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 QML Estimators in Linear Regression Models with Functional Coefficient Autoregressive Processes

2010 ◽  
Vol 2010 ◽  
pp. 1-30 ◽  
Author(s):  
Hongchang Hu
Keyword(s):  
Maximum Likelihood ◽  
Linear Regression ◽  
Regression Models ◽  
Asymptotic Properties ◽  
Asymptotic Distributions ◽  
Autoregressive Processes ◽  
Linear Regression Models ◽  
Unknown Parameters ◽  
Quasi Maximum Likelihood ◽  
Functional Coefficient

This paper studies a linear regression model, whose errors are functional coefficient autoregressive processes. Firstly, the quasi-maximum likelihood (QML) estimators of some unknown parameters are given. Secondly, under general conditions, the asymptotic properties (existence, consistency, and asymptotic distributions) of the QML estimators are investigated. These results extend those of Maller (2003), White (1959), Brockwell and Davis (1987), and so on. Lastly, the validity and feasibility of the method are illuminated by a simulation example and a real example.

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 Regression models for estimating chick hatchling weight from some egg geometry traits

2018 ◽  
Vol 34 (3) ◽  
pp. 323-334
Author(s):  
Nadya Mincheva ◽  
Mitko Lalev ◽  
Magdalena Oblakova ◽  
Pavlina Hristakieva
Keyword(s):  
Linear Regression ◽  
Surface Area ◽  
Regression Models ◽  
Linear Models ◽  
Geometric Mean ◽  
Coefficient Of Determination ◽  
Regression Equations ◽  
Linear Regression Models ◽  
Egg Weight ◽  
Mean Diameter

The prediction of chicks? weight before hatching is an important element of selection, aimed at improving the uniformity rate and productivity of birds. With this regards, our goal was to develop and evaluate optimum models for similar prediction in two White Plymouth Rock chickens lines - line L and line K on the basis of the incubation egg weight and egg geometry characteristics - egg maximum breadth (B), egg length (L), geometric mean diameter (Dg), egg volume (V), egg surface area (S). A total of 280 eggs (140 from each line) laid by 40-weekold hens were randomly selected. Mean arithmetic values, standard deviations and coefficients of variation of studied parameters were determined for each line. Correlation coefficients between the weight of hatchlings and predictors were the highest for egg weight, geometric mean diameter, volume and surface area of eggs (r=0.731-0.779 for line L; r=0.802-0.819 for line ?). Nine linear regression models were developed and their accuracy evaluated. The regression equations of hatchlings? weight vs egg length had the lowest coefficient of determination (0.175 for line K and 0.291 for line L), but when egg length and breadth entered the model together, its value increased significantly up to 0.541 and 0.665 for lines L and K, respectively. The weight of day-old chicks from line L could be predicted with higher accuracy with a model involving egg surface area apart egg weight (ChW=0.513EW+0.282S - 10.345; R2=0.620). In line ? a more accurate prognosis was attained by adding egg breadth as an additional predictor to the weight in the model (ChW=0.587EW+0.566? - 19.853; R2=0.692). The study demonstrated that multiple linear regression models were more precise that single linear models.

scholarly journals Robust Model Selection Criteria Based on Pseudodistances

Entropy ◽  
2020 ◽  
Vol 22 (3) ◽  
pp. 304 ◽  
Author(s):  
Aida Toma ◽  
Alex Karagrigoriou ◽  
Paschalini Trentou
Keyword(s):  
Model Selection ◽  
Regression Models ◽  
Selection Criteria ◽  
Selection Criterion ◽  
Superior Performance ◽  
Linear Regression Models ◽  
Limit Laws ◽  
Model Selection Criteria ◽  
Robust Model ◽  
Robust Model Selection

In this paper, we introduce a new class of robust model selection criteria. These criteria are defined by estimators of the expected overall discrepancy using pseudodistances and the minimum pseudodistance principle. Theoretical properties of these criteria are proved, namely asymptotic unbiasedness, robustness, consistency, as well as the limit laws. The case of the linear regression models is studied and a specific pseudodistance based criterion is proposed. Monte Carlo simulations and applications for real data are presented in order to exemplify the performance of the new methodology. These examples show that the new selection criterion for regression models is a good competitor of some well known criteria and may have superior performance, especially in the case of small and contaminated samples.

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

Sign in / Sign up

Export Citation Format

Share Document