Rank-based shrinkage estimation for identification in semiparametric additive models

This paper focuses on robust estimation for varying coefficient partially functional linear regression model (VCPFLM) without specification of the error distributions. The proposed estimators of the nonparametric coefficients and slope function are based on B-spline approximation and rank regression, which demonstrates that the proposed estimation is robust for non-normal error distributions compared with that of least square estimate. In addition, the optimal convergence rates of the estimators are established under some mild regularity conditions. Finally, simulation study and a real data analysis are conducted to illustrate the finite sample performance of the proposed method.

Exploring nonlinear association between prenatal methylmercury exposure from fish consumption and child development: evaluation of the Seychelles Child Development Study nine-year data using semiparametric additive models

BackgroundGlobally, anemia poses a serious health challenge for children under the age of five, and Ethiopia is one of the countries significantly affected by this issue. The 2016 Ethiopian Demographic and Health Survey (DHS) data sets were employed to evaluate anemia risk among children aged 6–59 months. Due to limited research has been conducted on childhood anemia spatial disparities at the Ethiopian zonal level, and it is essential for developing zonal-level interventions for inform policy recommendations.MethodsThis study was examined the geospatial disparities in anemia prevalence among children aged 6–59 months. We used a semi-parametric additive model with spatial smoothing to assess zone-level variation in anemia risk while adjusting for key covariates. Each predictor variable was spatially adjusted using non-parametric smoothing techniques based on geolocation parameters, and corresponding maps for each predictor.ResultsA regularized random forest techniques was employed to identify the most influential predictors of childhood anemia and enhance the model predictive performance. Our findings revealed that the regional states of Somalia, Afar, and Dire Dawa exhibit the highest risk levels for childhood anemia. Furthermore, the risk of anemia in children varies spatially across different zones in Ethiopia. The most prominent hotspots for childhood anemia were in the country's Northeastern, Eastern, and Southeastern regions. In contrast, the areas with the lowest risk were in Northwestern, Western, and Southwestern zones of Ethiopia.ConclusionThe significant spatial disparities in anemia risk across the administrative zones of Ethiopia, indicating that the distribution of each predictor variable is not uniform. These findings provide valuable insights for policymakers, enabling the development of geographically targeted interventions to mitigate anemia risk at the zonal level.

This paper deals with the construction of efficient estimators in semiparametric models without the sample splitting technique. Schick (1987) gave sufficient conditions using the leave-one-out technique for a construction without sample splitting. His conditions are stronger and more cumbersome to verify than the necessary and sufficient conditions for the existence of efficient estimators which suffice for the construction based on sample splitting. In this paper we use a conditioning argument to weaken Schick′s conditions. We shall then show that in a large class of semiparametric models and for properly chosen estimators of the score function the resulting weaker conditions reduce to the minimal conditions for the construction with sample splitting. In other words, in these models efficient estimators can be constructed without sample splitting under the same conditions as those used for the construction with sample splitting. We demonstrate our results by constructing an efficient estimator using these ideas in a semiparametric additive regression model.

Recurrent event data often arises in biomedical studies, and individuals within a cluster might not be independent. We propose a semiparametric additive rates model for clustered recurrent event data, wherein the covariates are assumed to add to the unspecified baseline rate. For the inference on the model parameters, estimating equation approaches are developed, and both large and finite sample properties of the proposed estimators are established.

Model averaging has long been used as a powerful approach to reduce the risk of model misspecification. However, there is little work on model averaging methods under generalized semiparametric models. In this article, we study model averaging in generalized partially linear varying‐coefficient models and propose a semiparametric model averaging estimation (SMAE) method for the canonical parameters. Specifically, we take the partially linear varying‐coefficient model as candidate models in which there is only one varying‐coefficient component. The different covariates could enjoy the benefit of matching the optimal degrees of freedom and each candidate model can take into account the confounding effects among predictors as well. Moreover, the weight choice criterion based on the Kullback–Leibler divergence is adopted to determine the weights. We prove that the corresponding model averaging estimator is asymptotically optimal under certain regularity conditions. Finally, some simulation studies and a real data analysis are conducted to compare with existing methods, and the results show that the proposed method has better out‐of‐sample performance.

A procedure for the experimental identification of the material standard linear solid model parameters by means of dynamic mechanical analysis test instrument measurements is presented. Since the standard linear solid material stress–strain functional D(ω) relationship in the frequency domain formally depends on the standard linear solid material parameters, a procedure able to identify these parameters from test measurement estimates is proposed in this work. Nevertheless, a critical, nonlinear and non-parametric approach is to be followed since the number of the material standard linear solid block components is generally unknown, and the material D(ω) shows a highly nonlinear dependency on the unknown standard linear solid material parameters. For these reasons, measurement and test model noise is expected to strongly influence the accuracy of the identification results. A multi-step procedure is presented, consisting first in the non-parametric identification of a frequency dependent, two degrees of freedom model instrument frame by means of a polynomial rational function, where polynomial order and parameters, such as polynomial coefficients and pole-residue couples, are optimally identified by means of an algebraic numerical technique and of an iterative stabilization procedure. Another procedure able to identify the material D(ω) polynomial rational functional relationship in the frequency domain is also proposed, taking into account the dynamic contribution of the instrument frame, of the inertial contribution of the distributed mass of the beam and of the lumped mass of the instrument force measuring system. An effective procedure, able to identify the standard linear solid material model parameters in the time domain from the identified material physical poles, is finally proposed. Some application examples, concerning the identification of the standard linear solid model of a known material and of an unknown composite material, are shown and discussed as well.

As an important part of modern health care, medical imaging data, which can be regarded as densely sampled functional data, have been widely used for diagnosis, screening, treatment, and prognosis, such as finding breast cancer through mammograms. The aim of this paper is to propose a functional linear regression model for using functional (or imaging) predictors to predict clinical outcomes (e.g., disease status), while addressing missing clinical outcomes. We introduce an exponential tilting semiparametric model to account for the nonignorable missing data mechanism. We develop a set of estimating equations and its associated computational methods for both parameter estimation and the selection of the tuning parameters. We also propose a bootstrap resampling procedure for carrying out statistical inference. Under some regularity conditions, we systematically establish the asymptotic properties (e.g., consistency and convergence rate) of the estimates calculated from the proposed estimating equations. Simulation studies and a real data analysis are used to illustrate the finite sample performance of the proposed methods.

Among several semiparametric models, the Cox proportional hazard model is widely used to assess the association between covariates and the time-to-event when the observed time-to-event is interval-censored. Often, covariates are measured with error. To handle this covariate uncertainty in the Cox proportional hazard model with the interval-censored data, flexible approaches have been proposed. To fill a gap and broaden the scope of statistical applications to analyze time-to-event data with different models, in this paper, a general approach is proposed for fitting the semiparametric linear transformation model to interval-censored data when a covariate is measured with error. The semiparametric linear transformation model is a broad class of models that includes the proportional hazard model and the proportional odds model as special cases. The proposed method relies on a set of estimating equations to estimate the regression parameters and the infinite-dimensional parameter. For handling interval censoring and covariate measurement error, a flexible imputation technique is used. Finite sample performance of the proposed method is judged via simulation studies. Finally, the suggested method is applied to analyze a real data set from an AIDS clinical trial.

The filtered monotonic polynomial (FMP) model is a semi-parametric item response model that allows flexible response function shapes but also includes traditional item response models as special cases. The flexmet package for R facilitates the routine use of the FMP model in real data analysis and simulation studies. This tutorial provides several code examples illustrating how the flexmet package may be used to simulate FMP model parameters and data (both for dichotomous and polytomously scored items), estimate FMP model parameters, transform traditional item response models to different metrics, and more. This tutorial serves as both an introduction to the unique features of the FMP model and as a practical guide to its implementation in R via the flexmet package.

Summary Instrumental variables are widely used to deal with unmeasured confounding in observational studies and imperfect randomized controlled trials. In these studies, researchers often target the so-called local average treatment effect as it is identifiable under mild conditions. In this paper we consider estimation of the local average treatment effect under the binary instrumental variable model. We discuss the challenges of causal estimation with a binary outcome and show that, surprisingly, it can be more difficult than in the case with a continuous outcome. We propose novel modelling and estimation procedures that improve upon existing proposals in terms of model congeniality, interpretability, robustness and efficiency. Our approach is illustrated via simulation studies and a real data analysis.

A semiparametric additive model is used to study the relationship between protected area, income, trade, population, education, and political institutions in a sample of 89 countries. The results show the nonexistence of an environmental Kuznets curve in the data sample. The study also points out the existence of nonlinearity in the relationship between protected area and the ratio of net secondary school enrolment.

This paper introduces an important model that can be widely used in semi-parametric methods in recent years, the analysis of the additivity model, to more accurately describe the deep impact of information technology on national economic innovation and subdivides information technology into inflows and outflows, and examines the direction and intensity of the impact of inflows and outflows of information technology on China's national economic innovation. When the linear part is constrained, we construct Ridge Estimators Based on profile least squares method and backfitting method, discuss the properties of the estimators, and finally verify the validity of the estimators by numerical simulation. We hope to more fully reveal the reasons for the unbalanced development of China's regional development caused by the flow of information technology.

Wang et al. studied the high-dimensional sparse penalized rank regression and established its nice theoretical properties. Compared with the least squares, rank regression can have a substantial gain in estimation efficiency while maintaining a minimal relative efficiency of 86.4 % . However, the computation of penalized rank regression can be very challenging for high-dimensional data, due to the highly nonsmooth rank regression loss. In this work we view the rank regression loss as a nonsmooth empirical counterpart of a population level quantity, and a smooth empirical counterpart is derived by substituting a kernel density estimator for the true distribution in the expectation calculation. This view leads to the convoluted rank regression loss and consequently the sparse penalized convoluted rank regression (CRR) for high-dimensional data. We prove some interesting asymptotic properties of CRR. Under the same key assumptions for sparse rank regression, we establish the rate of convergence of the l 1 -penalized CRR for a tuning free penalization parameter and prove the strong oracle property of the folded concave penalized CRR. We further propose a high-dimensional Bayesian information criterion for selecting the penalization parameter in folded concave penalized CRR and prove its selection consistency. We derive an efficient algorithm for solving sparse convoluted rank regression that scales well with high dimensions. Numerical examples demonstrate the promising performance of the sparse convoluted rank regression over the sparse rank regression. Our theoretical and numerical results suggest that sparse convoluted rank regression enjoys the best of both sparse least squares regression and sparse rank regression. Supplementary materials for this article are available online.

ABSTRACTBased on B-spline basis functions and smoothly clipped absolute deviation (SCAD) penalty, we present a new estimation and variable selection procedure based on modal regression for partially linear additive models. The outstanding merit of the new method is that it is robust against outliers or heavy-tail error distributions and performs no worse than the least-square-based estimation for normal error case. The main difference is that the standard quadratic loss is replaced by a kernel function depending on a bandwidth that can be automatically selected based on the observed data. With appropriate selection of the regularization parameters, the new method possesses the consistency in variable selection and oracle property in estimation. Finally, both simulation study and real data analysis are performed to examine the performance of our approach.