied degrees of misspecification of the parametric restrictions, and the asymptotic upper bound is weakly less than zero. The averaging estimator, along with an easy-to-implement inference method, is demonstrated in an example.

Maximum Likelihood Estimation for Shape-restricted Single-index Hazard Models.

Single-index models are becoming increasingly popular in many scientific applications as they offer the advantages of flexibility in regression modeling as well as interpretable covariate effects. In the context of survival analysis, the single-index hazards models are natural extensions of the Cox proportional hazards models. In this paper, we propose a novel estimation procedure for single-index hazard models under a monotone constraint of the index. We apply the profile likelihood method to obtain the semiparametric maximum likelihood estimator, where the novelty of the estimation procedure lies in estimating the unknown monotone link function by embedding the problem in isotonic regression with exponentially distributed random variables. The consistency of the proposed semiparametric maximum likelihood estimator is established under suitable regularity conditions. Numerical simulations are conducted to examine the finite-sample performance of the proposed method. An analysis of breast cancer data is presented for illustration.

Semiparametric estimation of the transformation model by leveraging external aggregate data in the presence of population heterogeneity.

Leveraging information in aggregate data from external sources to improve estimation efficiency and prediction accuracy with smaller scale studies has drawn a great deal of attention in recent years. Yet, conventional methods often either ignore uncertainty in the external information or fail to account for the heterogeneity between internal and external studies. This article proposes an empirical likelihood-based framework to improve the estimation of the semiparametric transformation models by incorporating information about the t-year subgroup survival probability from external sources. The proposed estimation procedure incorporates an additional likelihood component to account for uncertainty in the external information and employs a density ratio model to characterize population heterogeneity. We establish the consistency and asymptotic normality of the proposed estimator and show that it is more efficient than the conventional pseudopartial likelihood estimator without combining information. Simulation studies show that the proposed estimator yields little bias and outperforms the conventional approach even in the presence of information uncertainty and heterogeneity. The proposed methodologies are illustrated with an analysis of a pancreatic cancerstudy.

Improved semiparametric estimation of the proportional rate model with recurrent event data.

Owing to its robustness properties, marginal interpretations, and ease of implementation, the pseudo-partial likelihood method proposed in the seminal papers of Pepe and Cai and Lin etal. has become the default approach for analyzing recurrent event data with Cox-type proportional rate models. However, the construction of the pseudo-partial score function ignores the dependency among recurrent events and thus can be inefficient. An attempt to investigate the asymptotic efficiency of weighted pseudo-partial likelihood estimation found that the optimal weight function involves the unknown variance-covariance process of the recurrent event process and may not have closed-form expression. Thus, instead of deriving the optimal weights, we propose to combine a system of pre-specified weighted pseudo-partial score equationsvia the generalized method of moments and empirical likelihood estimation. We show that a substantial efficiency gain can be easily achieved without imposing additional model assumptions. More importantly, the proposed estimation procedures can be implemented with existing software. Theoretical and numerical analyses show that the empirical likelihood estimator is more appealing than the generalized method of moments estimator when the sample size is sufficiently large. An analysis of readmission risk in colorectal cancer patients is presented to illustrate the proposedmethodology.

The impact of climate change on China's agricultural green total factor productivity

Using China's province-level panel data from 2001 to 2019 and the unexpected super efficiency MetaFrontier-Malmquist model (MinDS) to compute the super efficiency MinDS index for the green total factor productivity of China's agricultural sector, the paper analyses the temporal evolution in the agricultural sector's green total factor productivity across China's three economic regions by kernel density estimation. The effects of general climate factors and extreme weather events on the agricultural sector's green total factor productivity are empirically tested. The results show that precipitation, temperature, and humidity significantly impact agricultural green total factor productivity. The semi-parametric panel estimation method fits the nonlinear relationship between climate change and agricultural productivity. In addition, the impacts are found to vary across grouping levels. The mechanism test shows that climate change affects agricultural green total factor productivity through output, input, and structure effects. The test of the synthetic control method based on counterfactual thought shows that extreme weather has a significant negative impact on agricultural green total factor productivity in severely affected areas and is shown to display spatial and dynamic sustainability. The paper's results encourage policymakers in China to actively promote the coordinated and high-quality development of regional green agriculture under the condition of climate change.

Instrumented difference-in-differences.

Unmeasured confounding is a key threat to reliable causal inference based on observational studies. Motivated from two powerful natural experiment devices, the instrumental variables and difference-in-differences, we propose a new method called instrumented difference-in-differences that explicitly leverages exogenous randomness in an exposure trend to estimate the average and conditional average treatment effect in the presence of unmeasured confounding. We develop the identification assumptions using the potential outcomes framework. We propose a Wald estimator and a class of multiply robust and efficient semiparametric estimators, with provable consistency and asymptotic normality. In addition, we extend the instrumented difference-in-differences to a two-sample design to facilitate investigations of delayed treatment effect and provide a measure of weak identification. We demonstrate our results in simulated and realdatasets.

Semiparametric partial linear modeling of risk factors for ear infections: the Early Childhood Longitudinal Study

The Early Childhood Longitudinal Study–Kindergarten Class of 2010–2011 (ECLS-K:2011) ascertained timing of ear infections within age specified intervals and parent's/caregiver's report of medically diagnosed hearing loss. In this nationally representative, school-based sample of children followed from kindergarten entry through fifth grade, academic performance in reading, mathematics, and science was assessed longitudinally. Prior investigations of this ECLS-K:2011 cohort showed that age has a non-linear, monotonically increasing functional relationship with academic performance. Because of this knowledge, a semiparametric partial linear model is proposed, in which the effect of age is modeled by an unknown monotonically increasing function along with other regression parameters. The parameters are estimated by a semiparametric maximum likelihood estimator. A test of a constant effect of age is also proposed. Simulation studies are conducted to evaluate the performance of the proposed method, as compared with the commonly used linear model; the former outperforms the latter based on several criteria. We then analyzed ECLS-K:2011 data to compare results of the partial linear parametric model estimation with that of classical linear regression models.