{"title":"Elicitation of the Parameters of Multiple Linear Models","authors":"C. Barrera-Causil, J. C. Correa-Morales","doi":"10.15446/RCE.V44N1.83525","DOIUrl":"https://doi.org/10.15446/RCE.V44N1.83525","url":null,"abstract":" \u0000Estimating the parameters of a multiple linear model is a common task in all areas of sciences. In order to obtain conjugate distributions, the Bayesian estimation of these parameters is usually carried out using noninformative priors. When informative priors are considered in the Bayesian estimation an important problem arises because techniques arerequired to extract information from experts and represent it in an informative prior distribution. Elicitation techniques can be used for suchpurpose even though they are more complex than the traditional methods.\u0000In this paper, we propose a technique to construct an informative prior distribution from expert knowledge using hypothetical samples. Our proposal involves building a mental picture of the population of responses at several specific points of the explanatory variables of a given model andindirectly eliciting the mean and the variance at each of these points. In addition, this proposal consists of two steps: the first step describes the elicitation process and the second step shows a simulation process to estimate the model parameters.\u0000","PeriodicalId":54477,"journal":{"name":"Revista Colombiana De Estadistica","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-01-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45730666","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"On a new procedure for identifying a dynamic common factor model","authors":"Stevenson Bolívar, Fabio H. Nieto, D. Peña","doi":"10.15446/rce.v44n1.84816","DOIUrl":"https://doi.org/10.15446/rce.v44n1.84816","url":null,"abstract":"In the context of the exact dynamic common factor model, canonical correlations in a multivariate time series are used to identify the number of latent common factors. In this paper, we establish a relationship between canonical correlations and the autocovariance function of the factor process, in order to modify a pre-established statistical test to detect the number of common factors. In particular, the test power is increased. Additionally, we propose a procedure to identify a vector ARMA model for the factor process, which is based on the so-called simple and partial canonical autocorrelation functions. We illustrate the proposed methodology by means of some simulated examples and a real data application.","PeriodicalId":54477,"journal":{"name":"Revista Colombiana De Estadistica","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-01-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42854383","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Comparison of Correction Factors and Sample Size Required to Test the Equality of the Smallest Eigenvalues in Principal Component Analysis","authors":"Eduard Gañan-Cardenas, J. C. Correa-Morales","doi":"10.15446/RCE.V44N1.83987","DOIUrl":"https://doi.org/10.15446/RCE.V44N1.83987","url":null,"abstract":"In the inferential process of Principal Component Analysis (PCA), one of the main challenges for researchers is establishing the correct number of components to represent the sample. For that purpose, heuristic and statistical strategies have been proposed. One statistical approach consists in testing the hypothesis of the equality of the smallest eigenvalues in the covariance or correlation matrix using a Likelihood-Ratio Test (LRT) that follows a χ2 limit distribution. Different correction factors have been proposed to improve the approximation of the sampling distribution of the statistic. We use simulation to study the significance level and power of the test under the use of these different factors and analyze the sample size required for an dequate approximation. The results indicate that for covariance matrix, the factor proposed by Bartlett offers the best balance between the objectives of low probability of Type I Error and high Power.\u0000 \u0000 \u0000 \u0000 \u0000 \u0000 \u0000If the correlation matrix is used, the factors W ∗\u0000 \u0000 \u0000 \u0000 \u0000 \u0000 \u0000and cχ2\u0000 \u0000 \u0000 \u0000 \u0000 \u0000 \u0000are the most\u0000 \u0000 \u0000 \u0000 \u0000 \u0000 \u0000 \u0000recommended. Empirically, we can observe that most factors require sample sizes 10 or 20 times the number of variables if covariance or correlationmatrices, respectively, are implemented.","PeriodicalId":54477,"journal":{"name":"Revista Colombiana De Estadistica","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-01-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45538688","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Combining Interval Time Series Forecasts. A First Step in a Long Way (Research Agenda)","authors":"C. Maté","doi":"10.15446/RCE.V44N1.85116","DOIUrl":"https://doi.org/10.15446/RCE.V44N1.85116","url":null,"abstract":"We observe every day a world more complex, uncertain, and riskier than the world of yesterday. Consequently, having accurate forecasts in economics, finance, energy, health, tourism, and so on; is more critical than ever. Moreover, there is an increasing requirement to provide other types of forecasts beyond point ones such as interval forecasts. After more than 50 years of research, there are two consensuses, “combining forecasts reduces the final forecasting error” and “a simple average of several forecasts often outperforms complicated weighting schemes”, which was named “forecast combination puzzle (FCP)”. The introduction of intervalvalued time series (ITS) concepts and several forecasting methods has been proposed in different papers and gives answers to some big data challenges. Hence, one main issue is how to combine several forecasts obtained for one ITS. This paper proposes some combination schemes with a couple or various ITS forecasts. Some of them extend previous crisp combination schemes incorporating as a novelty the use of Theil’s U. The FCP under the ITS forecasts framework will be analyzed in the context of different accuracy measures and some guidelines will be provided. An agenda for future research in the field of combining forecasts obtained for ITS will be outlined. ","PeriodicalId":54477,"journal":{"name":"Revista Colombiana De Estadistica","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-01-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43297001","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Felipe Rodríguez-Berrio, F. Rodríguez-Cortés, J. Mateu, G. Adelfio
{"title":"On Some Statistical Properties of the Spatio-Temporal Product Density","authors":"Felipe Rodríguez-Berrio, F. Rodríguez-Cortés, J. Mateu, G. Adelfio","doi":"10.15446/RCE.V44N1.84779","DOIUrl":"https://doi.org/10.15446/RCE.V44N1.84779","url":null,"abstract":"We present an extension of the non-parametric edge-corrected Ohser-type kernel estimator for the spatio-temporal product density function. We derive the mean and variance of the estimator and give a closed-form approximation for a spatio-temporal Poisson point process. Asymptotic properties of this second-order characteristic are derived, using an approach based on martingale theory. Taking advantage of the convergence to normality, confidence surfaces under the homogeneous Poisson process are built. A simulation study is presented to compare our approximation for the variance with Monte Carlo estimated values. Finally, we apply the resulting estimator and its properties to analyse the spatio-temporal distribution of the invasive meningococcal disease in the Rhineland Regional Council in Germany.","PeriodicalId":54477,"journal":{"name":"Revista Colombiana De Estadistica","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-01-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42755633","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Stress-Strength Reliability Estimation of Time-Dependent Models with Fixed Stress and Phase Type Strength Distribution","authors":"Joby K. Jose, M. Drisya","doi":"10.15446/RCE.V44N1.86519","DOIUrl":"https://doi.org/10.15446/RCE.V44N1.86519","url":null,"abstract":"The time-dependent stress-strength reliability models deal with systems whose strength or the stress imposed on it or both are time-dependent. In this paper, we consider time-dependent stress-strength reliability model which is subjected to constant stress and it causes a change in the strength of the system over each run of the system. Assuming a continuous phase- type distribution for the initial strength and exponential distribution for the duration of each run of the system called cycle time we derived the expression for the stress-strength reliability of the system at time t. The model is further extended to the cases where cycle time distribution is Gamma and Weibull. Simulation studies are conducted to assess the variations in stress-strength reliability, R(t) at different time points, corresponding to the changes in the initial strength distribution and cycle time distribution.","PeriodicalId":54477,"journal":{"name":"Revista Colombiana De Estadistica","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-01-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49181721","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Lenin Alexander Bulla Cruz, L. Lyons, Enrique Darghan
{"title":"Complete-Linkage Clustering Analysis of Surrogate Measures for Road Safety Assessment in Roundabouts","authors":"Lenin Alexander Bulla Cruz, L. Lyons, Enrique Darghan","doi":"10.15446/rce.v44n1.81937","DOIUrl":"https://doi.org/10.15446/rce.v44n1.81937","url":null,"abstract":"This paper presents the findings of a comparative road safety assessment between an existing two-lane roundabout and proposed basic turboroundabout, both designed for the same intersection, to determine which one is safer, based on traffic conflicts and surrogate safety measures. We performed microsimulation models in VISSIM to replicate the fieldobserved traffic operation, and the SSAM to determinate six surrogate measures. We validated the consistency of values obtained by several statistical analyzes. The number of conflicts was 72% lower at the turboroundabout. Through a complete-linkage clustering analysis and Euclidean distances of the surrogate measures, we found that traffic conflicts at the turbo-roundabout tend to cluster in a group, whereas conflicts at the roundabout are scattered, suggesting better organization of traffic flows at the turbo-roundabout. Three-dimensional graphical analysis of clusters and its centroids allowed verifying that surrogate measures point out a safer operation at the turbo-roundabout, even though it presented higher operating speeds. Reducing the dimensionality by principal components analysis, the cumulative variance for the first two components (87.72%) allowed observing results on a two-dimensional graph and their clusters. To endorse conflicts classification, resulting of clusters, we used discriminant analysis. Results validate the methodology and the safety benefits of the turbo-roundabout.","PeriodicalId":54477,"journal":{"name":"Revista Colombiana De Estadistica","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-01-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43042810","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
A. Mota, P. Ramos, P. Ferreira, V. Tomazella, F. Louzada
{"title":"A Reparameterized Weighted Lindley Distribution: Properties, Estimation and Applications","authors":"A. Mota, P. Ramos, P. Ferreira, V. Tomazella, F. Louzada","doi":"10.15446/RCE.V44N1.86566","DOIUrl":"https://doi.org/10.15446/RCE.V44N1.86566","url":null,"abstract":"In this paper, we discuss several mathematical properties and estimation methods for a reparameterized version of the weighted Lindley (RWL) distribution. The RWL distribution can be particularly useful for modeling reliability (survival) data with bathtub-shaped or increasing hazard rate function. The inferential procedure to obtain the parameter estimates is conducted via the maximum likelihood approach considering random right-censoring. Extensive numerical simulations are carried out to investigate and evaluate the performance of the proposed estimation method. Finally, the potentiality of the RWL model is analyzed by employing two real data sets.","PeriodicalId":54477,"journal":{"name":"Revista Colombiana De Estadistica","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-01-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44156884","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Concursos de modelos bayesianos para el salón de clases","authors":"Arthur Berg","doi":"10.15446/RCE.V44N2.89102","DOIUrl":"https://doi.org/10.15446/RCE.V44N2.89102","url":null,"abstract":"","PeriodicalId":54477,"journal":{"name":"Revista Colombiana De Estadistica","volume":"44 1","pages":"243-252"},"PeriodicalIF":0.0,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"67050718","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}