Semiparametric Varying Coefficient Model Research Articles

Semiparametric varying-coefficient expectile model for estimating value at risk on dependent samples

We introduce a semiparametric varying-coefficient model to study the expectile-based value at risk (EVaR) based on the $\\alpha$-mixing assumption. The model considers the risk factors as well as the dynamic structure and the interaction of these factors. Meanwhile, EVaR not only has great advantages such as the subadditivity or easy to calculate, but also is very sensitive to the scale of losses compared with the conventional quantile-based value at risk (QVaR), which makes it as a more mature and efficient way of the risk measure in extreme risk situations. We develop a three-stage method to estimate the parameters of the varying-coefficient part and the constant-coefficient part. We also establish the challenging consistency and the asymptotic normality of all the resultant estimation in three stages under the time series samples. To save computing time, we propose to use a one-step procedure to compute the estimation. Financial time series samples are not independent data. It has more challenge to establish the large sample properties of the estimators. We introduce the dividing methods to prove the limittheory of the $\\alpha$-mixing series, and obtain the asymptotic properties of the parametric constant coefficients and the nonparametric varying-coefficients. In our simulation, three models results show the accuracy and robustness of our estimation. The real financial data example performs as an application of our model at the end of our study.

A Bayesian natural cubic B-spline varying coefficient method for non-ignorable dropout

BackgroundDropout is a common problem in longitudinal clinical trials and cohort studies, and is of particular concern when dropout occurs for reasons that may be related to the outcome of interest. This paper reviews common parametric models to account for dropout and introduces a Bayesian semi-parametric varying coefficient model for exponential family longitudinal data with non-ignorable dropout.MethodsTo demonstrate these methods, we present results from a simulation study and estimate the impact of drug use on longitudinal CD4 + T cell count and viral load suppression in the Women’s Interagency HIV Study. Sensitivity analyses are performed to consider the impact of model assumptions on inference. We compare results between our semi-parametric method and parametric models to account for dropout, including the conditional linear model and a parametric frailty model. We also compare results to analyses that fail to account for dropout.ResultsIn simulation studies, we show that semi-parametric methods reduce bias and mean squared error when parametric model assumptions are violated. In analyses of the Women’s Interagency HIV Study data, we find important differences in estimates of changes in CD4 + T cell count over time in untreated subjects that report drug use between different models used to account for dropout. We find steeper declines over time using our semi-parametric model, which makes fewer assumptions, compared to parametric models. Failing to account for dropout or to meet parametric assumptions of models to account for dropout could lead to underestimation of the impact of hard drug use on CD4 + cell count decline in untreated subjects. In analyses of subjects that initiated highly active anti-retroviral treatment, we find that the estimated probability of viral load suppression is lower in models that account for dropout.ConclusionsNon-ignorable dropout is an important consideration when analyzing data from longitudinal clinical trials and cohort studies. While methods that account for non-ignorable dropout must make some unavoidable assumptions that cannot be verified from the observed data, many methods make additional parametric assumptions. If these assumptions are not met, inferences can be biased, making more flexible methods with minimal assumptions important.

Measuring the impact of national guidelines: What methods can be used to uncover time-varying effects for healthcare evaluations?

We examine the suitability of three methods using patient-level data to evaluate the time-varying impacts of national healthcare guidelines. Such guidelines often codify progressive change and are implemented gradually; for example, National Institute for Health and Care Excellence (NICE) suspected-cancer referral guidelines. These were revised on June 23, 2015, to include more cancer symptoms and test results ("features"), partly reflecting changing practice. We explore the time-varying impact of guideline revision on time to colorectal cancer diagnosis, which is linked to improved outcomes in decision-analytic models. We included 11,842 patients diagnosed in 01/01/2006-31/12/2017 in the Clinical Practice Research Datalink with England cancer registry data linkage. Patients were classified by whether their first pre-diagnostic cancer feature was in the original guidelines (NICE-2005) or was added during the revision (NICE-2015-only). Outcome was diagnostic interval: time from first cancer feature to diagnosis. All analyses adjusted for age and sex. Two difference-in-differences analyses used either a Pre (01/08/2012-31/12/2014, n=2243) and Post (01/08/2015-31/12/2017, n=1017) design, or event-study cohorts (2006-2017 vs 2015) to estimate change in diagnostic interval attributable to official implementation of the revised guidelines. A semiparametric varying-coefficient model analysed the difference in diagnostic interval between the NICE groups over time. After model estimation, primary and broader treatment effects of guideline content and implementation were measured. The event-study difference-in-differences and the semiparametric varying-coefficient methods showed that shorter diagnostic intervals were attributable to official implementation of the revised guidelines. This impact was only detectable by pre-to-post difference-in-differences when the pre/post periods were selected according to the estimation results from the varying-coefficient model. Formal tests of the parametric models, which are special cases of the semiparametric model, suggest that they are misspecified. We conclude that the semiparametric method is well suited to explore the time-varying impacts of guidelines codifying progressive change.

Exploring the Heterogeneous Effects of Export Promotion

Abstract A semiparametric varying coefficient model is used to explore the heterogeneity in returns to export promotion across countries. Differences in characteristics of export-promotion agencies drive the heterogeneity in returns. Interestingly, characteristics that matter for export growth do not necessarily matter for GDP per capita growth. A 1 percent increase in export-promotion budgets is associated with an average increase in exports of 0.10 percent and an average increase in GDP per capita of 0.06 percent. However, these average returns hide a lot of heterogeneity. Returns in terms of exports vary from 0 percent in Cyprus and Vietnam to 0.22 percent in Portugal. Returns in terms of GDP per capita show less heterogeneity, varying from 0.05 in Malawi to 0.10 percent in Portugal and Nicaragua.

Analysis of longitudinal data with semiparametric varying-coefficient mean–covariance models

The efficient estimation of regression coefficients in the longitudinal data analysis requires a correct specification of the covariance structure. Existing approaches usually focus on modeling the mean with specification of certain covariance structures, which may lead to inefficient or biased estimators of parameters in the mean if misspecification occurs. In this article, we propose a novel data-driven approach based on semiparametric varying-coefficient models to model the mean and the covariance simultaneously, motivated by the modified Cholesky decomposition. An iterative estimation method is proposed, consisting of an orthogonality-based technique for parameters, an adaptive jump-preserving estimation method for varying coefficients, a modification of local linear smoothing technique for the autoregressive coefficient function, and a kernel smoothing technique for the variance function. Theoretical properties of the resulting estimators including uniform consistency and asymptotic normality are explicitly studied under certain mild conditions. Simulation studies are carried out to evaluate the efficacy of the proposed methods, and an analysis of a real data example is provided for illustration.

OPTIMAL MODEL AVERAGING OF VARYING COEFFICIENT MODELS

We consider the problem of model averaging over a set of semiparametric varying coefficient models where the varying coefficients can be functions of continuous and categorical variables. We propose a Mallows model averaging procedure that is capable of delivering model averaging estimators with solid finite-sample performance. Theoretical underpinnings are provided, finite-sample performance is assessed via Monte Carlo simulation, and an illustrative application is presented. The approach is very simple to implement in practice and R code is provided in an appendix.

Semiparametric varying-coefficient regression analysis of recurrent events with applications to treatment switching.

This paper investigates the semiparametric statistical methods for recurrent events. The mean number of the recurrent events are modeled with the generalized semiparametric varying-coefficient model that can flexibly model three types of covariate effects: time-constant effects, time-varying effects, and covariate-varying effects. We assume that the time-varying effects are unspecified functions of time and the covariate-varying effects are parametric functions of an exposure variable specified up to a finite number of unknown parameters. Different link functions can be selected to provide a rich family of models for recurrent events data. The profile estimation methods are developed for the parametric and nonparametric components. The asymptotic properties are established. We also develop some hypothesis testing procedures to test validity of the parametric forms of covariate-varying effects. The simulation study shows that both estimation and hypothesis testing procedures perform well. The proposed method is applied to analyze a data set from an acyclovir study and investigate whether acyclovir treatment reduces the mean relapse recurrences.

Estimation for semiparametric varying coefficient models with different smoothing variables under random right censoring

In this paper we study a semiparametric varying coefficient model when the response is subject to random right censoring. The model gives an easy interpretation due to its direct connectivity to the classical linear model and is very flexible since nonparametric functions which accommodates various nonlinear interaction effects between covariates are admitted in the model. We propose estimators for this model using mean-preserving transformation and establish their asymptotic properties. The estimation procedure is based on the profiling and the smooth backfitting techniques. A simulation study is presented to show the reliability of the proposed estimators and an automatic bandwidth selector is given in a data-driven way.

Two-stage orthogonality based estimation for semiparametric varying-coefficient models and its applications in analyzing AIDS data.

Semiparametric smoothing methods are usually used to model longitudinal data, and the interest is to improve efficiency for regression coefficients. This paper is concerned with the estimation in semiparametric varying-coefficient models (SVCMs) for longitudinal data. By the orthogonal projection method, local linear technique, quasi-score estimation, and quasi-maximum likelihood estimation, we propose a two-stage orthogonality-based method to estimate parameter vector, coefficient function vector, and covariance function. The developed procedures can be implemented separately and the resulting estimators do not affect each other. Under some mild conditions, asymptotic properties of the resulting estimators are established explicitly. In particular, the asymptotic behavior of the estimator of coefficient function vector at the boundaries is examined. Further, the finite sample performance of the proposed procedures is assessed by Monte Carlo simulation experiments. Finally, the proposed methodology is illustrated with an analysis of an acquired immune deficiency syndrome (AIDS) dataset.

Optimal Model Averaging of Varying Coefficient Models

We consider the problem of model averaging over a set of semiparametric varying coefficient models where the varying coefficients can be functions of continuous and categorical variables. We propose a Mallows model averaging procedure that is capable of delivering model averaging estimators with solid finite-sample performance. Theoretical underpinnings are provided, finite-sample performance is assessed via Monte Carlo simulation, and an illustrative application is presented. The approach is very simple to implement in practice and R code is provided in an appendix.

Semiparametric Varying Coefficient Models with Endogenous Covariates

Though parametric methods are popular in applied settings, practitioners often require nonparametric alternatives.However,fully nonparametric methods are known to suffer from the curse-of-dimensionality, which limits their practical application. Semiparametric methods occupy a middle ground, have the desirable feature that they are both flexible,and provide an attractive alternative to fully nonparametric methods, while attenuating the curse-of-dimensionality.Traditional semiparametric methods, such as the popular 'varying coefficient' specification, do not account for endogenous covariates, which restricts their application. In this paper we consider the estimation of semiparametric varying coefficient models when the functional coefficients may contain (continuous) endogenous covariates thereby extending the reach of this fl exible and powerful class of models.

Variable selection for spatial semivarying coefficient models

Spatial semiparametric varying coefficient models are a useful extension of spatial linear model. Nevertheless, how to conduct variable selection for it has not been well investigated. In this paper, by basis spline approximation together with a general M-type loss function to treat mean, median, quantile and robust mean regressions in one setting, we propose a novel partially adaptive group $$L_{r} (r\ge 1)$$ penalized M-type estimator, which can select variables and estimate coefficients simultaneously. Under mild conditions, the selection consistency and oracle property in estimation are established. The new method has several distinctive features: (1) it achieves robustness against outliers and heavy-tail distributions; (2) it is more flexible to accommodate heterogeneity and allows the set of relevant variables to vary across quantiles; (3) it can keep balance between efficiency and robustness. Simulation studies and real data analysis are included to illustrate our approach.

Generalized semiparametric varying-coefficient model for longitudinal data with applications to adaptive treatment randomizations.

This article investigates a generalized semiparametric varying-coefficient model for longitudinal data that can flexibly model three types of covariate effects: time-constant effects, time-varying effects, and covariate-varying effects. Different link functions can be selected to provide a rich family of models for longitudinal data. The model assumes that the time-varying effects are unspecified functions of time and the covariate-varying effects are parametric functions of an exposure variable specified up to a finite number of unknown parameters. The estimation procedure is developed using local linear smoothing and profile weighted least squares estimation techniques. Hypothesis testing procedures are developed to test the parametric functions of the covariate-varying effects. The asymptotic distributions of the proposed estimators are established. A working formula for bandwidth selection is discussed and examined through simulations. Our simulation study shows that the proposed methods have satisfactory finite sample performance. The proposed methods are applied to the ACTG 244 clinical trial of HIV infected patients being treated with Zidovudine to examine the effects of antiretroviral treatment switching before and after HIV develops the T215Y/F drug resistance mutation. Our analysis shows benefits of treatment switching to the combination therapies as compared to continuing with ZDV monotherapy before and after developing the 215-mutation.

Semiparametric varying-coefficient model with right-censored and length-biased data

The analysis of right-censored and length-biased data is commonly encountered in prevalent cohort studies. The special structure of length-biased data is different from the structure of traditional survival data and the methods for traditional survival data cannot be directly applied to length-biased data, because the assumption of independent censoring is often violated in the presence of biased sampling and the assumed model for the underlying population is no longer satisfied. In this paper, we propose a flexible semiparametric varying-coefficient model for analyzing the covariate effects on the population survival time under length-biased sampling. To estimate the parameters, we develop a three-stage estimation procedure, which can improve the efficiency of the estimators. In addition to the case where the censoring variable is independent of the covariates, we consider the case where the censoring variable depends on covariates. The asymptotic properties of the proposed estimators are derived under regularity conditions, and a resampling procedure is used to confirm the methods through simulations. Finally, we illustrate the methods using data concerning the Academy Awards.

Semiparametric Varying Coefficient Models with Endogenous Covariates

Though parametric methods are popular in applied settings, practitioners often require nonparametric alternatives. However, fully nonparametric methods are known to suffer from the curse of dimensionality, which limits their practical application. Semiparametric methods occupy a middle ground, have the desirable feature that they are both exible, and provide an attractive alternative to fully nonparametric methods, while attenuating the curse-of-dimensionality. Traditional semiparametric methods, such as the popular `varying coefficient' specification, do not account for endogenous covariates, which restricts their application. In this paper we consider the estimation of semiparametric varying coeffcient models when the functional coeffcients may contain (continuous) endogenous covariates thereby extending the reach of this exible and powerful class of models.

Quantile regression methods with varying-coefficient models for censored data

Considerable intellectual progress has been made to the development of various semiparametric varying-coefficient models over the past ten to fifteen years. An important advantage of these models is that they avoid much of the curse of dimensionality problem as the nonparametric functions are restricted only to some variables. More recently, varying-coefficient methods have been applied to quantile regression modeling, but all previous studies assume that the data are fully observed. The main purpose of this paper is to develop a varying-coefficient approach to the estimation of regression quantiles under random data censoring. We use a weighted inverse probability approach to account for censoring, and propose a majorize–minimize type algorithm to optimize the non-smooth objective function. The asymptotic properties of the proposed estimator of the nonparametric functions are studied, and a resampling method is developed for obtaining the estimator of the sampling variance. An important aspect of our method is that it allows the censoring time to depend on the covariates. Additionally, we show that this varying-coefficient procedure can be further improved when implemented within a composite quantile regression framework. Composite quantile regression has recently gained considerable attention due to its ability to combine information across different quantile functions. We assess the finite sample properties of the proposed procedures in simulated studies. A real data application is also considered.

A CONSISTENT NONPARAMETRIC TEST ON SEMIPARAMETRIC SMOOTH COEFFICIENT MODELS WITH INTEGRATED TIME SERIES

In this paper, we propose a simple nonparametric test for testing the null hypothesis of constant coefficients against nonparametric smooth coefficients in a semiparametric varying coefficient model with integrated time series. We establish the asymptotic distributions of the proposed test statistic under both null and alternative hypotheses. Moreover, we derive a central limit theorem for a degenerate second order U-statistic, which contains a mixture of stationary and nonstationary variables and is weighted locally on a stationary variable. This result is of independent interest and useful in other applications. Monte Carlo simulations are conducted to examine the finite sample performance of the proposed test.

A Varying-Coefficient Panel Data Model with Fixed Effects: Theory and an Application to U.S. Commercial Banks

In this paper, we propose a panel data semiparametric varying-coefficient model in which covariates (variables affecting the coefficients) are purely categorical. This model has two features: first, fixed effects are included to allow for correlation between individual unobserved heterogeneity and the regressors; second, it allows for cross-sectional dependence through a general spatial error dependence structure. We derive a semiparametric estimator for our model by using a modified within transformation, and then show the asymptotic and finite properties for this estimator. Finally, we illustrate our model by analyzing the effects of state-level banking regulations on the returns to scale of commercial banks in the U.S.. Our empirical results suggest that returns to scale is higher in more regulated states than in less regulated states.

Volatility Spillover Effect: A Semiparametric Analysis of Non-Cointegrated Process

Stock market volatility is highly persistent and exhibits large fluctuations so that it is likely to be an integrated or a near integrated process. Stock markets' volatilities from different countries are intercorrelated, but are generally not cointegrated as many other (domestic) factors also affect volatility. In this paper, we use a semiparametric varying coefficient model to examine stock market volatility spillover effects. Using the estimation method proposed by Sun et al. (2011), we study the U.S./U.K. and U.S./Canadian stock market volatility spillover effects. We find striking similar patterns in both the U.S./U.K. and the U.S./Canadian markets. The stock market volatility spillover effects are strengthened when the currency markets experience high movement, and the spillover effects are asymmetric depending on whether a foreign currency is appreciating or depreciating.

A semiparametric varying coefficient model of monotone auction bidding processes

We propose an econometric model of the price processes of online auctions. Since auction bids monotonically increase within individual auctions but can differ considerably across auctions, we construct a monotone series estimator with a common relative price growth curve and auction-specific slopes. Furthermore, because the impacts of auction-specific attributes may evolve along the course of auctions, we employ a varying coefficient approach to accommodate these possibly time-varying effects. We present an algorithm to solve the proposed partially linear panel model with a nonparametric monotone component. We apply the proposed model to eBay auctions of a Palm personal digital assistant. The estimates capture closely the overall pattern of online auction price processes, in particular, the bidding drought midway through auctions and the bid acceleration associated with bid sniping (last-minute bidding) at the end of auctions.