تقديرات النماذج شبه المعلمية بالتطبيق على بيانات العشارى

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...

New insights into the spatial distribution of particle number concentrations by applying non-parametric land use regression modelling

In genome-enabled prediction, parametric, semi-parametric, and non-parametric regression models have been used. This study assessed the predictive ability of linear and non-linear models using dense molecular markers. The linear models were linear on marker effects and included the Bayesian LASSO, Bayesian ridge regression, Bayes A, and Bayes B. The non-linear models (this refers to non-linearity on markers) were reproducing kernel Hilbert space (RKHS) regression, Bayesian regularized neural networks (BRNN), and radial basis function neural networks (RBFNN). These statistical models were compared using 306 elite wheat lines from CIMMYT genotyped with 1717 diversity array technology (DArT) markers and two traits, days to heading (DTH) and grain yield (GY), measured in each of 12 environments. It was found that the three non-linear models had better overall prediction accuracy than the linear regression specification. Results showed a consistent superiority of RKHS and RBFNN over the Bayesian LASSO, Bayesian ridge regression, Bayes A, and Bayes B models.

This chapter reviews the literature on variable selection in nonparametric and semiparametric regression models via shrinkage. We highlight recent developments on simultaneous variable selection and estimation through the methods of least absolute shrinkage and selection operator (Lasso), smoothly clipped absolute deviation (SCAD), or their variants, but restrict our attention to nonparametric and semiparametric regression models. In particular, we consider variable selection in additive models, partially linear models, functional/varying coefficient models, single index models, general nonparametric regression models, and semiparametric/nonparametric quantile regression models.

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 this paper I compare parametric and nonparametric regression models with the help of a simulated data set. Doing so, I have two main objectives. The first one is to differentiate five concepts of simplicity and assess their respective importance. The second one is to show that the scope of the existing philosophical literature on simplicity and model selection is too narrow because it does not take the nonparametric approach into account (Sober in Philosophy of Science 69(S3), S112–S123, 2002; Forster and Sober in The British Journal for the Philosophy of Science 45(1), 1–35, 1994; Forster, 2001, in Philosophy of Science 74(5), 588–600, 2007; Hitchcock and Sober in The British Journal for the Philosophy of Science 55(1), 1–34, 2004; Mikkelson in Philosophy of Science 73(4), 440–447, 2006; Baker 2013). More precisely, I point out that a measure of simplicity in terms of the number of adjustable parameters is inadequate to characterise nonparametric models and to compare them with parametric models. This allows me to weed out false claims about what makes a model simpler than another. Furthermore, I show that the importance of simplicity in model selection cannot be captured by the notion of parametric simplicity. ‘Simplicity’ is an umbrella term. While parametric simplicity can be ignored, there are other notions of simplicity that need to be taken into consideration when we choose a model. Such notions are not discussed in the previously mentioned literature. The latter therefore portrays an incomplete picture of why simplicity matters when we choose a model. Overall I support a pluralist view according to which we cannot give a general and interesting (epistemic or pragmatic) justification for the importance of simplicity in science.

Lack-of-fit checking for parametric and semiparametric models is essential in reducing misspecification. The efficiency of most existing model-checking methods drops rapidly as the dimension of the covariates increases. We propose to check a model by projecting the fitted residuals along a direction that adapts to the systematic departure of the residuals from the desired pattern. Consistency of the method is proved for parametric and semiparametric regression models. A bootstrap implementation is also discussed. Simulation comparisons with several existing methods are made, suggesting that the proposed methods are more efficient than the existing methods when the dimension increases. Air pollution data from Chicago are used to illustrate the procedure.

This dissertation consists of two chapters: Chapter 1 develops nonparametric and semiparametric regression methodologies which relate the group testing responses to the individual covariates information. In this chapter, we extend the parametric regression model of Xie (2001) for binary group testing data to the nonparametric and semiparametric models. We fit nonparametric and semiparametric models and obtain estimators of the parameters by maximizing penalized likelihood function. For implementation, we apply EM algorithm considering the individual responses as complete data and the group testing responses as observed data. Simulation studies are performed to illustrate the methodologies and to evaluate the finite sample performance of our methods. In general, group testing involves a large number of subjects, hence, the computational aspect is also discussed. The results show that our estimation methods perform well for estimating both the individual probability of positive outcome and the prevalence rate in the population.Chapter 2 studies a partially linear regression model with missing response variable and develops semiparametric efficient inference for the parametric component of the model. The missingness considered here includes a broad range of missing patterns. For the estimation method, we use the concept of least favorable curve, least favorable direction and the generalized profile likelihood in Severini and Wong (1992). Asymptotic distributions for the estimators of the parametric components are obtained. It is shown that the estimators are asymptotically normally distributed under some conditions. Furthermore, we prove that the asymptotic covariance of the estimators achieves the semiparametric lower bound under the regularity conditions and additional conditions given in the appendix.We also propose an algorithm which runs iteratively between fitting parametric components and fitting nonparametric components while holding the other fixed. EM algorithms are used in estimating the parametric components by a semiparametric estimating equation and in estimating the nonparametric components by smoothing methods. It is proved that the estimators from this iterative algorithm equal to the conditional expectations (conditioned on observed data) of the semiparametric efficient estimators from complete data. The methodology is illustrated and evaluated by numerical examples.

Background: Nowadays, forecasting models based on nonparametric models have been developed in many branches of science such as mathematics and economics. However, the relatively complicated structure of these models has made them less practical in medical sciences. Objectives: In this study, we investigated the application of a nonparametric regression model to predict the psychological symptoms appearing six months after mild traumatic brain injury. We also made a comparison between the performance of nonparametric regression and artificial neural network models in predicting the psychological symptoms. Methods: In a six-month period during 2015 - 2017, information of 100 mild traumatic patients was included in a prospective cohort study. The data were then divided randomly into two groups of training (n = 50) and testing (n = 50) for 100 times. In the training group, the focus was on 100 artificial neural network and nonparametric regression models. However, in the testing group, a comparison was made between the values obtained using the two final models. To compare the models, the ROC curve and the accuracy rate were finally applied. Results: According to the obtained results, the nonparametric regression model showed an accuracy rate of 91.25% while the neural network model had an accuracy rate of 85.34%. In the experimental set for both neural network and nonparametric regression models, the area under the ROC curve appeared to be 81.51% and 85.73 %, respectively. Conclusions: The nonparametric regression model appeared to be more powerful than the neural network model in predicting psychological symptoms.

Purpose: The research aims to estimate models representing phenomena that follow the logic of circular (angular) data, accounting for the 24-hour periodicity in measurement. Theoretical framework: The regression model is developed to account for the periodic nature of the circular scale, considering the periodicity in the dependent variable y, the explanatory variables x, or both. Design/methodology/approach: Two estimation methods were applied: a parametric model, represented by the Simple Circular Regression (SCR) model, and a nonparametric model, represented by the Nadaraya-Watson Circular Regression (NW) model. The analysis used real data from 50 patients at Al-Kindi Teaching Hospital in Baghdad. Findings: The Mean Circular Error (MCE) criterion was used to compare the two models, leading to the conclusion that the Nadaraya-Watson (NW) circular model outperformed the parametric model in estimating the parameters of the circular regression model. Research, Practical & Social Implications: The recommendation emphasized using the Nadaraya-Watson nonparametric smoothing method to capture the nonlinearity in the data. Originality/value: The results indicated that the Nadaraya-Watson circular model (NW) outperformed the parametric model. Paper type Research paper.

Nonparametric regression modelling for data applies the relationship between predictor and response variables without considering any particular trend. The main principle of nonparametric regression is estimating an unknown smooth function. Local polynomial regression is one of several methods for estimating smooth functions used in nonparametric regression models. There are two parameters in the local polynomial regression model the smoothing parameter and the polynomial degree parameter. Generalized Cross Validation is a classical method used to determine optimal smoothing parameter in nonparametric regression. The smoothing parameter that gives the minimum value of Generalized Cross-Validation is the optimal parameter. We apply the optimal smoothing parameter for local polynomial regression modelling using data on the regional domestic product growth rate of the business field in North Sumatra Province. The simulation results show a polynomial of degree two is better than degree one. Investigation of the effects of the Covid-19 pandemic shows that the predicted growth rate is far from the expected growth.

Identifying risk factors for road traffic injuries can be considered one of the main priorities of transportation agencies. More than 12,000 fatal work zone crashes were reported between 2000 and 2013. Despite recent efforts to improve work zone safety, the frequency and severity of work zone crashes are still a big concern for transportation agencies. Although many studies have been conducted on different work zone safety-related issues, there is a lack of studies that investigate the effect of adverse weather conditions on work zone crash severity. This paper utilizes probit–classification tree, a relatively recent and promising combination of machine learning technique and conventional parametric model, to identify factors affecting work zone crash severity in adverse weather conditions using 8 years of work zone weather-related crashes (2006–2013) in Washington State. The key strength of this technique lies in its capability to alleviate the shortcomings of both parametric and nonparametric models. The results showed that both presence of traffic control device and lighting conditions are significant interacting variables in the developed complementary crash severity model for work zone weather-related crashes. Therefore, transportation agencies and contractors need to invest more in lighting equipment and better traffic control strategies at work zones, specifically during adverse weather conditions.

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.

For checking on heteroscedasticity in regression models, a unified approach is proposed to constructing test statistics in parametric and nonparametric regression models. For nonparametric regression, the test is not affected sensitively by the choice of smoothing parameters which are involved in estimation of the non parametric regression function. The limiting null distribution of the test statistic remains the same in a wide range of the smoothing parameters. When the covariate is one-dimensional, the tests are, under some conditions, asymptotically distribution-free. In the high-dimensional cases, the validity of bootstrap approximations is investigated. It is shown that a variant of the wild bootstrap is consistent while the classical bootstrap is not in the general case, but is applicable if some extra assumption on conditional variance of the squared error is imposed. A simulation study is performed to provide evidence of how the tests work and compare with tests that have appeared in the literature. The approach mayreadily be extended to handle partial linear, and linear autoregressive models.

This book reviews and develops Bayesian non-parametric and semi-parametric methods for applications in microeconometrics and quantitative marketing. Most econometric models used in microeconomics and marketing applications involve arbitrary distributional assumptions. As more data becomes available, a natural desire to provide methods that relax these assumptions arises. Peter Rossi advocates a Bayesian approach in which specific distributional assumptions are replaced with more flexible distributions based on mixtures of normals. The Bayesian approach can use either a large but fixed number of normal components in the mixture or an infinite number bounded only by the sample size. By using flexible distributional approximations instead of fixed parametric models, the Bayesian approach can reap the advantages of an efficient method that models all of the structure in the data while retaining desirable smoothing properties. Non-Bayesian non-parametric methods often require additional ad hoc rules to avoid “overfitting,” in which resulting density approximates are nonsmooth. With proper priors, the Bayesian approach largely avoids overfitting, while retaining flexibility. This book provides methods for assessing informative priors that require only simple data normalizations. The book also applies the mixture of the normals approximation method to a number of important models in microeconometrics and marketing, including the non-parametric and semi-parametric regression models, instrumental variables problems, and models of heterogeneity. In addition, the author has written a free online software package in R, “bayesm,” which implements all of the non-parametric models discussed in the book.