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Stats, Volume 2, Issue 2 (June 2019)

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Open AccessArticle
A Bayes Inference for Ordinal Response with Latent Variable Approach
Stats 2019, 2(2), 321-331; https://doi.org/10.3390/stats2020023 - 16 Jun 2019
Viewed by 410
Abstract
In this paper, we propose a Bayesian model for the analysis of categorical data with an ordered outcome. The method provides a latent variable approach with an informative prior transformed from a Dirichlet distribution for the boundary parameters. A simulation study is carried [...] Read more.
In this paper, we propose a Bayesian model for the analysis of categorical data with an ordered outcome. The method provides a latent variable approach with an informative prior transformed from a Dirichlet distribution for the boundary parameters. A simulation study is carried out to assess the performance of the methods under various settings of the data structure. Our method produces predictive accuracy over the conventional classification procedures. Real data are analyzed to demonstrate the efficiency of the proposed method. Full article
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Open AccessArticle
INARMA Modeling of Count Time Series
Stats 2019, 2(2), 284-320; https://doi.org/10.3390/stats2020022 - 03 Jun 2019
Viewed by 422
Abstract
While most of the literature about INARMA models (integer-valued autoregressive moving-average) concentrates on the purely autoregressive INAR models, we consider INARMA models that also include a moving-average part. We study moment properties and show how to efficiently implement maximum likelihood estimation. We analyze [...] Read more.
While most of the literature about INARMA models (integer-valued autoregressive moving-average) concentrates on the purely autoregressive INAR models, we consider INARMA models that also include a moving-average part. We study moment properties and show how to efficiently implement maximum likelihood estimation. We analyze the estimation performance and consider the topic of model selection. We also analyze the consequences of choosing an inadequate model for the given count process. Two real-data examples are presented for illustration. Full article
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Open AccessArticle
Risk Prediction Model for Dengue Transmission Based on Climate Data: Logistic Regression Approach
Stats 2019, 2(2), 272-283; https://doi.org/10.3390/stats2020021 - 10 May 2019
Viewed by 494
Abstract
Dengue fever is a mosquito-borne viral disease prevalent in more than one hundred tropical and subtropical countries. Annually, an estimated 390 million infections occur worldwide. It is transmitted by the bite of an Aedes mosquito infected with the virus. It has become a [...] Read more.
Dengue fever is a mosquito-borne viral disease prevalent in more than one hundred tropical and subtropical countries. Annually, an estimated 390 million infections occur worldwide. It is transmitted by the bite of an Aedes mosquito infected with the virus. It has become a major public health challenge in recent years for many countries, including Sri Lanka. It is known that climate factors such as rainfall, temperature, and relative humidity influence the generation of mosquito offspring, thus increasing dengue incidences. Identifying the climate factors that affect the spread of dengue fever would be helpful in order for the relevant authorities to take necessary actions. The objective of this study is to build a model for predicting the likelihood of having high dengue incidences based on climate factors. A logistic regression approach was utilized for model formulation. This study found a significant association between high numbers of dengue incidences and rainfall. Furthermore, it was observed that the influence of rainfall on dengue incidences was expected to be visible after some lag period. Full article
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Open AccessReview
Setting Alarm Thresholds in Measurements with Systematic and Random Errors
Stats 2019, 2(2), 259-271; https://doi.org/10.3390/stats2020020 - 07 May 2019
Viewed by 315
Abstract
For statistical evaluations that involve within-group and between-group variance components (denoted σW2 and σB2, respectively), there is sometimes a need to monitor for a shift in the mean of time-ordered data. Uncertainty in the estimates σ^W [...] Read more.
For statistical evaluations that involve within-group and between-group variance components (denoted σ W 2 and σ B 2 , respectively), there is sometimes a need to monitor for a shift in the mean of time-ordered data. Uncertainty in the estimates σ ^ W 2 and σ ^ B 2 should be accounted for when setting alarm thresholds to check for a mean shift as both σ W 2 and σ B 2 must be estimated. One-way random effects analysis of variance (ANOVA) is the main tool for analysing such grouped data. Nearly all of the ANOVA applications assume that both the within-group and between-group components are normally distributed. However, depending on the application, the within-group and/or between-group probability distributions might not be well approximated by a normal distribution. This review paper uses the same example throughout to illustrate the possible approaches to setting alarm limits in grouped data, depending on what is assumed about the within-group and between-group probability distributions. The example involves measurement data, for which systematic errors are assumed to remain constant within a group, and to change between groups. The false alarm probability depends on the assumed measurement error model and its within-group and between-group error variances, which are estimated while using historical data, usually with ample within-group data, but with a small number of groups (three to 10 typically). This paper illustrates the parametric, semi-parametric, and non-parametric options to setting alarm thresholds in such grouped data. Full article
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Open AccessArticle
A Distribution for Instantaneous Failures
Stats 2019, 2(2), 247-258; https://doi.org/10.3390/stats2020019 - 07 May 2019
Viewed by 328
Abstract
A new one-parameter distribution is proposed in this paper. The new distribution allows for the occurrence of instantaneous failures (inliers) that are natural in many areas. Closed-form expressions are obtained for the moments, mean, variance, a coefficient of variation, skewness, kurtosis, and mean [...] Read more.
A new one-parameter distribution is proposed in this paper. The new distribution allows for the occurrence of instantaneous failures (inliers) that are natural in many areas. Closed-form expressions are obtained for the moments, mean, variance, a coefficient of variation, skewness, kurtosis, and mean residual life. The relationship between the new distribution with the exponential and Lindley distributions is presented. The new distribution can be viewed as a combination of a reparametrized version of the Zakerzadeh and Dolati distribution with a particular case of the gamma model and the occurrence of zero value. The parameter estimation is discussed under the method of moments and the maximum likelihood estimation. A simulation study is performed to verify the efficiency of both estimation methods by computing the bias, mean squared errors, and coverage probabilities. The superiority of the proposed distribution and some of its concurrent distributions are tested by analyzing four real lifetime datasets. Full article
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Open AccessArticle
New Equivalence Tests for Approximate Independence in Contingency Tables
Stats 2019, 2(2), 239-246; https://doi.org/10.3390/stats2020018 - 23 Apr 2019
Viewed by 328
Abstract
We introduce new equivalence tests for approximate independence in two-way contingency tables. The critical values are calculated asymptotically. The finite sample performance of the tests is improved by means of the bootstrap. An estimator of boundary points is developed to make the bootstrap [...] Read more.
We introduce new equivalence tests for approximate independence in two-way contingency tables. The critical values are calculated asymptotically. The finite sample performance of the tests is improved by means of the bootstrap. An estimator of boundary points is developed to make the bootstrap based tests statistically efficient and computationally feasible. We compare the performance of the proposed tests for different table sizes by simulation. Then we apply the tests to real data sets. Full article
Open AccessArticle
A Bayesian Approach to Predict the Number of Goals in Hockey
Stats 2019, 2(2), 228-238; https://doi.org/10.3390/stats2020017 - 21 Apr 2019
Viewed by 466
Abstract
In this paper, we use a Bayesian methodology to analyze the outcome of a hockey game using different sources of information, such as points in previous games, home advantage, and specialists’ opinions. Two different models to predict the number of goals are considered, [...] Read more.
In this paper, we use a Bayesian methodology to analyze the outcome of a hockey game using different sources of information, such as points in previous games, home advantage, and specialists’ opinions. Two different models to predict the number of goals are considered, taking into account that it is the nature of hockey that goals are infrequent and rarely exceed six per team per game. A Bayesian predictive density to predict the number of the goals using each model will be used and the possible winner of the game will be predicted. The corresponding prediction error for each model will be addressed. Full article
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Open AccessArticle
Foreign Exchange Expectation Errors and Filtration Enlargements
Stats 2019, 2(2), 212-227; https://doi.org/10.3390/stats2020016 - 09 Apr 2019
Viewed by 436
Abstract
Extrapolations of future market forward rates are a better predictor of the 30-days ahead BRL-USD exchange rate than forecasts from the Central Bank Focus survey of Brazilian market participants. This is puzzling because market participants observe forward rates as they submit predictions, and [...] Read more.
Extrapolations of future market forward rates are a better predictor of the 30-days ahead BRL-USD exchange rate than forecasts from the Central Bank Focus survey of Brazilian market participants. This is puzzling because market participants observe forward rates as they submit predictions, and thus these agents perform biased forecasts even though they have access to a set of unbiased forecasts, consistent with a martingale process for the exchange rate. We argue that this rational conundrum can be explained by a mechanism through which new information enlarges the information set (a filtration), changing the underlying measure and inducing a drift into the martingale process, turning the process into a strict local martingale and generating a forecast bias. Empirical results suggest that Focus survey forecasts indeed display characteristics of a strict local martingale, while spot exchange rates and forward rates are consistent with a martingale process. Full article
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Open AccessArticle
Assessing the Impact of School Rules and Regulations on Students’ Perception Toward Promoting Good Behavior: Sabian Secondary School, Dire Dawa, Ethiopia
Stats 2019, 2(2), 202-211; https://doi.org/10.3390/stats2020015 - 04 Apr 2019
Viewed by 476
Abstract
Discipline is an important component of human behavior, and one could assert that without it, an organization cannot function well toward the achievement of its goals. The aim of this study was to assess the impact of school rules and regulations on students’ [...] Read more.
Discipline is an important component of human behavior, and one could assert that without it, an organization cannot function well toward the achievement of its goals. The aim of this study was to assess the impact of school rules and regulations on students’ perception toward promoting good behavior. The data were obtained from 438 respondents through a mailed questionnaire instrument. The data were tabulated, and Pearson’s chi-square test was applied for inferential analysis. Around 33.1% of the students had a negative perception of school rules and regulations about promoting good behavior, whereas 66.9% of them had a positive perception. A p-value of 0.015 (<5% significance level) indicated that there is a significant association between students’ awareness on school rules and regulations and their perception toward promoting good behavior. Students’ attitudes on school rules and regulations and perception toward promoting good behavior were statistically associated at a p-value of 0.012. Parents’ educational levels had a significant effect on students’ perception toward promoting good behavior. Generally, students’ awareness on school rules and regulations, parents’ education levels, civics and ethical education scores, and students’ attitudes toward promoting good behavior were found as significant effects on perception toward promoting good behavior. Full article
Open AccessArticle
A Parametric Bayesian Approach in Density Ratio Estimation
Stats 2019, 2(2), 189-201; https://doi.org/10.3390/stats2020014 - 30 Mar 2019
Viewed by 531
Abstract
This paper is concerned with estimating the ratio of two distributions with different parameters and common supports. We consider a Bayesian approach based on the log–Huber loss function, which is resistant to outliers and useful for finding robust M-estimators. We propose two different [...] Read more.
This paper is concerned with estimating the ratio of two distributions with different parameters and common supports. We consider a Bayesian approach based on the log–Huber loss function, which is resistant to outliers and useful for finding robust M-estimators. We propose two different types of Bayesian density ratio estimators and compare their performance in terms of frequentist risk function. Some applications, such as classification and divergence function estimation, are addressed. Full article
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Open AccessArticle
Improved Small Sample Inference Methods for a Mixed-Effects Model for Repeated Measures Approach in Incomplete Longitudinal Data Analysis
Stats 2019, 2(2), 174-188; https://doi.org/10.3390/stats2020013 - 28 Mar 2019
Viewed by 461
Abstract
The mixed-effects model for repeated measures (MMRM) approach has been widely applied for longitudinal clinical trials. Many of the standard inference methods of MMRM could possibly lead to the inflation of type I error rates for the tests of treatment effect, when the [...] Read more.
The mixed-effects model for repeated measures (MMRM) approach has been widely applied for longitudinal clinical trials. Many of the standard inference methods of MMRM could possibly lead to the inflation of type I error rates for the tests of treatment effect, when the longitudinal dataset is small and involves missing measurements. We propose two improved inference methods for the MMRM analyses, (1) the Bartlett correction with the adjustment term approximated by bootstrap, and (2) the Monte Carlo test using an estimated null distribution by bootstrap. These methods can be implemented regardless of model complexity and missing patterns via a unified computational framework. Through simulation studies, the proposed methods maintain the type I error rate properly, even for small and incomplete longitudinal clinical trial settings. Applications to a postnatal depression clinical trial are also presented. Full article
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