Root-n-consistent and efficient estimation in semiparametric additive regression models

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.

IntroductionRandomized controlled trial (RCT) data are analyzed by two challengeable adjusted and non-adjusted approaches. Performing appropriate adjusted analysis leads to a more interpretable and efficient estimation of treatment effects. Semiparametric adjustment approach modifies the estimating equations solved by the marginal treatment effect estimator by adding an augmentation function, which makes use of the baseline covariates and estimate the unbiased marginal treatment effect with improved precision. The effect of the intervention obtained using the semi-parametric adjustment method, similar to the unadjusted method and contrary to the adjusted parametric method, is marginal, resulting in better interpretability. Moreover, due to leveraging baseline covariates, it is more efficient compared to the unadjusted models. This study aimed to estimate the effect of beractant (Beraksurf™, Tekzima Company), compared with the Poractant alfa (Curosurf®, Chiesi Pharmaceuticals), as surfactant replacement therapy, on the need for Intermittent Positive Pressure Ventilation (IPPV) in Neonatal Respiratory Distress Syndrome (NRDS) more precisely by fitting a semi-parametric efficient model adjusted for appropriate covariates.MethodThis study is secondary and we re-analyzing data of a published RCT. This RCT was conducted in the NICU of Alzahra Hospital in Tabriz, Iran for eight months, and 200 infants were assigned to two groups receiving either 100 mg/kg BeraksurfTM (n = 99) or 200 mg/kg Curosurf® (n = 101). The effect of the treatments was evaluated regarding the need for IPPV by fitting semi-parametric logistic regression models, adjusted for the best subset of covariates selected by the forward variable selection algorithm and confounders identified by the expert panel. IPPV in our study was administered via an endotracheal tube, as per the protocol followed in the primary trial. The need for IPPV was determined based on the clinical judgment of neonatologists, considering the infants' respiratory distress levels, oxygen saturation, and arterial blood gas measurements. The decision was made within the first 72 h after surfactant administration.ResultsThe proportions of the required IPPV outcome were 29.3% and 59.4% in the BeraksurfTM group and Curosurf®, respectively. While the unadjusted comparison between the two treatments was significant (OR = .283, 95% CI: (.157, .509), P-value < .001), adjusted OR in semi-parametric logistic regression by adjusting for the best subset of covariates selected by forward method including steroids, Apgar score at min1, and initial Fio2 wasn’t significant (OR = .751, 95% CI: (.510, 1.111), P-value = .151). The efficacy of this semi-parametric model over the unadjusted model was 1.81. The results of the expert-based adjusted model, adjusting for the gestational age, birth weight, and initial FiO2, were consistent with those derived from the R2-based selection, supporting the robustness of our findings (OR = .685, 95% CI: (.449, 1.529), P-value = .078).ConclusionFitting a semi-parametric model adjusted for the baseline covariates resulted in a marginal, unbiased, more efficient and interpretable estimation of BeraksurfTM versus Curosurf® effects. Although the crude model showed that BeraksurfTM was more effective than Curosurf®, the results of the efficient semi-parametric model with adjustment for the best subset of covariates revealed no statistically significant difference between the two drugs regarding their effects. We hope that the use of this method and its findings will contribute to a better understanding of covariate adjustment.

Parameter estimates are proposed for semiparametric regression models with either linear or nonlinear parametric component, and arbitrarily many regressors in the nonparametric component. The estimates, which utilize nearest neighbour nonparametric regression, are shown to be consistent under mild conditions.

Binary logistic semiparametric regression analysis is a commonly used statistical technique when the dependent variable is dichotomous or binary. In this analysis, the relationship between the success probability and certain explanatory variables is assumed to have a linear form, while the relationship to other variables is unknown. Multicollinearity is a serious problem that arises when explanatory variables in logistic semiparametric regression are highly correlated. It is well known that the variance of the maximum likelihood estimator is inflated due to multicollinearity in the semiparametric logistic regression model. Therefore, a novel stochastic restricted iterative weighted ridge estimator for logistic semiparametric regression is introduced, and its statistical properties are extracted asymptotically. Moreover, an extension of the generalized cross validation (GCV) function is introduced and applied for choosing the best values of the ridge parameter and the bandwidth of the kernel smoother. Additionally, some theorems are developed to illustrate the convergence of the GCV mean. Ultimately, the Monte-Carlo simulation studies and an actual real-life data set are conducted to support our theoretical discussion, and the findings indicated that the new estimator outperformed the other estimators under consideration.

This paper considers the estimation of a semiparametric isotonic regression model when the covariates are measured with additive errors and the response is randomly right censored by a censoring time. The authors show that the proposed estimator of the regression parameter is rootn consistent and asymptotically normal. The authors also show that the isotonic estimator of the functional component, at a fixed point, is cubic root-n consistent and converges in distribution to the slope at zero of the greatest convex minorant of the sum of a two-sided standard Brownian motion and the square of the time parameter. A simulation study is carried out to investigate the performance of the estimators proposed in this article.

SUMMARY When there are covariate effects to be considered, multi-state survival analysis is dominated either by parametric Markov regression models or by semiparametric Markov regression models using Cox's (1972) proportional hazards models for transition intensities between the states. The purpose of this research work is to study alternatives to Cox's model in a general finite-state Markov process setting. We shall look at two alternative models, Aalen's (1989) nonparametric additive hazards model and Lin & Ying's (1994) semiparametric additive hazards model. The former allows the effects of covariates to vary freely over time, while the latter assumes that the regression coefficients are constant over time. With the basic tools of the product integral and the functional delta-method, we present an estimator of the transition probability matrix and develop the large-sample theory for the estimator under each of these two models. Data on 1459 HLA identical sibling transplants for acute leukaemia from the International Bone Marrow Transplant Registry serve as illustration.

Semiparametric regression is a regression model consisting of two components, namely the parametric and the nonparametric component. The parametric component is a component with curves are known and the nonparametric component is a component with unknown shape of the curve. Bi-response semiparametric regression is regression analysis which has two response variables with the combination of parametric and nonparametric curves. The purpose of this research is to compare the bi-response semiparametric regression model using spline truncated with component parametric linear and quadratic. In this research, the method that used for the estimation parameter is WLS (Weighted Least Square) and the selection of optimal knot points is done by looking at the minimum GCV (Generalized Cross-Validation) value. WLS is minimizing partial derivative based on a parameter in the model. Each the linear bi-responsese semiparametric regression and quadratic bi-responsese semiparametric regression using spline truncated has two parameters that are parameter for parametric and nonparametric components. The difference between the two models contained in the parametric component of the predictor variable and parameter matrix of parametric component is estimator linear bi-response semiparametric regression model and is estimator quadratic bi-response semiparametric regression model using spline truncated.

Recent research and studies show widespread interest in semiparametric regression model analysis, which combines parametric and nonparametric components. This interest is because it gives accurate and effective statistical model estimates. This paper proposes to improve estimates of semiparametric regression models using opposition-based learning technology on the golden Jackal Optimization algorithm to increase the accuracy of these models, accelerate convergence, and expand the exploration area. The effectiveness of using this algorithm was evaluated by comparing it with the original algorithm before optimization and the most commonly used methods for estimating the model statistically, such as CV and GCV. Using simulation, the results showed that the improvement in the OBL-GJO algorithm in terms of accuracy and convergence speed outperformed the original algorithm and traditional methods by a large margin in calculating the simulation results of the kernel semiparametric regression models. We strongly advocate for applying the GJO algorithm across various domains within machine learning, particularly in the realms of deep learning and reinforcement learning. Furthermore, we have employed enhanced and evolved algorithms to optimize semiparametric regression models effectively. To address the challenges encountered by any algorithm operating within a vast search landscape, we suggest an in-depth exploration of optimization techniques and integrating diverse algorithms, which could lead to more robust and efficient solutions.

ملخص:- تحتوي نماذج الانحدار على مکونين أحدهما مکون عشوائي يمثل حد الخطأ (Error Term) والأخر مکون غير عشوائي يمثل متغير الاستجابة(Response Variable) وهذا المکون هو محل الاهتمام فيتم تقديره بإحدى الطريقتين هما: الطريقة المعلمية أو الطريقة اللامعلمية أو کلاهما. نموذج الانحدار المعلمي (Parametric Regression Model) هو النموذج الأکثر شيوعا حيث أنه يفترض أن متغير الاستجابة له صيغه دالية محدده مسبقا والتي تم الحصول عليها من معلومات سابقه حول هيکل دالة الانحدار من خلال ذلک يتم تقدير فئة من المعالم. ورغم أن النماذج المعلمية تعد أحد أهم أدوات تحليل البيانات؛ لأنها فعاله ويمکن تفسيرها بسهوله، إلا انها لم تستطع ان تکون کافية في بعض الحالات. أما نموذج الانحدار اللامعلمي (Nonparametric Regression Model) فانه يعتمد على تقدير دالة الانحدار مباشرة من البيانات کما أنه لا يفترض فروضا معينه لتقدير معالم النموذج مثل التي يفترضها النموذج المعلمي وبالتالي فهو يتمتع بمرونة أکثر لاکتشاف البيانات التي قد تکون مفقودة او في الحالات التي لا تتوافر فيها معلومات سابقة. يتم انشاء نموذج الانحدار شبه المعلمي (Semi parametric Regression Model) من خلال مزج الطريقتين السابقتين معا. فغالبا ما يتم استخدام هذا النموذج في المواقف التي تکون فيها الافتراضات المعلمية غير محددة وغير متسقة، أو أن النموذج اللامعلمي لا يعمل بشکل کامل. يشتمل هذا البحث على تطبيق نماذج الانحدار المعلمية وشبه المعلمية بالإضافة إلى النموذج اللامعلمى کحالة خاصة من نموذج الانحدار شبه المعلمى لتقدير الدالة الافتراضية وتحديد شکل العلاقة بين المتغير التابع والمتغيرات المستقلة بالاضافة الى شکل انتشار البيانات مع خط (أو منحني) التقدير وذلک على بيانات واقعية تم الحصول عليها من الإتحاد المصري لألعاب القوى والمعروفة بـبيانات لعبة العشاري . Regression models contain two components, one of which is a random component that represents the Error Term and the other is a non-random component that represents the response variable and this component is of interest and is estimated in one of two methods: the parametric method or the nonparametric method or both. Parametric regression model is the most common model since it assumes that the response variable has a predetermined functional formula which was obtained from previous information about the structure of the regression function by which a class of parameters is estimated. Although parameter models are one of the most important tools for analyzing data; Because it is effective and can be explained easily, but it could not be sufficient in some cases. As for the nonparametric regression model, it relies on estimating the regression function directly from the data, as it does not assume specific assumptions for estimating the model parameters, such as those assumed by the parametric model, and thus it has more flexibility to discover data that may be missing or in cases where previous information is not available. The semi-parametric regression model is constructed by blending the two previous methods together. This model is often used in situations where the parametric assumptions are indeterminate and inconsistent, or the nonparametric model is not fully functional. This research includes the application of parametric and semi-parametric regression models in addition to the nonparametric model as a special case of the semi-parametric regression model for estimating the hypothetical function and determining the form of the relationship between the dependent variable and the independent variables in addition to the data spread form with a line (or curve) estimation on realistic data On it from the Egyptian Athletics Federation, known as Decathlon data.

Recurrent event data are often encountered in biomedical research, for example, recurrent infections or recurrent hospitalizations for patients after renal transplant. In many studies, there are more than one type of events of interest. Cai and Schaubel (2004) advocated a proportional marginal rate model for multiple type recurrent event data. In this paper, we propose a general additive marginal rate regression model. Estimating equations approach is used to obtain the estimators of regression coefficients and baseline rate function. We prove the consistency and asymptotic normality of the proposed estimators. The finite sample properties of our estimators are demonstrated by simulations. The proposed methods are applied to the India renal transplant study to examine risk factors for bacterial, fungal and viral infections.

Semiparametric regression with shape-constrained penalized splines

We consider the problem of fitting semiparametric transformation regression models to data from a modified case‐cohort study in which the censoring times of all the censored subjects in the cohort are observed. We propose to maximise a conditional profile likelihood to obtain the estimator of the regression parameter. Under the assumption that the censoring is independent of the covariates, the estimator is shown to be consistent and asymptotically normally distributed. Numerical studies suggest that the relative eciency of the estimator is very high and that the estimator is often less biased than the estimator from the complete‐case analysis and more accurate than the pseudolikelihood estimator.

This article investigates modeling and calibration issues that are associated with inertially stabilized platforms to achieve accurate pointing. In modeling part, the Denavit–Hartenberg notation is used to perform an error analysis of the kinematics of inertially stabilized platforms. A physical model is then established to illustrate the effects of geometric errors that are caused by imprecision in the manufacturing and assembly processes on the pointing accuracy of inertially stabilized platforms. In the calibration part, an improved hybrid model denoted as the semi-parametric regression model is developed to compensate for remaining nonlinear errors. With applications to a two-degree-of-freedom miniature inertially stabilized platform, semi-parametric regression model is shown to outperform physical model substantially in all cases. The experimental results also indicate that the proposed semi-parametric regression model eliminates both the geometric and nonlinear errors, and that the pointing accuracy of miniature inertially stabilized platform significantly improves after compensation.

Regression analysis is one method in statistics that used to know the pattern of functional relationships between response variables and predictor variables. Combination of parametric and nonparametric regression is semi parametric regression. The most popular estimator for nonparametric or semi parametric regression is spline truncated estimator. Problems in everyday life often using regression modeling with longitudinal data. Longitudinal data is a combination of cross-section data and time-series data. In longitudinal data, between subjects are independent of each other but between observations in the subject are dependent. One of the most important parts of statistical inference is interval estimation. Interval estimation aims to determine predictor variables that have a significant effect on the response variable. This study aims to obtain the form of interval estimation for parameters of semi parametric regression models using spline truncated estimator in longitudinal data. To solve this problem, the Weighted Least Square method and a pivotal quantity method were used for unknown population variance cases. The result of the theoretical study was that pivotal quantity distributed student-t. The shortest parameter interval estimation of semi parametric spline truncated regression model was obtained through the optimization process using the method of Lagrange.Regression analysis is one method in statistics that used to know the pattern of functional relationships between response variables and predictor variables. Combination of parametric and nonparametric regression is semi parametric regression. The most popular estimator for nonparametric or semi parametric regression is spline truncated estimator. Problems in everyday life often using regression modeling with longitudinal data. Longitudinal data is a combination of cross-section data and time-series data. In longitudinal data, between subjects are independent of each other but between observations in the subject are dependent. One of the most important parts of statistical inference is interval estimation. Interval estimation aims to determine predictor variables that have a significant effect on the response variable. This study aims to obtain the form of interval estimation for parameters of semi parametric regression models using spline truncated estimator in longitudinal data. To solve this problem, t...

Size-biased sampling arises when a positive-valued outcome variable is sampled with selection probability proportional to its size. In this article, we propose a semiparametric linear regression model to analyze size-biased outcomes. In our proposed model, the regression parameters of covariates are of major interest, while the distribution of random errors is unspecified. Under the proposed model, we discover that regression parameters are invariant regardless of size-biased sampling. Following this invariance property, we develop a simple estimation procedure for inferences. Our proposed methods are evaluated in simulation studies and applied to two real data analyses.