Semiparametric Approach Research Articles

Estimation of Peer Effects in Endogenous Social Networks: Control Function Approach

Abstract We propose methods of estimating the linear-in-means model of peer effects in which the peer group, defined by a social network, is endogenous in the outcome equation for peer effects. Endogeneity is due to unobservable individual characteristics that influence both link formation in the network and the outcome of interest. We propose two estimators of the peer effect equation that control for the endogeneity of the social connections using a control function approach. We leave the functional form of the control function unspecified, estimate the model using a sieve semiparametric approach and establish asymptotics of the semiparametric estimator.

Estimation of covariate effects on net survivals in the relative survival progressive illness-death model.

Recently, there has been a lot of development in relative survival field. In the absence of data on the cause of death, the research has tended to focus on the estimation of survival probability of a cancer (as a disease of interest). In many cancers, one nonfatal event that decreases the survival probability can occur. There are a few methods that assess the role of prognostic factors for multiple types of clinical events while dealing with uncertainty about the cause of death. However, these methods require proportional hazard or Markov assumptions. In practice, one or both of these assumptions might be violated. Violation of the proportional hazard assumption can lead to estimates that are biased, and difficult to interpret and violation of Markov assumption results in inconsistent estimators. In this work, we propose a semi-parametric approach to estimate the possibly time-varying regression coefficients in the likely non-Markov relative survival progressive illness-death model. The performance of the proposed estimator is investigated through simulations. We illustrate our approach using data from a study on rectal cancer resected for cure conducted in two French population-based digestive cancer registries.

Parametric and Semiparametric Efficiency Frontiers in Fishery Analysis: Overview and Case Study on the Falkland Islands

Provision of adequately valued individual transferable quotas and effort quotas is essential for sustainability and profitability of a fishery. Despite possible misleading consequences for policy-making, the extent to which fishery inefficiency estimates and rankings may depend on the model used, has received less attention. This paper first reviews determinants of fishers’ behaviour under regulated harvesting, with the Falkland Islands as focus case. Next, a ‘best scenario’ long-term equilibrium framework is outlined, under a regime of transferable effort quotas and fishing seasons as implemented in the Islands, followed by an overview of panel data stochastic frontier models, with specific regard to fisheries. To test hypotheses and impact of a mainly ITEQ-based regime for Falkland fisheries, two parametric and one semiparametric model rely on different assumptions on frontiers and inefficiency scores. Relative to companies operating in Falkland seas, regression estimates highlight the relevance of economies of scale, vessel ownership, and climatic factors among others, with improved cost effectiveness, and revenue efficiency frontier-enhancing/inefficiency-reducing effects, following the implementation of the new regime. Within either modelling approach, inefficiency differs marginally across regression specifications, but mismatches in levels and rankings emerge between parametric and semiparametric models. Relative to southern hake catches by Falkland trawlers, the semiparametric approach suggests upward shifts in output frontiers under the new fishery regime, with inefficiency scores substantially unaltered between two functional specifications.

A Bayesian semiparametric approach for inference on the population partly conditional mean from longitudinal data with dropout.

Studies of memory trajectories using longitudinal data often result in highly nonrepresentative samples due to selective study enrollment and attrition. An additional bias comes from practice effects that result in improved or maintained performance due to familiarity with test content or context. These challenges may bias study findings and severely distort the ability to generalize to the target population. In this study, we propose an approach for estimating the finite population mean of a longitudinal outcome conditioning on being alive at a specific time point. We develop a flexible Bayesian semiparametric predictive estimator for population inference when longitudinal auxiliary information is known for the target population. We evaluate the sensitivity of the results to untestable assumptions and further compare our approach to other methods used for population inference in a simulation study. The proposed approach is motivated by 15-year longitudinal data from the Betula longitudinal cohort study. We apply our approach to estimate lifespan trajectories in episodic memory, with the aim to generalize findings to a target population.

Estimation of Undirected Graph with Finite Mixture of Nonparanormal Distribution

In this paper, the nonparanormal graphical mixture model is introduced as a flexible multivariate analysis tool with a semiparametric approach. In this model, mixture component densities are nonparanormal distributions with different covariance matrices. Therefore, each mixture component may have a different dependency structure with the probability of the respective mixture proportion. Our suggested estimation algorithm uses expectation maximization algorithm for maximization of $$\ell _1$$ -regularized likelihood function. Graphical lasso algorithm and extended Bayesian information criterion are used in each iteration of the EM algorithm for the model selection purposes. Simulation studies show that the proposed method performs better than the alternative Gaussian graphical mixture model, especially for non-Gaussian heterogeneous data. The proposed method is also applied to water-level dataset and is compared with the results of Gaussian mixture model.

A Bayesian semiparametric vector Multiplicative Error Model

Interactions among multiple time series of positive random variables are crucial in diverse financial applications, from spillover effects to volatility interdependence. A popular model in this setting is the vector Multiplicative Error Model (vMEM) which poses a linear iterative structure on the dynamics of the conditional mean, perturbed by a multiplicative innovation term. A main limitation of vMEM is however its restrictive assumption on the distribution of the random innovation term. A Bayesian semiparametric approach that models the innovation vector as an infinite location-scale mixture of multidimensional kernels with support on the positive orthant is used to address this major shortcoming of vMEM. Computational complications arising from the constraints to the positive orthant are avoided through the formulation of a slice sampler on the parameter-extended unconstrained version of the model. The method is applied to simulated and real data and a flexible specification is obtained that outperforms the classical ones in terms of fitting and predictive power.

A semiparametric modeling approach for analyzing clinical biomarkers restricted to limits of detection

Before biomarkers can be used in clinical trials or patients' management, the laboratory assays that measure their levels have to go through development and analytical validation. One of the most critical performance metrics for validation of any assay is related to the minimum amount of values that can be detected and any value below this limit is referred to as below the limit of detection (LOD). Most of the existing approaches that model such biomarkers, restricted by LOD, are parametric in nature. These parametric models, however, heavily depend on the distributional assumptions, and can result in loss of precision under the model or the distributional misspecifications. Using an example from a prostate cancer clinical trial, we show how a critical relationship between serum androgen biomarker and a prognostic factor of overall survival is completely missed by the widely used parametric Tobit model. Motivated by this example, we implement a semiparametric approach, through a pseudo-value technique, that effectively captures the important relationship between the LOD restricted serum androgen and the prognostic factor. Our simulations show that the pseudo-value based semiparametric model outperforms a commonly used parametric model for modeling below LOD biomarkers by having lower mean square errors of estimation.

The effect of exports on labour share: A semiparametric approach using Chinese manufacturing panel data

AbstractWe distinguish the effects of export on labour share into a stand‐alone direct effect and indirect effects, which alter the marginal impact of three key determinants of labour share found in the literature. While the direct effect of export has been extensively studied, the potential indirect effects remain unexplored. We investigate both effects of exports using micro‐level Chinese firm‐level data from 1998 to 2007. We employ a fixed‐effect varying coefficient model to reveal the potential nonlinearity of the effects of exports while alleviating the risk of model mis‐specification. Our model is estimated by a spline‐backfitted kernel estimator, which is more efficient and computationally attractive than alternative estimators. We find that while exports directly increase labour share as expected, it declines labour share indirectly through intensifying the negative marginal impact of firms’ capital intensity, monopoly power and capital‐augmented technological progress on labour share. As a result, the net effect of exports is not beneficial to labour's share of income and varies in magnitude across firm characteristics, regions and time periods.

Long Memory in Earthquake Time Series: The Case Study of the Geysers Geothermal Field

The present study aims at proving the existence of long memory (or long-range dependence) in the earthquake process through the analysis of time series of induced seismicity. Specifically, we apply alternative statistical techniques borrowed from econometrics to the seismic catalog of The Geysers geothermal field (California), the world’s largest geothermal field. The choice of the study area is essentially guided by the completeness of the seismic catalog at smaller magnitudes (a drawback of conventional catalogs of natural seismicity). Contrary to previous studies, where the long-memory property was examined by using non-parametric approaches (e.g., rescaled range analysis), we assume a fractional integration model for which the degree of memory is defined by a real parameterd, which is related to the best known Hurst exponent. In particular, long-memory behavior is observed ford> 0. We estimate and test the value ofd(i.e., the hypothesis of long memory) by applying parametric, semi-parametric, and non-parametric approaches to time series describing the daily number of earthquakes and the logarithm of the (total) seismic moment released per day. Attention is also paid to examining the sensitivity of the results to the uncertainty in the completeness magnitude of the catalog, and to investigating to what extent temporal fluctuations in seismic activity induced by injection operations affect the value ofd. Temporal variations in the values ofdare analyzed together with those of theb-value of the Gutenberg and Richter law. Our results indicate strong evidence of long memory, withdmostly constrained between 0 and 0.5. We observe that the value ofdtends to decrease with increasing the magnitude completeness threshold, and therefore appears to be influenced by the number of information in the chain of intervening related events. Moreover, we find a moderate but significant negative correlation betweendand theb-value. A negative, albeit weaker correlation is found betweendand the fluid injection, as well as betweendand the annual number of earthquakes.

Modeling Multiple Time-Varying Related Groups: A Dynamic Hierarchical Bayesian Approach With an Application to the Health and Retirement Study

As the population of the older individuals continues to grow, it is important to study the relationship among the variables measuring financial health and physical health of the older individuals to better understand the demand for healthcare, and health insurance. We propose a semiparametric approach to jointly model these variables. We use data from the Health and Retirement Study which includes a set of correlated longitudinal variables measuring financial and physical health. In particular, we propose a dynamic hierarchical matrix stick-breaking process prior for some of the model parameters to account for the time dependent aspects of our data. This prior introduces dependence among the parameters across different groups which varies over time. A Lasso type shrinkage prior is specified for the covariates with time-invariant effects for selecting the set of covariates with significant effects on the outcomes. Through joint modeling, we are able to study the physical health of the older individuals conditional on their financial health, and vice-versa. Based on our analysis, we find that the health insurance (medicare) provided by the government (of the United States) to the older individuals is very effective, and it covers most of the medical expenditures. However, none of the health insurances conveniently cover the additional medical expenses due to chronic diseases like cancer and heart problem. Simulation studies are performed to assess the operating characteristics of our proposed modeling approach. Supplementary materials for this article, including a standardized description of the materials available for reproducing the work, are available as an online supplement.

Estimation of different types of entropies for the Kumaraswamy distribution.

The estimation of the entropy of a random system or process is of interest in many scientific applications. The aim of this article is the analysis of the entropy of the famous Kumaraswamy distribution, an aspect which has not been the subject of particular attention previously as surprising as it may seem. With this in mind, six different entropy measures are considered and expressed analytically via the beta function. A numerical study is performed to discuss the behavior of these measures. Subsequently, we investigate their estimation through a semi-parametric approach combining the obtained expressions and the maximum likelihood estimation approach. Maximum likelihood estimates for the considered entropy measures are thus derived. The convergence properties of these estimates are proved through a simulated data, showing their numerical efficiency. Concrete applications to two real data sets are provided.

Semi-parametric estimation of multinomial choice model with unobserved heterogeneity

We propose a semi-parametric method for estimating the multinomial choice model using cyclical monotonicity moment inequalities. In our semiparametric approach, we do not specify the parametric distribution for the utility shocks, thus accommodating a wide variety of substitution patterns among alternatives. Compared with the conditional likelihood estimation method proposed by Chamberlain and the method proposed by Shi, Shum, and Song, simulations show that our method has some advantages in terms of mean bias, standard deviation and root mean squared error.

Evaluation of mean-time-to-failure based on nonlinear degradation data with applications

In reliability engineering, obtaining lifetime information for highly reliable products is a challenging problem. When a product quality characteristic whose degradation over time can be related to lifetime, then the degradation data can be used to estimate the first-passage (failure) time distribution and the Mean-Time-To-Failure (MTTF) for a given threshold level. To model the degradation data, the commonly used Lévy process modeling approach assumes that the degradation measurements are linearly related to time throughout the lifetime of the product. However, the degradation data may not be linearly related to time in practice. For this reason, trend-renewal-process-type models can be considered for degradation modeling in which a proper trend function is used to transform the degradation data so that the Lévy process approach can be applied. In this article, we study several parametric and semiparametric models and approaches to estimate the first-passage time distribution and MTTF for degradation data that may be not linearly related to time. A Monte Carlo simulation study is used to demonstrate the performance of the proposed methods. In addition, a model selection procedure is proposed to select among different models. Two numerical examples of lithium-ion battery degradation data are applied to illustrate the proposed methodologies.

Bayesian Bandwidths in Semiparametric Modelling for Nonnegative Orthant Data with Diagnostics

Multivariate nonnegative orthant data are real vectors bounded to the left by the null vector, and they can be continuous, discrete or mixed. We first review the recent relative variability indexes for multivariate nonnegative continuous and count distributions. As a prelude, the classification of two comparable distributions having the same mean vector is done through under-, equi- and over-variability with respect to the reference distribution. Multivariate associated kernel estimators are then reviewed with new proposals that can accommodate any nonnegative orthant dataset. We focus on bandwidth matrix selections by adaptive and local Bayesian methods for semicontinuous and counting supports, respectively. We finally introduce a flexible semiparametric approach for estimating all these distributions on nonnegative supports. The corresponding estimator is directed by a given parametric part, and a nonparametric part which is a weight function to be estimated through multivariate associated kernels. A diagnostic model is also discussed to make an appropriate choice between the parametric, semiparametric and nonparametric approaches. The retention of pure nonparametric means the inconvenience of parametric part used in the modelization. Multivariate real data examples in semicontinuous setup as reliability are gradually considered to illustrate the proposed approach. Concluding remarks are made for extension to other multiple functions.

Bayesian semi-parametric G-computation for causal inference in a cohort study with MNAR dropout and death.

Causal inference with observational longitudinal data and time-varying exposures is often complicated by time-dependent confounding and attrition. The G-computation formula is one approach for estimating a causal effect in this setting. The parametric modeling approach typically used in practice relies on strong modeling assumptions for valid inference, and moreover depends on an assumption of missing at random, which is not appropriate when the missingness is missing not at random (MNAR) or due to death. In this work we develop a flexible Bayesian semi-parametric G-computation approach for assessing the causal effect on the subpopulation that would survive irrespective of exposure, in a setting with MNAR dropout. The approach is to specify models for the observed data using Bayesian additive regression trees, and then use assumptions with embedded sensitivity parameters to identify and estimate the causal effect. The proposed approach is motivated by a longitudinal cohort study on cognition, health, and aging, and we apply our approach to study the effect of becoming a widow on memory. We also compare our approach to several standard methods.

A Semiparametric Approach for Structural Equation Modeling with Ordinal Data

ABSTRACT There is currently a lack of methods for non-linear structural equation modeling (NSEM) for non-parametric relationships between latent variables when data are ordinal. To this end, a semiparametric approach for flexible NSEMs without parametric forms is developed for ordinal data. An indirect application of a finite mixture of structural equation models (SEMM) is employed for modeling the conditional expected mean of endogenous latent variables. In this context, the latent classes are not to be interpreted as groups of observations belonging to those classes, rather they serve as means to model flexible non-linear functions as locally linear functions which together approximate a globally non-linear function. The proposed method is based on a hybrid of direct maximization and expectation-maximization algorithms. Two simulation studies are performed which show that parameter estimates are associated with low bias and a non-linear functional form is satisfactorily estimated using the proposed approach.

Determinants of flood adaptation: Parametric and semiparametric assessment

AbstractFlood adaptation measures are indispensable to offset agricultural losses emanating from the increasing frequency and intensity of floods. Therefore, it is necessary to identify key precursors of adaptation for the success of flood‐related adaptation programs. Using cross‐sectional household survey data from rice farmers of eastern Nepal, this study explores existing adaptation practices along with the factors influencing farmers' adaptation strategies. Both parametric and semiparametric forms of the binary choice model are employed to assess key determinants of flood adaptation. The results reveal that existing adaptation practices are limited to conventional seed storage and few (bio)engineering techniques. Both household and farm characteristics, including flood impact indicators, significantly influence farmers' adaptation to flooding hazards. Thus, consideration of these multiple factors in adaptation‐related programs is anticipated to cope with future floods. Prioritising crop insurance over disaster relief programs and revitalization of existing adaptation measures are suggested. Furthermore, this study demonstrates that the semiparametric approach offers a better alternative by lifting the basic assumptions of parametric models. Findings from this article could aid in developing localised adaptation strategies that would ultimately contribute to the resiliency of farming households and the flood‐prone communities as a whole.

Semiparametric Inference for Nonmonotone Missing-Not-at-Random Data: The No Self-Censoring Model

We study the identification and estimation of statistical functionals of multivariate data missing nonmonotonically and not-at-random, taking a semiparametric approach. Specifically, we assume that the missingness mechanism satisfies what has been previously called “no self-censoring” or “itemwise conditionally independent nonresponse,” which roughly corresponds to the assumption that no partially observed variable directly determines its own missingness status. We show that this assumption, combined with an odds ratio parameterization of the joint density, enables identification of functionals of interest, and we establish the semiparametric efficiency bound for the nonparametric model satisfying this assumption. We propose a practical augmented inverse probability weighted estimator, and in the setting with a (possibly high-dimensional) always-observed subset of covariates, our proposed estimator enjoys a certain double-robustness property. We explore the performance of our estimator with simulation experiments and on a previously studied dataset of HIV-positive mothers in Botswana. Supplementary materials for this article are available online.

Modeling nonstationary extremes of storm severity: Comparing parametric and semiparametric inference

AbstractThis article compares the modeling of nonstationary extreme events using parametric models with local parametric and semiparametric approaches also motivated by extreme value theory. Specifically, three estimators are compared based on (a) (local) semiparametric moment estimation, (b) (local) maximum likelihood estimation, and (c) spline‐based maximum likelihood estimation. Inference is performed in a sequential manner, highlighting the synergies between the different approaches to estimating extreme quantiles, including the T‐year level and right endpoint when finite. We present a novel heuristic to estimate nonstationary extreme value threshold with exceedances varying on a circular domain, and hypothesis‐testing procedures for identifying max‐domain of attraction in the nonstationary setting. Bootstrapping is used to estimate nonstationary confidence bounds throughout. We provide step‐by‐step guides for estimation, and explore the different inference strategies in application to directional modeling of hindcast storm peak significant wave heights recorded in the North Sea.

Semiparametric analysis of interval‐censored failure time data with outcome‐dependent observation schemes

AbstractDisease progression is often monitored by intermittent follow‐up “visits” in longitudinal cohort studies, resulting in interval‐censored failure time outcomes. Furthermore, the timing and frequency of visits is often found related to a person's history of disease‐related variables in practice. This article develops a semiparametric estimation approach using weighted binomial regression and a kernel smoother to analyze interval‐censored failure time data. Visit times are allowed to be subject‐specific and outcome‐dependent. We consider a collection of widely used semiparametric regression models, including additive hazards and linear transformation models. For additive hazards models, the nonparametric component has a closed‐form estimator and the estimators of regression coefficients are shown to be asymptotically multivariate normal with sandwich‐type covariance matrices. Simulations are conducted to examine the finite sample performance of the proposed estimators. A data set from the Toronto Psoriatic Arthritis (PsA) Cohort Study is used to illustrate the proposed methodology.