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In this study, we suggest policy implications for managing the risk of bankruptcy in housing presale projects in Korea. In conclusion, we find that the competing risk Cox proportional hazard model (PHM) is the best model for explaining the bankruptcy factors of projects and the banks that lend construction funds and policy authorities need to manage presale projects by considering bankruptcy factors (the initial presale rate, regional factor, the credit rating of the developers, the housing common factor). This study differs from previous studies in that it uses the competing risk Cox proportional hazard model and single-index model methodologies for empirical analysis, distinguishes the causes of business failure as default and the default of repurchase agreement options that are similar to actual defaults, and suggests policy implications based on the analysis. [ABSTRACT FROM AUTHOR]

This article considers the estimation of quantile treatment effects under the assumption of unconfoundedness given quasi-experimental data. We propose a semiparametric single-index method to estimate the propensity score. Our approach overcomes the curse of dimensionality issue of a nonparametric propensity score and can handle a moderately large dimension of covariates. It is more flexible than the parametric propensity score and thereby alleviates the possible model misspecification problem. We derive the asymptotic distribution of the quantile treatment effect estimator that is based on the semiparametric propensity score. We also propose a consistent variance estimator and construct the confidence intervals for the QTE estimator. Monte Carlo simulation results show that the proposed estimator performs well in finite samples and the confidence intervals have adequate coverage rates. We demonstrate the usefulness of our method by applying it to a study of the quantile treatment effects of college education on income. [ABSTRACT FROM AUTHOR]

We propose a flexible functional varying-coefficient single-index quantile regression model where the functional covariates of the linear part have time-varying coefficients and the single-index component offers great model flexibility in data analysis while circumventing the curse of dimensionality. The proposed model includes many existing quantile regression models for functional/longitudinal data as special cases. We use B-splines to estimate the link and coefficient functions. Under some mild conditions, we establish the asymptotic normality of the estimated index parameter vector, and obtain the convergence rates of the estimated link and coefficient functions. Moreover, we propose a score test to examine whether the effects of some covariates on the functional response are time-varying. Finally, we provide some numerical studies including Monte Carlo simulations and an empirical application to illustrate the proposed method. [ABSTRACT FROM AUTHOR]

Single-index model is one of the most popular semiparametric models in applied econometrics. Estimation of the derivative function is often of crucial importance, as studying "marginal effects" serves as a cornerstone of microeconomics. A prerequisite for the successful application of nonparametric/semiparametric kernel estimation methods is to select smoothing parameters properly to balance the estimation squared bias and variance. Henderson et al. (2015) propose a novel method for selecting the smoothing parameters optimally for derivative function estimation. However, their method suffers from the "curse of diemnsionality" problem in a multivariate nonparametric regression model. In this article, we extend the work of Henderson et al. (2015) to estimation of the derivative function of a single-index model. Specifically, we propose a data-driven method to select smoothing parameters optimally for single-index model derivative function estimation. We also derive the asymptotic distribution of the resulting local linear estimator of the derivative function. Both simulations and empirical applications show that the proposed method works well in practice. [ABSTRACT FROM AUTHOR]

In this article, we consider the problem of hypothesis testing in high-dimensional single-index models. First, we study the feasibility of applying the classical F-test to a single-index model when the dimension of covariate vector and sample size are of the same order, and derive its asymptotic null distribution and asymptotic local power function. For the ultrahigh-dimensional single-index model, we construct F-statistics based on lower-dimensional random projections of the data, and establish the asymptotic null distribution and the asymptotic local power function of the proposed test statistics for the hypothesis testing of global and partial parameters. The new proposed test possesses the advantages of having a simple structure as well as being easy to compute. We compare the proposed test with other high-dimensional tests and provide sufficient conditions under which the proposed tests are more efficient. We conduct simulation studies to evaluate the finite-sample performances of the proposed tests and demonstrate that it has higher power than some existing methods in the models we consider. The application of real high-dimensional gene expression data is also provided to illustrate the effectiveness of the method. for this article are available online. [ABSTRACT FROM AUTHOR]

Beta distributions are commonly used to model proportion valued response variables, often encountered in longitudinal studies. In this article, we develop semi-parametric Beta regression models for proportion valued responses, where the aggregate covariate effect is summarized and flexibly modeled, using a interpretable monotone time-varying single index transform of a linear combination of the potential covariates. We utilize the potential of single index models, which are effective dimension reduction tools and accommodate link function misspecification in generalized linear mixed models. Our Bayesian methodology incorporates the missing-at-random feature of the proportion response and utilize Hamiltonian Monte Carlo sampling to conduct inference. We explore finite-sample frequentist properties of our estimates and assess the robustness via detailed simulation studies. Finally, we illustrate our methodology via application to a motivating longitudinal dataset on obesity research recording proportion body fat. [ABSTRACT FROM AUTHOR]

Single-index quantile regression (QR) models can avoid the curse of dimensionality in nonparametric problems by assuming that the response is only related to a single linear combination of the covariates. Like the standard parametric or nonparametric QR whose estimated curves may cross, the single-index QR can also suffer quantile crossing, leading to an invalid distribution for the response. This issue has attracted considerable attention in the literature in the recent year. In this article, we consider single-index models, develop methods for QR that guarantee noncrossing quantile curves, and extend the methods and results to composite quantile regression. The asymptotic properties of the proposed estimators are derived and their advantages over existing methods are explained. Simulation studies and a real data application are conducted to illustrate the finite sample performance of the proposed methods. [ABSTRACT FROM AUTHOR]

A Distributional (Single) Index Model (DIM) is a semiparametric model for distributional regression, that is, estimation of conditional distributions given covariates. The method is a combination of classical single-index models for the estimation of the conditional mean of a response given covariates, and isotonic distributional regression. The model for the index is parametric, whereas the conditional distributions are estimated nonparametrically under a stochastic ordering constraint. We show consistency of our estimators and apply them to a highly challenging dataset on the length of stay (LoS) of patients in intensive care units. We use the model to provide skillful and calibrated probabilistic predictions for the LoS of individual patients, which outperform the available methods in the literature. [ABSTRACT FROM AUTHOR]

In this paper, we propose a novel estimation for heteroscedastic single-index models with covariate measurement errors, in which both the conditional mean and conditional variance functions of the response given the covariates have a single-index structure. When covariates are directly observable, we show that the index parameter vector can be estimated consistently by the estimation obtained by fitting a misspecified linear quantile regression model under some mild regularity conditions. It is well known that naively treating mismeasured covariates as error-free usually leads to inconsistent estimators. To account for measurement errors in covariates, we establish a new estimation procedure based on corrected quantile loss function, and obtain the asymptotic consistency and normality of the resulting estimators. Finally, the finite sample performance of the proposed estimation method is illustrated by simulation studies and an empirical analysis of a real dataset. [ABSTRACT FROM AUTHOR]

Multivariate nonparametric regression faces great challenges when overburdened with large amounts of covariates. For this reason, single-index models (SIMs) have been frequently used for reducing the parameters to be estimated in nonparametric and semiparametric models. In this paper, we develop a scale-space statistical tool, known as significant zero crossings of derivatives (SiZer), for SIM. It offers the comme il faut methodology for finding important structure within data in scale-space. The average derivative is used as the coefficient vector of the SIM, which is estimated by a local-likelihood approach weighted by kernel functions. By demonstration, the proposed SiZer for the SIM successfully captures trends in simulation and in real applications. Furthermore, we provide an extension from our proposed SiZer methodology of regression to generalized linear models. [ABSTRACT FROM AUTHOR]

An important factor in house prices is its location. However, measurement errors arise frequently in the process of observing variables such as the latitude and longitude of the house. The single-index models with measurement errors are used to study the relationship between house location and house price. We obtain the estimators by a SIMEX method based on the local linear method and the estimating equation. To test the significance of the index coefficient and the linearity of the link function, we establish the generalized likelihood ratio (GLR) tests for the models. We demonstrate that the asymptotic null distributions of the established GLR tests follow χ 2 -distributions which are independent of nuisance parameters or functions. Finally, two simulated examples and a real estate valuation data set are given to illustrate the effect of GLR tests. [ABSTRACT FROM AUTHOR]

This paper proposes the use of the Bernstein–Dirichlet process prior for a new nonparametric approach to estimating the link function in the single-index model (SIM). The Bernstein–Dirichlet process prior has so far mainly been used for nonparametric density estimation. Here we modify this approach to allow for an approximation of the unknown link function. Instead of the usual Gaussian distribution, the error term is assumed to be asymmetric Laplace distributed which increases the flexibility and robustness of the SIM. To automatically identify truly active predictors, spike-and-slab priors are used for Bayesian variable selection. Posterior computations are performed via a Metropolis-Hastings-within-Gibbs sampler using a truncation-based algorithm for stick-breaking priors. We compare the efficiency of the proposed approach with well-established techniques in an extensive simulation study and illustrate its practical performance by an application to nonparametric modelling of the power consumption in a sewage treatment plant. [ABSTRACT FROM AUTHOR]

The last few years, the applications of Support Vector Machine (SVM) for solving classification and regression problems have been increasing, due to its high performance and ability to transform the non-linear relationships among variables to linear form by employing the kernel idea (kernel function). In this work, we develop a semi-parametric approach to fit single-index models to deal with high-dimensional problems. To achieve this goal, we use support vector regression (SVR) for estimating the unknown nonparametric link function, while the single-index is determined by using the semi-parametric least squares method (Ichimura 1993). This development enhances the ability of SVR to solve high-dimensional problem. We design a three simulation examples with high-dimensional problems (linear and nonlinear). The simulations demonstrate the superior performance of the proposed method versus the standard SVR method. This is further illustrated by applying the real data. [ABSTRACT FROM AUTHOR]

Estimation of the single-index model with a discontinuous unknown link function is considered in this paper. Existed refined minimum average variance estimation (rMAVE) method can estimate the single-index parameter and unknown link function simultaneously by minimising the average pointwise conditional variance, where the conditional variance can be estimated using the local linear fit method with centred kernel function. When there are jumps in the link function, big biases around jumps can appear. For this reason, we embed the jump-preserving technique in the rMAVE method, then propose an adaptive jump-preserving estimation procedure for the single-index model. Concretely speaking, the conditional variance is obtained by the one among local linear fits with centred, left-sided and right-sided kernel functions who has minimum weighted residual mean squares. The resulting estimators can preserve the jumps well and also give smooth estimates of the continuity parts. Asymptotic properties are established under some mild conditions. Simulations and real data analysis show the proposed method works well. [ABSTRACT FROM AUTHOR]

We study the efficient estimation procedure of a new single-index model which can reflect the time-dynamic effects for longitudinal covariates. We propose a efficient estimator of the single-index parameter by using a feasible bias-corrected generalized estimating equation. In order to achieve this goal, we use the working independence estimator as an initial estimation, and then a non parametric smoothing technique is used to model the covariance matrix. With appropriate initial estimates of the parametric index, the proposed estimators are shown to be √ n-consistent and asymptotically normally distributed, and the two-stage estimator is shown to be more efficient than the first-stage estimator. We also address the non parametric estimation of regression functions and provide estimates with optimal convergence rates. The finite-sample properties of the estimator are illustrated by some simulation examples, as well as a real data application. [ABSTRACT FROM AUTHOR]

In this article, a new composite quantile regression estimation approach is proposed for estimating the parametric part of single-index model. We use local linear composite quantile regression (CQR) for estimating the nonparametric part of single-index model (SIM) when the error distribution is symmetrical. The weighted local linear CQR is proposed for estimating the nonparametric part of SIM when the error distribution is asymmetrical. Moreover, a new variable selection procedure is proposed for SIM. Under some regularity conditions, we establish the large sample properties of the proposed estimators. Simulation studies and a real data analysis are presented to illustrate the behavior of the proposed estimators. [ABSTRACT FROM AUTHOR]

For regression problems with grouped covariates, we adapt the idea of sparse group lasso (SGL) [10] to the framework of the sufficient dimension reduction. Assuming that the regression falls into a single-index structure, we propose a method called thesparse group sufficient dimension reductionto conduct group and within-group variable selections simultaneously without assuming a specific link function. Simulation studies show that our method is comparable to the SGL under the regular linear model setting and outperforms SGL with higher true positive rates and substantially lower false positive rates when the regression function is nonlinear. One immediate application of our method is to the gene pathway data analysis where genes naturally fall into groups (pathways). An analysis of a glioblastoma microarray data is included for illustration of our method. [ABSTRACT FROM PUBLISHER]

Motivated by the analysis of imaging data, we propose a novel functional varying-coefficient single-index model (FVCSIM) to carry out the regression analysis of functional response data on a set of covariates of interest. FVCSIM represents a new extension of varying-coefficient single-index models for scalar responses collected from cross-sectional and longitudinal studies. An efficient estimation procedure is developed to iteratively estimate varying coefficient functions, link functions, index parameter vectors, and the covariance function of individual functions. We systematically examine the asymptotic properties of all estimators including the weak convergence of the estimated varying coefficient functions, the asymptotic distribution of the estimated index parameter vectors, and the uniform convergence rate of the estimated covariance function and their spectrum. Simulation studies are carried out to assess the finite-sample performance of the proposed procedure. We apply FVCSIM to investigate the development of white matter diffusivities along the corpus callosum skeleton obtained from Alzheimer’s Disease Neuroimaging Initiative (ADNI) study. Supplementary material for this article is available online. [ABSTRACT FROM PUBLISHER]

A new estimation procedure is proposed for the single-index quantile regression model. Compared to existing work, this approach is non-iterative and hence, computationally efficient. The proposed method not only estimates the index parameter and the link function but also selects variables simultaneously. The performance of the variable selection is enhanced by a fully adaptive penalty function motivated by the sliced inverse regression technique. Finite sample performance is studied through a simulation study that compares the proposed method with existing work under several criteria. A data analysis is given that highlights the usefulness of the proposed methodology. [ABSTRACT FROM AUTHOR]

In this article, we consider the penalized LAD regression which deals with variable selection and estimation simultaneously for single-index models. The proposed estimator is robust and efficient with respect to heavy tailed errors or outliers in the response. Then, we introduce a practical algorithm where the unknown link function is estimated by local linear smoothing combined with LAD regression and the parametric index is estimated through linear LAD regression. Furthermore, we show that, under certain appropriate conditions, the penalized LAD estimator has desired large sample properties including-consistency, and oracle property. Simulation studies and a real data application are carried to illustrate the performances of the proposed method for finite-sample cases. Finally, based on the idea of sure independence screening procedure and the distance correlation (DC-SIS) proposed by Li et al. (2012), a robust two-step estimator is introduced to deal with ultra-high dimensional data. [ABSTRACT FROM AUTHOR]

In this paper, we are concerned with a test for the index parameter and index function in the single-index model. Based on the estimates obtained by the quantile regression, we extend the generalized analysis-of-variance-type test to the single-index model. We investigate the asymptotic behavior of the proposed test and demonstrate that its limiting null distribution follows an asymptotically χ2-distribution. The simulation studies and real data applications are conducted to illustrate the finite sample performance of the proposed methods. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the empirical-likelihood-based inference for the construction of confidence intervals and regions of the parameters of interest in single index models with missing covariates at random. An augmented inverse probability weighted-type empirical likelihood ratio for the parameters of interest is defined such that this ratio is asymptotically standard chi-squared. Our approach is to directly calibrate the empirical log-likelihood ratio, and does not need multiplication by an adjustment factor for the original ratio. Our bias-corrected empirical likelihood is self-scale invariant and no plug-in estimator for the limiting variance is needed. Some simulation studies are carried out to assess the performance of our proposed method. [ABSTRACT FROM AUTHOR]

In this article, we use bockwise empirical likelihood technique to construct confidence regions for the parameter of the single-index models under negatively associated errors. It is shown that the blockwise empirical likelihood ratio statistic for the parameter of interest is asymptotically χ2-type distributed. The result can be used to obtain confidence regions for the parameter of interest. [ABSTRACT FROM AUTHOR]

In this paper, we introduce new parametric and semiparametric regression techniques for a recurrent event process subject to random right censoring. We develop models for the cumulative mean function and provide asymptotically normal estimators. Our semiparametric model which relies on a single-index assumption can be seen as a dimension reduction technique that, contrary to a fully nonparametric approach, is not stroke by the curse of dimensionality when the number of covariates is high. We discuss data-driven techniques to choose the parameters involved in the estimation procedures and provide a simulation study to support our theoretical results. [ABSTRACT FROM AUTHOR]

Partially linear single-index models play important roles in advanced non-/semi-parametric statistics due to their generality and flexibility. We generalise these models from univariate response to multivariate responses. A Bayesian method with free-knot spline is used to analyse the proposed models, including the estimation and the prediction, and a Metropolis-within-Gibbs sampler is provided for posterior exploration. We also utilise the partially collapsed idea in our algorithm to speed up the convergence. The proposed models and methods of analysis are demonstrated by simulation studies and are applied to a real data set. [ABSTRACT FROM AUTHOR]

In this paper, we propose a new full iteration estimation method for quantile regression (QR) of the single-index model (SIM). The asymptotic properties of the proposed estimator are derived. Furthermore, we propose a variable selection procedure for the QR of SIM by combining the estimation method with the adaptive LASSO penalized method to get sparse estimation of the index parameter. The oracle properties of the variable selection method are established. Simulations with various non-normal errors are conducted to demonstrate the finite sample performance of the estimation method and the variable selection procedure. Furthermore, we illustrate the proposed method by analyzing a real data set. [ABSTRACT FROM PUBLISHER]

Epidemiological studies have shown that the high levels of air pollution are associated with the increased mortality. To further characterise the health effects of air pollutants, we propose a spline-based partially linear Poisson single-index model to study the relationship of multi-dimensional air pollution exposure to mortality.B-splines are used to approximate the unknown regression function. A modified Fisher scoring method is applied to simultaneously estimate the linear coefficients and the regression function. The estimator of the regression function is consistent with a better than cubic root convergence rate and the estimators of regression parameters are asymptotically normal and efficient. Also a simple and consistent variance estimation approach based on least-squares method is proposed. An extensive Monte Carlo study is conducted to evaluate the finite sample performance of the proposed spline approach. The method is illustrated using data from an epidemiological study of ambient fine particles. [ABSTRACT FROM PUBLISHER]

In this paper, we consider the problem of variable selection for partially varying coefficient single-index model, and present a regularized variable selection procedure by combining basis function approximations with smoothly clipped absolute deviation penalty. The proposed procedure simultaneously selects significant variables in the single-index parametric components and the nonparametric coefficient function components. With appropriate selection of the tuning parameters, the consistency of the variable selection procedure and the oracle property of the estimators are established. Finite sample performance of the proposed method is illustrated by a simulation study and real data analysis. [ABSTRACT FROM PUBLISHER]

In this article, we consider semiparametric estimation in a partially linear single-index panel data model with fixed effects. Without taking the difference explicitly, we propose using a semiparametric minimum average variance estimation (SMAVE) based on a dummy variable method to remove the fixed effects and obtain consistent estimators for both the parameters and the unknown link function. As both the cross-section size and the time series length tend to infinity, we not only establish an asymptotically normal distribution for the estimators of the parameters in the single index and the linear component of the model, but also obtain an asymptotically normal distribution for the nonparametric local linear estimator of the unknown link function. The asymptotically normal distributions of the proposed estimators are similar to those obtained in the random effects case. In addition, we study several partially linear single-index dynamic panel data models. The methods and results are augmented by simulation studies and illustrated by application to two real data examples. This article has online supplementary materials. [ABSTRACT FROM AUTHOR]

When analysing a contingency table, it is often worth relating the probabilities that a given individual falls into different cells from a set of predictors. These conditional probabilities are usually estimated using appropriate regression techniques. In particular, in this paper, a semiparametric model is developed. Essentially, it is only assumed that the effect of the vector of covariates on the probabilities can entirely be captured by a single index, which is a linear combination of the initial covariates. The estimation is then twofold: the coefficients of the linear combination and the functions linking this index to the related conditional probabilities have to be estimated. Inspired by the estimation procedures already proposed in the literature for single-index regression models, four estimators of the index coefficients are proposed and compared, from a theoretical point-of-view, but also practically, with the aid of simulations. Estimation of the link functions is also addressed. [ABSTRACT FROM AUTHOR]

We consider a Gaussian process regression (GPR) approach to analysing a single-index model (SIM) from the Bayesian perspective. Specifically, the unknown link function is assumed to be a Gaussian process a priori and a prior on the index vector is considered based on a simple uniform distribution on the unit sphere. The posterior distributions for the unknown parameters are derived, and the posterior inference of the proposed approach is performed via Markov chain Monte Carlo methods based on them. Particularly, in estimating the hyperparameters, different numerical schemes are implemented: fully Bayesian methods and empirical Bayes methods. Numerical illustration of the proposed approach is also made using simulation data as well as well-known real data. The proposed approach broadens the scope of the applicability of the SIM as well as the GPR. In addition, we discuss the theoretical aspect of the proposed method in terms of posterior consistency. [ABSTRACT FROM AUTHOR]

In this article, we investigate how to apply the empirical likelihood method for the inference of average derivatives in nonparametric multiple regression models. Empirical likelihood ratios for the vectors of the average derivatives and the density-weighted average derivatives are defined and it is shown that their limiting distributions are weighted sums of independent chi-squared random variables with one degree of freedom. Monte Carlo simulation studies are presented to compare the empirical likelihood method with the normal-approximation-based method. It is found that the empirical likelihood method performs better than the normal-approximation-based method. [ABSTRACT FROM AUTHOR]