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We propose a varying-coefficient panel-data model with unobservable multiple interactive fixed effects that are correlated with the regressors. We approximate each coefficient function using B-splines, and propose a robust nonlinear iteration scheme based on the least squares method to estimate the coefficient functions of interest. We also establish the asymptotic theory of the resulting estimators under certain regularity assumptions, including the consistency, convergence rate, and asymptotic distributions. To construct the pointwise confidence intervals for the coefficient functions, we propose a residual-based block bootstrap method that reduces the computational burden and avoids accumulative errors. We extend our proposed procedure to partially linear varying-coefficient panel-data models with unobservable multiple interactive fixed effects, and examine the problem of constant coefficients versus function coefficients. Simulation studies and a real-data analysis are used to assess the performance of the proposed methods.

We propose a varying-coefficient autoregressive model that contains additive models, varying-coefficient models, partially linear models and low-dimensional interaction models as special cases. A global kernel backfitting method is proposed for the estimation and inference of parameters and unknown functions in this model. Key large-sample results are established, including estimation consistency, asymptotic normality and the generalized likelihood ratio test for parameters and non-parametric functions. The proposed methodology is examined by simulation studies and applied to examine the relationship between suicide news reports in the three leading newspapers and the daily number of suicides in Taiwan. The relationship between the media reporting and suicide incidence has been established and explored. Les auteurs présentent un modèle autorégressif à coefficients variables comprenant plusieurs cas particuliers notables dont les modèles additifs, les modèles à coefficients variables, les modèles partiellement linéaires et les modèles à interactions de basse dimension. Ils proposent une méthode globale de rétro-ajustement du noyau pour l’estimation et l’inférence des paramètres et des fonctions inconnus de ce modèle. Ils obtiennent des résultats asymptotiques clés, notamment la convergence, la normalité asymptotique et la validité du test au rapport de vraisemblance pour les paramètres et les fonctions non paramétriques. Les auteurs examinent la méthodologie proposée par une étude de simulation et l’illustrent en explorant la relation entre les nouvelles au sujet du suicide dans trois grands journaux et le nombre quotidien de suicides à Taiwan. Ils établissent qu’un lien existe entre les reportages médiatiques et la fréquence des suicides, et ils en étudient l’incidence.

The paper develops a parsimonious modelling framework to study the time-varying association between scalar outcomes and functional predictors observed at many instances, in longitudinal studies. The methods enable us to reconstruct the full trajectory of the response and are applicable to Gaussian and non-Gaussian responses. The idea is to model the time-varying functional predictors by using orthogonal basis functions and to expand the time-varying regression coefficient by using the same basis. Numerical investigation through simulation studies and data analysis show excellent performance in terms of accurate prediction and efficient computations, when compared with existing alternatives. The methods are inspired and applied to an animal science application, where of interest is to study the association between the feed intake of lactating sows and the minute-by-minute temperature throughout the 21 days of their lactation period. R code and an R illustration are provided.

Varying coefficient models are a useful extension of classical linear models. They arise naturally when one wishes to examine how regression coefficients change over different groups characterized by certain covariates such as age. The appeal of these models is that the coefficient functions can easily be estimated via a simple local regression. This yields a simple one-step estimation procedure. We show that such a one-step method cannot be optimal when different coefficient functions admit different degrees of smoothness. This drawback can be repaired by using our proposed two-step estimation procedure. The asymptotic mean-squared error for the two-step procedure is obtained and is shown to achieve the optimal rate of convergence. A few simulation studies show that the gain by the two-step procedure can be quite substantial. The methodology is illustrated by an application to an environmental data set.

Time-varying coefficient models are widely used in longitudinal data analysis. These models allow the effects of predictors on response to vary over time. In this article, we consider a mixed-effects time-varying coefficient model to account for the within subject correlation for longitudinal data. We show that when kernel smoothing is used to estimate the smooth functions in time-varying coefficient models for sparse or dense longitudinal data, the asymptotic results of these two situations are essentially different. Therefore, a subjective choice between the sparse and dense cases might lead to erroneous conclusions for statistical inference. In order to solve this problem, we establish a unified self-normalized central limit theorem, based on which a unified inference is proposed without deciding whether the data are sparse or dense. The effectiveness of the proposed unified inference is demonstrated through a simulation study and an analysis of Baltimore MACS data.

Nonparametric smoothing methods are used to model longitudinal data, but the challenge remains to incorporate correlation into nonparametric estimation procedures. In this article, we propose an efficient estimation procedure for varying‐coefficient models for longitudinal data. The proposed procedure can easily take into account correlation within subjects and deal directly with both continuous and discrete response longitudinal data under the framework of generalized linear models. The proposed approach yields a more efficient estimator than the generalized estimation equation approach when the working correlation is misspecified. For varying‐coefficient models, it is often of interest to test whether coefficient functions are time varying or time invariant. We propose a unified and efficient nonparametric hypothesis testing procedure, and further demonstrate that the resulting test statistics have an asymptotic chi‐squared distribution. In addition, the goodness‐of‐fit test is applied to test whether the model assumption is satisfied. The corresponding test is also useful for choosing basis functions and the number of knots for regression spline models in conjunction with the model selection criterion. We evaluate the finite sample performance of the proposed procedures with Monte Carlo simulation studies. The proposed methodology is illustrated by the analysis of an acquired immune deficiency syndrome (AIDS) data set.

Information asymmetry reflects the risk and uncertainty faced by investors and is a measure of a firm’s transparency. High information asymmetry could increase the cost of external financing, which in turn impedes a firm’s leverage (debt–asset ratio) adjustment. The paper studies the adjustment speed towards the target leverage in the presence of information asymmetry by using microlevel data from China. In contrast with previous studies, we allow heterogeneity in the adjustment speed coefficient by modelling it as a non-parametric function of information asymmetry and other firm characteristics. This refinement not only allows for more flexibility in the model, but it also facilitates further exploration into the differences and determinants of firms’financing behaviour. We uniquely build the firm level measure of information asymmetry into the traditional partial leverage adjustment framework. Based on our firm level measure of the adjustment speed, our paper explores why the leverage adjustment speed matters by examining its association with corporate performance indicators. We find that China’s firms do have leverage targets and they slowly adjust towards these targets. We also find that the adjustment speed decreases with an increase in information asymmetry. Overall, firms which converge towards their targets faster perform better in value, profitability, investment and costs.

A global smoothing procedure is developed using basis function approximations for estimating the parameters of a varying‐coefficient model with repeated measurements. Inference procedures based on a resampling subject bootstrap are proposed to construct confidence regions and to perform hypothesis testing. Conditional biases and variances of our estimators and their asymptotic consistency are developed explicitly. Finite sample properties of our procedures are investigated through a simulation study. Application of the proposed approach is demonstrated through an example in epidemiology. In contrast to the existing methods, this approach applies whether or not the covariates are time‐invariant and does not require binning of the data when observations are sparse at distinct observation times.

Motivated by two practical problems, we propose a new procedure for estimating a semivarying‐coefficient model. Asymptotic properties are established which show that the bias of the parameter estimator is of order h3 when a symmetric kernel is used, where h is the bandwidth, and the variance is of order n−1 and efficient in the semiparametric sense. Undersmoothing is unnecessary for the root‐n consistency of the estimators. Therefore, commonly used bandwidth selection methods can be employed. A model selection method is also developed. Simulations demonstrate how the proposed method works. Some insights are obtained into the two motivating problems by using the proposed models.

Right-censored and length-biased failure time data arise in many fields including cross-sectional prevalent cohort studies, and their analysis has recently attracted a great deal of attention. It is well-known that for regression analysis of failure time data, two commonly used approaches are hazard-based and quantile-based procedures, and most of the existing methods are the hazard-based ones. In this paper, we consider quantile regression analysis of right-censored and length-biased data and present a semiparametric varying-coefficient partially linear model. For estimation of regression parameters, a three-stage procedure that makes use of the inverse probability weighted technique is developed, and the asymptotic properties of the resulting estimators are established. In addition, the approach allows the dependence of the censoring variable on covariates, while most of the existing methods assume the independence between censoring variables and covariates. A simulation study is conducted and suggests that the proposed approach works well in practical situations. Also, an illustrative example is provided.