Modified Ridge Type Estimator in Partially Linear Regression Models and Numerical Comparisons

2016 ◽  
Vol 13 (10) ◽  
pp. 7040-7053 ◽  
Author(s):  
Dursun Aydın ◽  
Bahadır Yüzbaşı ◽  
S. Ejaz Ahmed
Keyword(s):  
Cross Validation ◽  
Risk Estimation ◽  
Real Data ◽  
Information Criterion ◽  
Smoothing Splines ◽  
Smoothing Parameter ◽  
Partially Linear Model ◽  
Linear Regression Models ◽  
Monte Carlo Simulation Study ◽  
Partially Linear

In this article, we introduce a modified ridge type estimator for the vector of parameters in a partially linear model. This estimator is a generalization of the well-known Speckman’s approach and is based on smoothing splines method. Most important in the implementation of this method is the choice of the smoothing parameter. Many Criteria of selecting smoothing parameters such as improved version of Akaike information criterion (AICc), generalized cross-validation (GCV), cross-validation (CV), Mallows’ Cp criterion, risk estimation using classical pilots (REC) and Bayes information criterion (BIC) are developed in literature. In order to illustrate the ideas in the paper, a real data example and a Monte Carlo simulation study are carried out. Thus, the appropriate selection criteria are provided for a suitable smoothing parameter selection.

scholarly journals Parametric and Semiparametric Estimations of Bivariate Truncated Type I Generalized Logistic Models driven from Copulas

2017 ◽  
Vol 7 (1) ◽  
pp. 72 ◽  
Author(s):  
Lamya A Baharith
Keyword(s):  
Logistic Models ◽  
Real Data ◽  
Information Criterion ◽  
Logistic Distribution ◽  
Type I ◽  
Copula Functions ◽  
Data Set ◽  
Monte Carlo Simulation Study ◽  
Generalized Logistic Distribution ◽  
Weibull Models

Truncated type I generalized logistic distribution has been used in a variety of applications. In this article, a new bivariate truncated type I generalized logistic (BTTGL) distributional models driven from three different copula functions are introduced. A study of some properties is illustrated. Parametric and semiparametric methods are used to estimate the parameters of the BTTGL models. Maximum likelihood and inference function for margin estimates of the BTTGL parameters are compared with semiparametric estimates using real data set. Further, a comparison between BTTGL, bivariate generalized exponential and bivariate exponentiated Weibull models is conducted using Akaike information criterion and the maximized log-likelihood. Extensive Monte Carlo simulation study is carried out for different values of the parameters and different sample sizes to compare the performance of parametric and semiparametric estimators based on relative mean square error.

scholarly journals New robust-ridge estimators for partially linear model

2019 ◽  
Vol 8 (2) ◽  
pp. 46
Author(s):  
Mervat M. Elgohary ◽  
Mohamed R. Abonazel ◽  
Nahed M. Helmy ◽  
Abeer R. Azazy
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Linear Model ◽  
Partially Linear Model ◽  
Least Trimmed Squares ◽  
Monte Carlo Simulation Study ◽  
Explanatory Variables ◽  
Partially Linear ◽  
Biased Estimators ◽  
Highly Correlated

This paper considers the partially linear model when the explanatory variables are highly correlated as well as the dataset contains outliers. We propose new robust biased estimators for this model under these conditions. The proposed estimators combine least trimmed squares and ridge estimations, based on the spline partial residuals technique. The performance of the proposed estimators and the Speckman-spline estimator has been examined by a Monte Carlo simulation study. The results indicated that the proposed estimators are more efficient and reliable than the Speckman-spline estimator.  

ASYMPTOTIC THEORY IN FIXED EFFECTS PANEL DATA SEEMINGLY UNRELATED PARTIALLY LINEAR REGRESSION MODELS

2013 ◽  
Vol 30 (2) ◽  
pp. 407-435 ◽  
Author(s):  
Jinhong You ◽  
Xian Zhou
Keyword(s):  
Panel Data ◽  
Linear Regression ◽  
Regression Model ◽  
Fixed Effects ◽  
Partially Linear Model ◽  
Regression Equations ◽  
Linear Regression Models ◽  
Finite Sample ◽  
Partially Linear ◽  
Contemporaneous Correlation

This paper deals with statistical inference for the fixed effects panel data seemingly unrelated partially linear regression model. The model naturally extends the traditional fixed effects panel data regression model to allow for semiparametric effects. Multiple regression equations are permitted, and the model includes the aggregated partially linear model as a special case. A weighted profile least squares estimator for the parametric components is proposed and shown to be asymptotically more efficient than those neglecting the contemporaneous correlation. Furthermore, a weighted two-stage estimator for the nonparametric components is also devised and shown to be asymptotically more efficient than those based on individual regression equations. The asymptotic normality is established for estimators of both parametric and nonparametric components. The finite-sample performance of the proposed methods is evaluated by simulation studies.

ON THE USE OF PARTIALLY LINEAR MODEL IN IDENTIFICATION OF ARCING-FAULT LOCATION ON OVERHEAD HIGH-VOLTAGE TRANSMISSION LINES

2004 ◽  
Vol 14 (06) ◽  
pp. 1975-1985
Author(s):  
RASTKO ŽIVANOVIĆ
Keyword(s):  
Linear Model ◽  
Dynamic Behavior ◽  
Nonlinear System Identification ◽  
Identification Problem ◽  
Parametric Modeling ◽  
Partially Linear Model ◽  
Practical Reasons ◽  
Partially Linear ◽  
Pull Out ◽  
Arcing Fault

The task of locating an arcing-fault on overhead line using sampled measurements obtained at a single line terminal could be classified as a practical nonlinear system identification problem. The practical reasons impose the requirement that the solution should be with maximum possible precision. Dynamic behavior of an arc in open air is influenced by the environmental conditions that are changing randomly, and therefore the useful practically application of parametric modeling is out of question. The requirement to identify only one parameter is yet another specific of this problem. The parameter we need is the one that linearly correlates the voltage samples with the current derivative samples (inductance). The correlation between the voltage samples and the current samples depends on the unpredictable arc dynamic behavior. Therefore this correlation is reconstructed using nonparametric regression. A partially linear model combines both, parametric and nonparametric parts in one model. The fit of this model is noniterative, and provides an efficient way to identify (pull out) a single linear correlation from the nonlinear time series.

scholarly journals Water Particles Monitoring in the Atacama Desert: SPC Approach Based on Proportional Data

Axioms ◽  
2021 ◽  
Vol 10 (3) ◽  
pp. 154
Author(s):  
Anderson Fonseca ◽  
Paulo Henrique Ferreira ◽  
Diego Carvalho do Nascimento ◽  
Rosemeire Fiaccone ◽  
Christopher Ulloa-Correa ◽  
...  
Keyword(s):  
Control Chart ◽  
Average Run Length ◽  
Atacama Desert ◽  
Real Data ◽  
Interval Data ◽  
Total Quality ◽  
Statistical Process ◽  
Monte Carlo Simulation Study ◽  
Run Length ◽  
Study Results

Statistical monitoring tools are well established in the literature, creating organizational cultures such as Six Sigma or Total Quality Management. Nevertheless, most of this literature is based on the normality assumption, e.g., based on the law of large numbers, and brings limitations towards truncated processes as open questions in this field. This work was motivated by the register of elements related to the water particles monitoring (relative humidity), an important source of moisture for the Copiapó watershed, and the Atacama region of Chile (the Atacama Desert), and presenting high asymmetry for rates and proportions data. This paper proposes a new control chart for interval data about rates and proportions (symbolic interval data) when they are not results of a Bernoulli process. The unit-Lindley distribution has many interesting properties, such as having only one parameter, from which we develop the unit-Lindley chart for both classical and symbolic data. The performance of the proposed control chart is analyzed using the average run length (ARL), median run length (MRL), and standard deviation of the run length (SDRL) metrics calculated through an extensive Monte Carlo simulation study. Results from the real data applications reveal the tool’s potential to be adopted to estimate the control limits in a Statistical Process Control (SPC) framework.

Approximate Bayesian inference for joint linear and partially linear modeling of longitudinal zero-inflated count and time to event data

2021 ◽  
pp. 096228022110028
Author(s):  
T Baghfalaki ◽  
M Ganjali
Keyword(s):  
Linear Model ◽  
Joint Modeling ◽  
Partially Linear Model ◽  
Event Data ◽  
Time To Event ◽  
Data Set ◽  
Partially Linear ◽  
Time To Event Data ◽  
Count Response ◽  
Approximate Bayesian

Joint modeling of zero-inflated count and time-to-event data is usually performed by applying the shared random effect model. This kind of joint modeling can be considered as a latent Gaussian model. In this paper, the approach of integrated nested Laplace approximation (INLA) is used to perform approximate Bayesian approach for the joint modeling. We propose a zero-inflated hurdle model under Poisson or negative binomial distributional assumption as sub-model for count data. Also, a Weibull model is used as survival time sub-model. In addition to the usual joint linear model, a joint partially linear model is also considered to take into account the non-linear effect of time on the longitudinal count response. The performance of the method is investigated using some simulation studies and its achievement is compared with the usual approach via the Bayesian paradigm of Monte Carlo Markov Chain (MCMC). Also, we apply the proposed method to analyze two real data sets. The first one is the data about a longitudinal study of pregnancy and the second one is a data set obtained of a HIV study.

scholarly journals Parsimonious Predictive Mortality Modeling by Regularization and Cross-Validation with and without Covid-Type Effect

Risks ◽  
2020 ◽  
Vol 9 (1) ◽  
pp. 5
Author(s):  
Karim Barigou ◽  
Stéphane Loisel ◽  
Yahia Salhi
Keyword(s):  
Life Insurance ◽  
Cross Validation ◽  
Cohort Effect ◽  
Information Criterion ◽  
Mortality Forecasting ◽  
Hand Model ◽  
Regularization Techniques ◽  
Bayes Information Criterion ◽  
The One ◽  
Regularized Model

Predicting the evolution of mortality rates plays a central role for life insurance and pension funds. Standard single population models typically suffer from two major drawbacks: on the one hand, they use a large number of parameters compared to the sample size and, on the other hand, model choice is still often based on in-sample criterion, such as the Bayes information criterion (BIC), and therefore not on the ability to predict. In this paper, we develop a model based on a decomposition of the mortality surface into a polynomial basis. Then, we show how regularization techniques and cross-validation can be used to obtain a parsimonious and coherent predictive model for mortality forecasting. We analyze how COVID-19-type effects can affect predictions in our approach and in the classical one. In particular, death rates forecasts tend to be more robust compared to models with a cohort effect, and the regularized model outperforms the so-called P-spline model in terms of prediction and stability.

scholarly journals The Gamma Generalized Pareto Distribution with Applications in Survival Analysis

2017 ◽  
Vol 6 (3) ◽  
pp. 141 ◽  
Author(s):  
Thiago A. N. De Andrade ◽  
Luz Milena Zea Fernandez ◽  
Frank Gomes-Silva ◽  
Gauss M. Cordeiro
Keyword(s):  
Monte Carlo Simulation ◽  
Pareto Distribution ◽  
Generalized Pareto Distribution ◽  
Real Data ◽  
Model Parameters ◽  
Monte Carlo Simulation Study ◽  
Lorenz Curves ◽  
Generalized Pareto ◽  
Mathematical Properties ◽  
Pareto Model

We study a three-parameter model named the gamma generalized Pareto distribution. This distribution extends the generalized Pareto model, which has many applications in areas such as insurance, reliability, finance and many others. We derive some of its characterizations and mathematical properties including explicit expressions for the density and quantile functions, ordinary and incomplete moments, mean deviations, Bonferroni and Lorenz curves, generating function, R\'enyi entropy and order statistics. We discuss the estimation of the model parameters by maximum likelihood. A small Monte Carlo simulation study and two applications to real data are presented. We hope that this distribution may be useful for modeling survival and reliability data.

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