Semiparametric Regression Approach Research Articles

Semiparametric nonlinear regression for detecting gene and environment interactions

It is commonly accepted that gene and environment (G×E) interactions play a pivotal role in determining the risk of human diseases. In conventional parametric models such as linear models and generalized linear models which are applied frequently to study statistical interactions, effects of covariates are decomposed into main effects and interaction effects (products of two components). Such decomposition, however, may not reflect the true interaction effect of gene and environment. In this paper, we propose a semiparametric regression approach to capture possible nonlinear G×E interactions. A profile quasi-log-likelihood estimation method is applied with asymptotic consistency and normality established for the profile estimators. Moreover, we develop Rao-score-type test procedures based on the profile estimation for regression parameters and nonparametric coefficient functions, respectively. Our models and methods are illustrated by both simulation studies and analysis of a dataset application.

Bayesian Semi-Parametric Regression for Quantile Residual Lifetime

The quantile residual life function has been effectively used to interpret results from the analysis of the proportional hazards model for censored survival data; however, the quantile residual life function is not always estimable with currently available semi-parametric regression methods in the presence of heavy censoring. A parametric regression approach may circumvent the difficulty of heavy censoring, but parametric assumptions on a baseline hazard function can cause a potential bias. This article proposes a Bayesian semi-parametric regression approach for inference on an unknown baseline hazard function while adjusting for available covariates. We consider a model-based approach but the proposed method does not suffer from strong parametric assumptions, enjoying a closed-form specification of the parametric regression approach without sacrificing the flexibility of the semi-parametric regression approach. The proposed method is applied to simulated data and heavily censored survival data to estimate various quantile residual lifetimes and adjust for important prognostic factors.

Statistical properties on semiparametric regression for evaluating pathway effects

Most statistical methods for microarray data analysis consider one gene at a time, and they may miss subtle changes at the single gene level. This limitation may be overcome by considering a set of genes simultaneously where the gene sets are derived from prior biological knowledge. We call a pathway as a predefined set of genes that serve a particular cellular or physiological function. Limited work has been done in the regression settings to study the effects of clinical covariates and expression levels of genes in a pathway on a continuous clinical outcome. A semiparametric regression approach for identifying pathways related to a continuous outcome was proposed by Liu et al. (2007), who demonstrated the connection between a least squares kernel machine for nonparametric pathway effect and a restricted maximum likelihood (REML) for variance components. However, the asymptotic properties on a semiparametric regression for identifying pathway have never been studied. In this paper, we study the asymptotic properties of the parameter estimates on semiparametric regression and compare Liu et al.'s REML with our REML obtained from a profile likelihood. We prove that both approaches provide consistent estimators, have n convergence rate under regularity conditions, and have either an asymptotically normal distribution or a mixture of normal distributions. However, the estimators based on our REML obtained from a profile likelihood have a theoretically smaller mean squared error than those of Liu et al.'s REML. Simulation study supports this theoretical result. A profile restricted likelihood ratio test is also provided for the non-standard testing problem. We apply our approach to a type II diabetes data set (Mootha et al., 2003).

A Bayesian Semiparametric Quantile Regression Model for Longitudinal Data with Application to Insurance Company Costs

This article examines the average cost function for property and casualty insurers. Cost function describes the relationship between a firm’s minimum production cost and outputs. The comparison of cost functions could shed light on the relative cost efficiency of individual firms, which is of interest to many market participants and has been given extensive attention in the insurance industry. To identify and compare the cost function of insurers, common practice is to assume an identical functional form between cost and outputs and to rank insurers according to the center (usually mean) of the cost distribution. Such assumption could be misleading because insurers tend to adopt different technologies that are reflected by the cost function in their production process. We find that the cost distribution is skewed with a heavy tail. Therefore, the center-based comparison could lead to biased inference regarding an insurer’s efficiency in operation. To address these issues, we propose Bayesian semiparametric quantile regression approach to model the longitudinal data on production cost of insurance companies. Particularly we formulate the quantile regression using the asymmetric Laplace distribution; the effects of various firm characteristics on the quantiles of cost are specified as a linear function; the firm-specific relation between cost and multiple outputs is captured by a single-index function based on a spline basis where the coefficients are assumed to have a Dirichlet process prior. The single-index formulation with splines renders flexibility in modeling the nonlinear cost-output relation and the use of Dirichlet process leads to a natural clustering of insurers with similar cost efficiency. The method is applied to data on US property casualty insurers from the National Association of Insurance Commissioners (NAIC). The analysis of average cost at different quantiles indicates that better insights on efficiency are gained by comparing the whole cost distribution. A comparison of the model results with an external financial strength ratings for property casualty insurers provides interesting insights on which part of the cost distribution are perhaps weighted more by the rating agency.

Semiparametric Autoregressive Conditional Duration Model: Theory and Practice

Many existing extensions of the Engle and Russell's (1998) Autoregressive Conditional Duration (ACD) model in the literature are aimed at providing additional flexibility either on the dynamics of the conditional duration model or the allowed shape of the hazard function, i.e. its two most essential components. This paper introduces an alternative semiparametric regression approach to a nonlinear ACD model; the use of a semiparametric functional form on the dynamics of the duration process suggests the model being called the Semiparametric ACD (SEMI-ACD) model. Unlike existing alternatives, the SEMI-ACD model allows simultaneous generalizations on both of the above -- mentioned components of the ACD framework. To estimate the model, we establish an alternative use of the existing Buhlmann and McNeil's (2002) iterative estimation algorithm in the semiparametric setting and provide the mathematical proof of its statistical consistency in our context. Furthermore, we investigate the asymptotic properties of the semiparametric estimators employed in order to ensure the statistical rigor of the SEMI-ACD estimation procedure. These asymptotic results are presented in conjunction with simulated examples, which provide an empirical evidence of the SEMI-ACD model's robust finite - sample performance. Finally, we apply the proposed model to study price duration process in the foreign exchange market to illustrate its usefulness in practice.

ON THE INFLUENCE OF CLIMATE AND SOCIO-ECONOMIC CONDITION TO THE DENGUE INCIDENCES: A SEMIPARAMETRIC PANEL REGRESSION APPROACH

Dengue is one of the most dangerous diseases in the worlds. In particularly in East Java province Indonesia, dengue has been identified as one of the major causes of death. Hence, it is important to investigate the factors that induce the number of dengue incidences in this region. This study examines climate and socio-economic conditions, which are assumed to influence the number of dengue in the examined region. The semiparametric panel regression approach has been applied and the results are compared with the standard panel regression. In this case, the socio-economic condition is treated parametrically while climate effect is modeled nonparametrically. The analysis showed that the number of dengue incidences is significantly influenced by the income per-capita and the number of inhabitant below 15 years. Furthermore, the dengue incidence is optimum under rainfall of 1500 to 3670 mm, temperature of 22 to 27 degree and humidity of 82 to 87%. The elasticity allows us to identify the most responsive and most irresponsive district towards the changes of climate variable. The study shows that Surabaya is the most responsive district with respect to the change of climate variables.

An Alternative Semiparametric Regression Approach to Nonlinear Duration Modeling: Theory and Practice

This paper puts forward an alternative semiparametric regression approach to a nonlinear ACD modeling. The semiparametric functional form of the dependence of the conditional intensity on past durations suggests that the model be called the Semiparametric ACD (SEMI{ACD) model. The development of the SEMI{ACD model relies on two important factors; namely (i) an iterative estimation algorithm, which is devised to address the latency problem arises because conditional expectation of duration with respect to the past history is not observable in practice, and (ii) an adaptive estimation of a partially linear additive autoregressive process. The model’s theoretical study involves two fundamental issues. The rst and by far the most important is the consistency of the estimation algorithm. Results will be exhibited for a variety of modes of consistency. Furthermore, to enrich the statistical rigor of the SEMI{ACD estimation procedure, the asymptotic properties of the semiparametric estimators are established under the conditions of the algorithm consistency. These asymptotic results are presented in conjunction with simulated examples which illustrate a robust nite{sample performance of the model. Finally, the paper applies the SEMI{ACD

Semiparametric Ridge Regression Approach in Partially Linear Models

In this article, we introduce a semiparametric ridge regression estimator for the vector-parameter in a partial linear model. It is also assumed that some additional artificial linear restrictions are imposed to the whole parameter space and the errors are dependent. This estimator is a generalization of the well-known restricted least-squares estimator and is confined to the (affine) subspace which is generated by the restrictions. Asymptotic distributional bias and risk are also derived and the comparison result is then given.

Modeling Unemployment Duration in Slovenia using Cox Regression Models

This paper applies the semi-parametric Cox regression approach to model unemployment duration in Slovenia. The empirical analysis is based on a comprehensive dataset that consists of all unemployment spells in Slovenia from 2002 to 2005. The impact of the variables age, gender, level of education, and region on the hazard ratio is discussed. It takes longer for female and older unemployed persons to find a job and on average the duration of unemployment decreases with increasing level of education. Surprisingly, unemployed persons with a professional college degree or a bachelor’s degree are better off than unemployed persons with a master’s degree. A comparison of the Cox proportional hazards model and the Cox regression model with a time-dependent covariate reveals that the more appropriate model with a time-dependent covariate places greater emphasis on higher levels of education.

Semiparametric analysis of mixture regression models with competing risks data

In the analysis of competing risks data, cumulative incidence function is a useful summary of the overall crude risk for a failure type of interest. Mixture regression modeling has served as a natural approach to performing covariate analysis based on this quantity. However, existing mixture regression methods with competing risks data either impose parametric assumptions on the conditional risks or require stringent censoring assumptions. In this article, we propose a new semiparametric regression approach for competing risks data under the usual conditional independent censoring mechanism. We establish the consistency and asymptotic normality of the resulting estimators. A simple resampling method is proposed to approximate the distribution of the estimated parameters and that of the predicted cumulative incidence functions. Simulation studies and an analysis of a breast cancer dataset demonstrate that our method performs well with realistic sample sizes and is appropriate for practical use.

The absolute health income hypothesis revisited: a semiparametric quantile regression approach

This paper uses the 1998–1999 Canadian National Population Health Survey data to examine the health–income relationship that underlies the absolute income hypothesis. To allow for nonlinearity and data heterogeneity, we use a partially linear semiparametric quantile regression model. The “absolute income hypothesis” is partially true; the negative aging effects appear more pronounced for the ill-healthy population than for the healthy population and when annual income is below 40,000 Canadian dollars.

Estimation in semiparametric spatial regression

Nonparametric methods have been very popular in the last couple of decades in time series and regression, but no such development has taken place for spatial models. A rather obvious reason for this is the curse of dimensionality. For spatial data on a grid evaluating the conditional mean given its closest neighbors requires a four-dimensional nonparametric regression. In this paper a semiparametric spatial regression approach is proposed to avoid this problem. An estimation procedure based on combining the so-called marginal integration technique with local linear kernel estimation is developed in the semiparametric spatial regression setting. Asymptotic distributions are established under some mild conditions. The same convergence rates as in the one-dimensional regression case are established. An application of the methodology to the classical Mercer and Hall wheat data set is given and indicates that one directional component appears to be nonlinear, which has gone unnoticed in earlier analyses.

Using daily store-level data to understand price promotion effects in a semiparametric regression model

Though it has been widely reported in the marketing literature that temporary price discounts generate substantial short-term sales increase, the shape of the deal effect curve constitutes a key research topic, for which there are still limited empirical results. To address this issue, a semiparametric regression approach is used to model the complex nature of this phenomenon. Our model is developed at the brand level using daily store-level scanner-data, which allows the study of several nonreported promotional effects, such as the influence of the day of the week both in promotional and nonpromotional periods. The results show that the weekend is the most effective in increasing promotional sales and that asymmetric and neighborhood effects hold. However, 9-ending promotional prices are not impactful.

The demand for selected nutrients by Greek households: an empirical analysis with quantile regressions

AbstractThe article uses information from the 1993–1994 Household Consumption Survey and the semiparametric quantile regression approach to analyze the demand for three macronutrients (carbohydrates, proteins, and fats) and three micronutrients (minerals, vitamins, and cholesterol) in Greece. According to the empirical results the age of the household head, the degree of urbanization, the percentage of food expenditure devoted to food away‐from‐home, and the per capita consumption expenditure affect the intakes of nutrients across all the five quantiles considered. The impact, however, of the household head's gender and the impact of his (her) educational achievement are located only at the lower and the higher quantiles, respectively. The expenditure elasticities are substantially lower than unity, suggesting inelastic responses of nutrient intakes to per capita consumption expenditure.

Crime Reporting as a Measure of Institutional Development

Crime Reporting as a Measure of Institutional Development

Semiparametric Regression Smoothing of Non‐linear Time Series

In this paper, we consider using a semiparametric regression approach to modelling non‐linear autoregressive time series. Based on a finite series approximation to non‐parametric components, an adaptive selection procedure for the number of summands in the series approximation is proposed. Meanwhile, a large sample study is detailed and a small sample simulation for the Mackey–Glass system is presented to support the large sample study.

Broken Biological Size Relationships: A Truncated Semiparametric Regression Approach with Measurement Error

Biological size relationships (i.e., regression of one size variable on another) are typically monotone but often break down at extreme values of the variables. Here we study the way in which a plant's biomass is apportioned to reproductive and other life activities. Working with a theory proposed by Weiner (1988) based an analogy between a biological plant and an industrial plant leads to a truncated regression model formulation. We consider a dataset involving 542 goldenrod plants that has been analyzed in a limited fashion by others. Important extensions that we provide include nonparametric modeling of the size relationship, introduction of covariate information, incorporation of heterogeneity across plant families, and inclusion of measurement error models for both response and explanatory variables. Our approach is through hierarchical models taking advantage of available prior information on the magnitudes of the size variables. Models are fitted using simulation methods enabling a full range of inference. An attractive model choice criterion demonstrates the need to accommodate all of the aforementioned aspects for the given dataset. Our flexible modeling approach can be adapted to investigate other biological size relationships.

Median regression for ordered discrete response

Abstract We introduce a semiparametric median regression approach to ordered discrete responses, generalizing the maximum score estimation of Manski (1985) for binary response. The identification and a.s. consistency are proved. We assume that there exists a latent continuous variable, and several variations of the median regression approach depending on the restriction on the thresholds for the latent variable are examined. For some cases, bounds for the scale are derived. We also derive bounds for the finite sample breakdown point of the median regression method to show its robustness.

Behavior of fluorides in the preservation of wood: R. Nowotny. ( Oester. Chem. Zeit., igro, xiii)

Most statistical methods for microarray data analysis consider one gene at a time, and they may miss subtle changes at the single gene level. This limitation may be overcome by considering a set of genes simultaneously where the gene sets are derived from prior biological knowledge. We call a pathway as a predefined set of genes that serve a particular cellular or physiological function. Limited work has been done in the regression settings to study the effects of clinical covariates and expression levels of genes in a pathway on a continuous clinical outcome. A semiparametric regression approach for identifying pathways related to a continuous outcome was proposed by Liu et al. (2007), who demonstrated the connection between a least squares kernel machine for nonparametric pathway effect and a restricted maximum likelihood (REML) for variance components. However, the asymptotic properties on a semiparametric regression for identifying pathway have never been studied. In this paper, we study the asymptotic properties of the parameter estimates on semiparametric regression and compare Liu et al.'s REML with our REML obtained from a profile likelihood. We prove that both approaches provide consistent estimators, have n convergence rate under regularity conditions, and have either an asymptotically normal distribution or a mixture of normal distributions. However, the estimators based on our REML obtained from a profile likelihood have a theoretically smaller mean squared error than those of Liu et al.'s REML. Simulation study supports this theoretical result. A profile restricted likelihood ratio test is also provided for the non-standard testing problem. We apply our approach to a type II diabetes data set (Mootha et al., 2003).