scholarly journals Influence Diagnostics in Log-Normal Regression Model with Censored Data

2021 ◽  
Vol 2021 ◽  
pp. 1-15
Author(s):  
Javeria Khaleeq ◽  
Muhammad Amanullah ◽  
Zahra Almaspoor

Dealing with the biological data, the skewed distribution is approximated by the Log-Normal Regression model (LNRM). Traditional estimation techniques for the LNRM are sensitive to unusual observations. These observations greatly affect the model analysis, which makes imprecise conclusions. To overcome this issue, we proposed to develop diagnostics measures based on local influence diagnostics to identify such curious observations in the LNRM under censoring. The proposed measures are derived by perturbing the case weight, response, and explanatory variables. Furthermore, we also consider the One-Step Newton-Raphson method and generalized cook’s distance. We study the Monte Carlo simulation and its application to real data to illustrate the developed approaches.

2017 ◽  
Vol 27 (11) ◽  
pp. 3207-3223 ◽  
Author(s):  
Thiago G Ramires ◽  
Gauss M Cordeiro ◽  
Michael W Kattan ◽  
Niel Hens ◽  
Edwin MM Ortega

Cure fraction models are useful to model lifetime data with long-term survivors. We propose a flexible four-parameter cure rate survival model called the log-sinh Cauchy promotion time model for predicting breast carcinoma survival in women who underwent mastectomy. The model can estimate simultaneously the effects of the explanatory variables on the timing acceleration/deceleration of a given event, the surviving fraction, the heterogeneity, and the possible existence of bimodality in the data. In order to examine the performance of the proposed model, simulations are presented to verify the robust aspects of this flexible class against outlying and influential observations. Furthermore, we determine some diagnostic measures and the one-step approximations of the estimates in the case-deletion model. The new model was implemented in the generalized additive model for location, scale and shape package of the R software, which is presented throughout the paper by way of a brief tutorial on its use. The potential of the new regression model to accurately predict breast carcinoma mortality is illustrated using a real data set.


2021 ◽  
Vol 2 (1) ◽  
pp. 12-20
Author(s):  
Kayode Ayinde, Olusegun O. Alabi ◽  
Ugochinyere Ihuoma Nwosu

Multicollinearity has remained a major problem in regression analysis and should be sustainably addressed. Problems associated with multicollinearity are worse when it occurs at high level among regressors. This review revealed that studies on the subject have focused on developing estimators regardless of effect of differences in levels of multicollinearity among regressors. Studies have considered single-estimator and combined-estimator approaches without sustainable solution to multicollinearity problems. The possible influence of partitioning the regressors according to multicollinearity levels and extracting from each group to develop estimators that will estimate the parameters of a linear regression model when multicollinearity occurs is a new econometrics idea and therefore requires attention. The results of new studies should be compared with existing methods namely principal components estimator, partial least squares estimator, ridge regression estimator and the ordinary least square estimators using wide range of criteria by ranking their performances at each level of multicollinearity parameter and sample size. Based on a recent clue in literature, it is possible to develop innovative estimator that will sustainably solve the problem of multicollinearity through partitioning and extraction of explanatory variables approaches and identify situations where the innovative estimator will produce most efficient result of the model parameters. The new estimator should be applied to real data and popularized for use.


2021 ◽  
Vol 11 (20) ◽  
pp. 9654
Author(s):  
Holger Billhardt ◽  
Alberto Fernández ◽  
Sascha Ossowski

Vehicle-sharing systems—such as bike-, car-, or motorcycle-sharing systems—have become increasingly popular in big cities in recent years. On the one hand, they provide a cheaper and environmentally friendlier means of transportation than private cars, and on the other hand, they satisfy the individual mobility demands of citizens better than traditional public transport systems. One of their advantages in this regard is their availability, e.g., the possibility of taking (or leaving) a vehicle almost anywhere in a city. This availability obviously depends on different strategic and operational management decisions and policies, such as the dimension of the fleet or the (re)distribution of vehicles. Agglutination problems—where, due to usage patterns, available vehicles are concentrated in certain areas, whereas no vehicles are available in others—are quite common in such systems, and need to be dealt with. Research has been dedicated to this problem, specifying different techniques to reduce imbalanced situations. In this paper, we present and compare strategies for recommending stations to users who wish to rent or return bikes in station-based bike-sharing systems. Our first contribution is a novel recommendation strategy based on queuing theory that recommends stations based on their utility to the user in terms of lower distance and higher probability of finding a bike or slot. Then, we go one step further, defining a strategy that recommends stations by combining the utility of a particular user with the utility of the global system, measured in terms of the improvement in the distribution of bikes and slots with respect to the expected future demand, with the aim of implicitly avoiding or alleviating balancing problems. We present several experiments to evaluate our proposal with real data from the bike sharing system BiciMAD in Madrid.


2019 ◽  
Vol 11 (01) ◽  
pp. 1950002
Author(s):  
Takayoshi Nakamoto ◽  
Ryuei Nishii ◽  
Shinto Eguchi

In this paper, as data, ellipsoids in a color coordinate called the Commission Internationale de l’Eclairage (CIE)-Lab system are given as data for 19 colors. Each ellipsoid is a region where all points are visually recognized as the same color at the center of the coordinate system. Our aim here is to predict the shape of an ellipsoid whose center is given by a new color. We proposed two prediction methods of positive definite matrices determining ellipsoids. The first one is a nonparametric method with Gaussian kernel. The prediction is provided as a weighted sum of positive definite matrices corresponding to 19 ellipsoids in the training data. The second one is to use a matrix-valued regression model applied to a logarithm of positive definite matrices where explanatory variables are three elements of color centers. The best result was obtained by the nonparametric methods with three bandwidth parameters. The log normal regression had a weaker performance, but even so the model estimation was easily carried out.


Mathematics ◽  
2021 ◽  
Vol 9 (6) ◽  
pp. 590
Author(s):  
Ang Shan ◽  
Fengkai Yang

Finite mixtures normal regression (FMNR) models are widely used to investigate the relationship between a response variable and a set of explanatory variables from several unknown latent homogeneous groups. However, the classical EM algorithm and Gibbs sampling to deal with this model have several weak points. In this paper, a non-iterative sampling algorithm for fitting FMNR model is proposed from a Bayesian perspective. The procedure can generate independently and identically distributed samples from the posterior distributions of the parameters and produce more reliable estimations than the EM algorithm and Gibbs sampling. Simulation studies are conducted to illustrate the performance of the algorithm with supporting results. Finally, a real data is analyzed to show the usefulness of the methodology.


2010 ◽  
Vol 7 (6) ◽  
pp. 644-654 ◽  
Author(s):  
Alexandre G. Patriota ◽  
Artur J. Lemonte ◽  
Mário de Castro

2021 ◽  
Vol 16 (3) ◽  
pp. 177-187
Author(s):  
Şaban Kızılarslan ◽  
Ceren Camkıran

The aim of this study is to compare the performance of robust estimators in the presence of explanatory variables with Generalized Extreme Value (GEV) distributions in the logistic regression model. Existence of extreme values in the logistic regression model negatively affects the bias and effectiveness of classical Maximum Likelihood (ML) estimators. For this reason, robust estimators that are less sensitive to extreme values have been developed. Random variables with extreme values may be fit in one of specific distributions. In study, the GEV distribution family was examined and five robust estimators were compared for the Fréchet, Gumbel and Weibull distributions. To the simulation results, the CUBIF estimator is prominent according to both bias and efficiency criteria for small samples. In medium and large samples, while the MALLOWS estimator has the minimum bias, the CUBIF estimator has the best efficiency. The same results apply for different contamination ratios and different scale parameter values of the distributions. Simulation findings were supported by a meteorological real data application.


Author(s):  
Emrah Altun ◽  
Haitham M. Yousof ◽  
GG Hamedani

A new four-parameter lifetime model called OddLog-Logistic Burr XII distribution, is defined and investigated. Some of itsmathematical properties are derived. Some useful characterization resultsbased on \ the ratio of two truncated moments, based on the hazard functionas well as on the conditional expectation of certain functions of the randomvariable are presented. The maximum likelihood method is used to estimatethe model parameters by means of a graphical Monte Carlo simulation study.Moreover, we introduce a new log-location regression model based on theproposed distribution. The Jackknife estimation method as an alternativemethod is used to estimate the unknown parameters of new regression model. Thegeneralized cook distance and likelihood distance measures are used todetect the possible influential observations. The martingale and modifieddeviance residuals are defined to detect outliers and evaluate the modelassumptions. The potentiality of the new regression model is illustrated bymeans of a real data set.


SERIEs ◽  
2021 ◽  
Author(s):  
Rodrigo Mulero ◽  
Alfredo García-Hiernaux

AbstractThis paper presents a method to improve the one-step-ahead forecasts of the Spanish unemployment monthly series. To do so, we use numerous potential explanatory variables extracted from searches in Google (Google Trends tool). Two different dimension reduction techniques are implemented (PCA and Forward Stepwise Selection) to decide how to combine the explanatory variables or which ones to use. The results of a recursive forecasting exercise reveal a statistically significant increase in predictive accuracy of 10–25%, depending on the dimension reduction method employed. A deep robustness analysis confirms these findings, as well as the relevance of using a large amount of Google queries together with a dimension reduction technique, when no prior information on which are the most informative queries is available.


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