Model robust regression: combining parametric, nonparametric, and semiparametric methods

Researchers use the nonparametric regression method because it provides excellent flexibility in the modeling process. Nonparametric regression procedures can be used if the relationship pattern between the predictor and response variables is unknown. The truncated spline method is one of the most frequently used nonparametric regression methods. A truncated spline is a polynomial slice with continuous segmented properties, and the resulting curve is relatively smooth. The advantage of truncated splines is that they can be used on data that experience behavior changes at specific intervals. The nonparametric spline truncated bi-response regression approach is used when one or more predictor variables affect the two response variables with the assumption that there is a correlation between the response variables. This study aimed to obtain the best spline truncated bi-response nonparametric regression model on life expectancy data and the prevalence of underweight children in Indonesia in 2021. The data used comes from the Central Bureau of Statistics and the Indonesian Ministry of Health. The optimal knot point selection method uses the Generalized Cross Validation (GCV) method. The results showed that the best model formed was obtained using three-knot points based on a minimum GCV value of 22.77 and a coefficient of determination of 99.58%.

This paper introduces goodness-of-fit tests for parametric circular regression models with spatially correlated errors, motivated by the analysis of wave direction data in the Adriatic Sea. The proposed methodology confronts a parametric model with a local linear kernel estimator that accounts for both the circular nature of the response and the spatial dependence in the observed field. Two test statistics are introduced: one based on the raw discrepancy between the parametric and nonparametric fits, and another that incorporates a smoothed version of the parametric model to improve robustness. Under suitable regularity conditions, we derive the asymptotic distribution of the test statistic based on the smoothed parametric fit, providing theoretical support for its validity. Calibration under the null hypothesis is achieved via spatial bootstrap techniques specifically adapted to circular data. A comprehensive simulation study demonstrates that the proposed tests are well-calibrated across various dependence scenarios and exhibit strong power against a wide range of alternatives. Finally, the methodology is illustrated through a detailed application to Adriatic Sea wave direction data, where a physically motivated parametric model is evaluated using the proposed tests. The results reveal no evidence against the model, supporting its adequacy as a parsimonious representation of the underlying spatial structure.

The nonparametric binary logistic model assumes that the logit function is a linear function in the parameter, where the parameter depends on arbitrary fixed point. This study discusses the estimation of a nonparametric binary logistic regression model using the local likelihood logit estimation method. This method assumes that the log likelihood logit function depends on the multivariate kernel weighting. The parameter estimation of a nonparametric binary logistic regression model is obtained by maximizing the log likelihood logit function. The parameter estimation result are implicit, so to estimate it started with determining the optimal bandwidth value based on the maximum Cross Validation value. Furthermore, the optimal bandwidth value is used to estimate parameters using the multivariate Newton-Raphson algorithm until converging iterations are obtained. The parameter estimation process is done by creating a program in OSS-R software. This study also discusses the application of parametric and nonparametric binary logistic regression models in the case study of Type II Diabetes Mellitus patients at the Surabaya Hajj General Hospital. The modeling results show that the classification accuracy value of the parametric and nonparametric binary logistic regression models is 80.2% and 100% for the cut of value of 0.5.

In the context of this study, changes in the vegetation coverage are to be detected in the Brittany region in France, based on seasonal and regional scales. Thus, many low resolution images from MODIS satellite are considered per season. Unfortunately, the Brittany region in the west of France is often covered by clouds, and few dates per season with clear coverage are available. A nonparametric regression procedure, depending on the presence of clear small zones during the season, for predicting the value of data contaminated by weather conditions is presented. The problem is the erroneous data (pixels contaminated by clouds or shadows), which may be seen as a problem of an incomplete data as soon as an outlier detection technique is properly chosen and applied. The idea is to use the Kohonen's self organizing map (SOM) onto clear zones (free of clouds and shadow) for training. Then, incomplete data may be recovered by projecting the data onto this trained SOM. To detect pixels contaminated by clouds and shadows, the box and whisker method has been used with an overall accuracy of 97.7636% and a kappa coefficient of 0.9652.

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...

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.

SUMMARY We consider estimation of a variance function g in regression problems. Such estimation requires simultaneous estimation of the mean function f. We obtain clear results on the extent to which the smoothness of f influences best rates of convergence for estimating g. For example, in nonparametric regression with two derivatives on g, ‘classical' rates of convergence are possible if and only if the unknown f satisfies a Lipschitz condition of order 13 or more. If a parametric model is known for g, then g may be estimated n1/2 consistently if and only if f is Lipschitz of order 12 or more. Optimal rates of convergence are attained by Kernel estimators.

This paper proposes a novel estimator for nonparametric instrumental regression while controlling for additive two-way fixed effects. In particular, the Landweber–Fridman regularization, to overcome the ill-posed inverse problem in the nonparametric instrumental regression procedure, is combined with the local-within two-ways fixed effect estimator presented by Lee, Y., D. Mukherjee, and A. Ullah. (2019. “Nonparametric Estimation of the Marginal Effect in Fixed-Effect Panel Data Models.” Journal of Multivariate Analysis 171: 53–67). Compared to other estimators in this context, an appealing feature is its flexible applicability with respect to different panel model specifications, i.e. models comprising either individual, temporal, or two-way fixed effects. The estimator’s performance is tested on simulated data, where a Monte Carlo study reveals good finite sample behaviour. Confidence intervals are provided by applying the wild bootstrap.

In this study, we reviewed methods, sensors and study areas in estimation of vegetation biophysical (VBph) and biochemical (VBch) parameters using satellite optical remote sensing, in terms of (1) their performance and (2) extent of their use. Performance of parametric regression methods is dependent on the type of sensor, vegetation parameter, vegetation cover and biome of study area. Artificial neural network, partial least-squares regression, random forest, support vector machine and Gaussian process regression (GPR) had acceptable performances in the estimations. Performance of physically based methods depends on selecting appropriate radiative transfer model, inversion method and cost function, optimal solution (e.g. mean of some of the best lookup-table solutions) and adding appropriate Gaussian noise. In recent years, the use of active learning techniques (especially Euclidean distance-based diversity), to optimize training datasets against field datasets, with machine learning regression algorithms (MLRAs) (especially GPR) has led to acceptable performances by hybrid methods in estimation of VBph and VBch parameters using real and/or simulated (Re/Si) satellite hyperspectral (and multispectral) data with dimensionality reduction techniques in the spectral domain (especially principal component analysis with 20 principal components). In overall, Re/Si satellite optical sensors data containing red-edge (mostly for VBch parameters) and/or short-wave infrared (mostly for VBph parameters) spectral band(s) performed well. Emerging trend observed in recent years in the estimations by using Re/Si medium spatial resolution sensors data with relatively good spectral resolutions (e.g. precursore iperspettrale della missione applicativa, environmental mapping and analysis program and Sentinel-2 multispectral instrument) and non-parametric regression (especially MLRAs) and hybrid methods.

This article employs Multivariate Adaptive Regression Spline (MARS) for determination of friction capacity of driven piles in clay. MARS is non-parametric adaptive regression procedure. Pile length, pile diameter, effective vertical stress, and undrained shear strength are considered as input of MARS and the output of MARS is friction capacity. The developed MARS gives an equation for determination of <TEX>$f_s$</TEX> of driven piles in clay. The results of the developed MARS have been compared with the Artificial Neural Network. This study shows that the developed MARS is a robust model for prediction of <TEX>$f_s$</TEX> of driven piles in clay.

Accurate modeling of arterial response to physiological or pathological loads may shed light on the processes leading to initiation and progression of a number of vascular diseases and may serve as a tool for prediction and diagnosis. In this study, a microstructure based hyperelastic constitutive model is developed for passive media of porcine coronary arteries. The most general model contains 12 independent parameters representing the three-dimensional inner fibrous structure of the media and includes the effects of residual stresses and osmotic swelling. Parameter estimation and model validation were based on mechanical data of porcine left anterior descending (LAD) media under radial inflation, axial extension, and twist tests. The results show that a reduced four parameter model is sufficient to reliably predict the passive mechanical properties. These parameters represent the stiffness and the helical orientation of each lamellae fiber and the stiffness of the interlamellar struts interconnecting these lamellae. Other structural features, such as orientational distribution of helical fibers and anisotropy of the interlamellar network, as well as possible transmural distribution of structural features, were found to have little effect on the global media mechanical response. It is shown that the model provides good predictions of the LAD media twist response based on parameters estimated from only biaxial tests of inflation and extension. In addition, good predictive capabilities are demonstrated for the model behavior at high axial stretch ratio based on data of law stretches.

In this paper we revisit the so-called non-stationary regression models for repeated categorical/multinomial data collected from a large number of independent individuals. The main objective of the study is to obtain consistent and efficient regression estimates after taking the correlations of the repeated multinomial data into account. The existing (1) ‘working’ odds ratios based GEE (generalized estimating equations) approach has both consistency and efficiency drawbacks. Specifically, the GEE-based regression estimates can be inconsistent which is a serious limitation. Some other existing studies use a MDL (multinomial dynamic logits) model among the repeated responses. As far as the estimation of the regression effects and dynamic dependence (i.e., correlation) parameters is concerned, they use either (2) a marginal or (3) a joint likelihood approach. In the marginal approach, the regression parameters are estimated for known correlation parameters by solving their respective marginal likelihood estimating equations, and similarly the correlation parameters are estimated by solving their likelihood equations for known regression estimates. Thus, this marginal approach is an iterative approach which may not provide quick convergence. In the joint likelihood approach, the regression and correlation parameters are estimated simultaneously by searching the maximum value of the likelihood function with regard to these parameters together. This approach may encounter computational drawback, specially when the number of correlation parameters gets large. In this paper, we propose a new estimation approach where the likelihood function for the regression parameters is developed from the joint likelihood function by replacing the correlation parameter with a consistent estimator involving unknown regression parameters. Thus the new approach relaxes the dimension issue, that is, the dimension of the correlation parameters does not affect the estimation of the main regression parameters. The asymptotic properties of the estimates of the main regression parameters (obtained based on consistent estimating functions for correlation parameters) are studied in detail.

We revisit the oft-studied asymptotic (in sample size) behavior of the parameter or weight estimate returned by any member of a large family of neural network training algorithms. By properly accounting for the characteristic property of neural networks that their empirical and generalization errors possess multiple minima, we rigorously establish conditions under which the parameter estimate converges strongly into the set of minima of the generalization error. Convergence of the parameter estimate to a particular value cannot be guaranteed under our assumptions. We then evaluate the asymptotic distribution of the distance between the parameter estimate and its nearest neighbor among the set of minima of the generalization error. Results on this question have appeared numerous times and generally assert asymptotic normality, the conclusion expected from familiar statistical arguments concerned with maximum likelihood estimators. These conclusions are usually reached on the basis of somewhat informal calculations, although we shall see that the situation is somewhat delicate. The preceding results then provide a derivation of learning curves for generalization and empirical errors that leads to bounds on rates of convergence.

BackgroundStochastic biochemical reaction networks are commonly modelled by the chemical master equation, and can be simulated as first order linear differential equations through a finite state projection. Due to the very high state space dimension of these equations, numerical simulations are computationally expensive. This is a particular problem for analysis tasks requiring repeated simulations for different parameter values. Such tasks are computationally expensive to the point of infeasibility with the chemical master equation.ResultsIn this article, we apply parametric model order reduction techniques in order to construct accurate low-dimensional parametric models of the chemical master equation. These surrogate models can be used in various parametric analysis task such as identifiability analysis, parameter estimation, or sensitivity analysis. As biological examples, we consider two models for gene regulation networks, a bistable switch and a network displaying stochastic oscillations.ConclusionsThe results show that the parametric model reduction yields efficient models of stochastic biochemical reaction networks, and that these models can be useful for systems biology applications involving parametric analysis problems such as parameter exploration, optimization, estimation or sensitivity analysis.

Nonparametric likelihood ratio model selection tests between parametric likelihood and moment condition models