Conditionally Unbiased Bounded-Influence Estimation in General Regression Models, with Applications to Generalized Linear Models

1989 ◽  
Vol 84 (406) ◽  
pp. 460-466 ◽  
Author(s):  
Hans R. Künsch ◽  
Leonard A. Stefanski ◽  
Raymond J. Carroll
Keyword(s):  
Generalized Linear Models ◽  
Regression Models ◽  
Linear Models ◽  
Bounded Influence ◽  
General Regression

scholarly journals Robust Statistical Inference in Generalized Linear Models Based on Minimum Renyi’s Pseudodistance Estimators

Entropy ◽  
2022 ◽  
Vol 24 (1) ◽  
pp. 123
Author(s):  
María Jaenada ◽  
Leandro Pardo
Keyword(s):  
Generalized Linear Models ◽  
Influence Function ◽  
Regression Models ◽  
Linear Models ◽  
Asymptotic Properties ◽  
Significant Loss ◽  
Superior Performance ◽  
Test Statistics ◽  
Linear Regression Models ◽  
Type Test

Minimum Renyi’s pseudodistance estimators (MRPEs) enjoy good robustness properties without a significant loss of efficiency in general statistical models, and, in particular, for linear regression models (LRMs). In this line, Castilla et al. considered robust Wald-type test statistics in LRMs based on these MRPEs. In this paper, we extend the theory of MRPEs to Generalized Linear Models (GLMs) using independent and nonidentically distributed observations (INIDO). We derive asymptotic properties of the proposed estimators and analyze their influence function to asses their robustness properties. Additionally, we define robust Wald-type test statistics for testing linear hypothesis and theoretically study their asymptotic distribution, as well as their influence function. The performance of the proposed MRPEs and Wald-type test statistics are empirically examined for the Poisson Regression models through a simulation study, focusing on their robustness properties. We finally test the proposed methods in a real dataset related to the treatment of epilepsy, illustrating the superior performance of the robust MRPEs as well as Wald-type tests.

scholarly journals Sunburns among beachgoers in the northern coast of Peru: frequency and factors associated

PeerJ ◽  
2021 ◽  
Vol 9 ◽  
pp. e11473
Author(s):  
Eliana L. Fernandez-Quiroz ◽  
Lizeth Gonzales-Chachapoyas ◽  
Ana L. Alcantara-Diaz ◽  
Binz Bulnes-Villalta ◽  
Zulmy Ayala-Porras ◽  
...  
Keyword(s):  
Generalized Linear Models ◽  
Regression Models ◽  
Linear Models ◽  
Secondary Data ◽  
Sun Exposure ◽  
Prevalence Ratio ◽  
Northern Coast ◽  
Factors Associated ◽  
Northern Peru ◽  
Skin Phototype

Background Overexposure to ultraviolet (UV) radiation has increased skin cancer incidence and the risk of sunburns, especially during the summer months. Objective Identify the frequency and factors associated with sunburns in a sample of beachgoers in the northern coast of Peru. Methods We conducted a secondary data analysis of a previous study that assessed the awareness, behavior and attitudes concerning sun exposure among beachgoers. We included adults between 18 and 59 years who went to a beach in northern Peru during summer (March 2018). Three generalized linear models of the Poisson family were constructed to evaluate the factors associated with having had at least one sunburn last summer. All regression models reported the adjusted prevalence ratio (aPR) with their respective 95% confidence interval (95% CI). Results Of a total of 402 participants, 225 (56.0%) had one to five sunburns and 25 (6.2%) had six or more. Beachgoers who were 1–15 days (aPR: 1.16, 95% CI [1.05–1.27]) or more than 15 days (aPR: 1.22, 95% CI [1.09–1.36]) exposed to the sun on the beach had a higher frequency of at least one sunburn. The non-regular wearing of a hat or cap also increased the frequency of sunburns (aPR: 1.06, 95% CI [1.01–1.12]). In contrast, those who had Skin Phototype III (aPR: 0.94, 95% CI [0.88–0.99]) or IV (aPR: 0.69, 95% CI [0.63–0.75]) had a lower frequency of sunburns. Conclusion Three out of five beachgoers had one or more sunburns in the last summer. The factors associated with a higher frequency were the time of sun exposure at the beach and the non-regular use of a hat or cap. Type III–IV skin phototypes were associated with a lower sunburn frequency.

scholarly journals On the Trends of Registered Birth and Death Rates in Nigeria: Evidence from Generalized Linear Models

2019 ◽  
Author(s):  
Monday Osagie Adenomon ◽  
Emmanuel Chukwuma Anikweze
Keyword(s):  
Generalized Linear Models ◽  
Regression Models ◽  
Linear Models ◽  
Negative Binomial ◽  
Negative Binomial Regression ◽  
Natural Increase ◽  
Negative Binomial Regression Model ◽  
Annual Data ◽  
Death Rates ◽  
Binomial Regression

This study investigated the trends of registered Death and Birth in Nigeria using Generalized Linear Models. Annual data on Death and Birth was collected from National Population Commission for the period of 2004 to 2017. The Natural increase calculated revealed a positive trend in the natural increase in Nigeria from 2004 to 2017. Evidence from summary statistics revealed some level of over dispersion (variance > mean). This study explored Poisson Regression Models and Negative Binomial Regression Models using two links (identity and log). The results revealed a positive increase in registration of birth and death rates in Nigeria and among the competing the models, Negative Binomial regression model with identity link emerged as the best model for modeling birth and death rates registration in Nigeria. Data on numbers of deaths and causes of death are essential if countries are to determine priorities, formulate and monitor policies for public health care as well as other government policies that may be based on such data

Regression models

2020 ◽  
pp. 65-92
Author(s):  
Bendix Carstensen
Keyword(s):  
Linear Regression ◽  
Regression Model ◽  
Generalized Linear Models ◽  
Linear Regression Model ◽  
Regression Models ◽  
Linear Models ◽  
General Linear Model ◽  
Simple Linear Regression ◽  
Response Variable ◽  
Quantitative Response

This chapter evaluates regression models, focusing on the normal linear regression model. The normal linear regression model establishes a relationship between a quantitative response (also called outcome or dependent) variable, assumed to be normally distributed, and one or more explanatory (also called regression, predictor, or independent) variables about which no distributional assumptions are made. The model is usually referred to as 'the general linear model'. The chapter then differentiates between simple linear regression and multiple regression. The term 'simple linear regression' covers the regression model where there is one response variable and one explanatory variable, assuming a linear relationship between the two. The chapter also discusses the model formulae in R; generalized linear models; collinearity and aliasing; and logarithmic transformations.

Correcting Misclassification Bias in Regression Models with Variables Generated via Data Mining

2021 ◽  
Author(s):  
Mengke Qiao ◽  
Ke-Wei Huang
Keyword(s):  
Data Mining ◽  
Generalized Linear Models ◽  
Regression Models ◽  
Science Studies ◽  
Linear Models ◽  
Classification Performance ◽  
Classification Error ◽  
Performance Metric ◽  
Review Helpfulness ◽  
Independent Variable

There is a surge of interest in social science studies in applying data mining methods to construct variables for regression analysis. For example, text classification was applied to classify whether the review is subjective or objective. The derived review subjectivity was used as an independent variable in the regression to examine its impact on review helpfulness. In the classification phase of these studies, researchers need to subjectively choose a classification performance metric for optimization. No matter which performance metric is chosen, the constructed variable still includes classification error because the variable cannot be classified perfectly. The misclassification of constructed variables will lead to inconsistent estimators of regression coefficients in the following phase. To correct the estimation inconsistency, we summarize and modify existing proofs in econometrics to derive theoretical formulas of consistent estimators in generalized linear models. The main implication of our theoretical result is that the inconsistency can be corrected by theoretical formulas, even when the classification accuracy is poor. Therefore, we propose that a classification algorithm should be tuned to minimize the standard error of the focal coefficient derived based on the corrected formula. As a result, researchers derive a consistent and most precise estimator in generalized linear models.

RATEMAKING OF DEPENDENT RISKS

2017 ◽  
Vol 47 (3) ◽  
pp. 875-894
Author(s):  
J. M. Andrade e Silva ◽  
M. de Lourdes Centeno
Keyword(s):  
Power Function ◽  
Generalized Linear Models ◽  
Regression Models ◽  
Linear Models ◽  
Negative Binomial ◽  
Laguerre Polynomial ◽  
Random Variable ◽  
Insurance Company ◽  
Dependent Risks ◽  
The Mean

AbstractWe start by describing how, in some cases, we can use variance-related premium principles in ratemaking, when the claim numbers and individual claim amounts are independent. We use quasi-likelihood generalized linear models, under the assumption that the variance function is a power function of the mean of the underlying random variable. We extend this approach to the cases where the claim numbers are correlated. Some alternatives to deal with dependent risks are presented, taking explicitly into account overdispersion. We present regression models covering the bivariate Poisson, the generalized bivariate negative binomial and the bivariate Poisson–Laguerre polynomial, which nest the bivariate negative binomial. We apply these models to a portfolio of the Portuguese insurance company Tranquilidade and compare the results obtained.

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