Abstract: Measuring bias is important as it helps identify flaws in quantitative forecasting methods or judgmental forecasts. It can, therefore, potentially help improve forecasts. Despite this, bias tends to be under-represented in the literature: many studies focus solely on measuring accuracy. Methods for assessing bias in single series are relatively well-known and well-researched, but for datasets containing thousands of observations for multiple series, the methodology for measuring and reporting bias is less obvious. We compare alternative approaches against a number of criteria when rolling-origin point forecasts are available for different forecasting methods and for multiple horizons over multiple series. We focus on relatively simple, yet interpretable and easy-to-implement metrics and visualization tools that are likely to be applicable in practice. To study the statistical properties of alternative measures we use theoretical concepts and simulation experiments based on artificial data with predetermined features. We describe the difference between mean and median bias, describe the connection between metrics for accuracy and bias, provide suitable bias measures depending on the loss function used to optimise forecasts, and suggest which measures for accuracy should be used to accompany bias indicators. We propose several new measures and provide our recommendations on how to evaluate forecast bias across multiple series. PubDate: Tue, 07 Sep 2021 01:23:28 +000

Abstract: Reviewer Acknowledgements for International Journal of Statistics and Probability, Vol. 10, No. 5, 2021 PubDate: Tue, 31 Aug 2021 01:17:30 +000

Abstract: Case-crossover designs have become widespread in biomedical investigations of transient associations. However, the most popular reference-selection strategy - the time-stratified scheme - may not be an optimum solution to control systematic bias in case-crossover studies. To prove this, we conducted a time series decomposition for daily ozone records and examined the capability of the time-stratified scheme to control for yearly, monthly, and weekly time trends; and observed its failure on the control for the weekly time trend. To solve this issue, we proposed a new logistic regression approach in which we suggest the adjustment for the weekly time trend. We compared the performance of the proposed with that of the traditional method by simulation. We further conducted an empirical study to explore the performance of the new logistic regression approach in examining potential associations between ambient air pollutants and acute myocardial infarction hospitalizations. The time-stratified scheme provides effective control for yearly and monthly time trends but not of the weekly time trend. Uncontrolled weekly time trends could be the dominant source of systematic bias in time-stratified case-crossover studies. In contrast, the proposed logistic regression approach can effectively minimize systematic bias in a case-crossover study. PubDate: Mon, 30 Aug 2021 08:48:20 +000

Abstract: Modeling dependence between random variables is accomplished effectively by using copula functions. Practitioners often rely on the single parameter Archimedean family which contains a large number of functions, exhibiting a variety of dependence structures. In this work we propose the use of the multiple-parameter compound Archimedean family, which extends the original family and allows more elaborate dependence structures. In particular, we use a copula of this type to model the dependence structure between the minimum daily electricity demand and the maximum daily temperature. It is shown that the compound Archimedean copula enhances the flexibility of the dependence structure and provides a better fit to the data. PubDate: Mon, 30 Aug 2021 08:00:44 +000

Abstract: In this paper, we proposed a bootstrap approach to construct the confidence interval of quantiles for current status data, which is computationally simple and efficient without estimating nuisance parameters. The reasonability of the proposed method is verified by the well performance presented in the extensive simulation study. We also analyzed a real data set as illustration. PubDate: Mon, 23 Aug 2021 09:40:26 +000

Abstract: Tungiasis is a neglected parasitic disease that significantly affects communities, especially in developing countries. This study developed a Bayesian severity of the jigger infestation model and its spatial counterpart. Putative determinants leading to different levels of infestation and the most affected areas were to be identified through the model. We collected data through a cross-sectional study with a multi-stage sampling design. A structured questionnaire was administered in each household to capture variables used for modelling jigger infestations. The severity of jigger infestation categorized for each individual was modelled against all the other predictor variables. It was also integrated with spatial data to determine the spatial distribution pattern of jigger infestation. A Bayesian multinomial logistic regression model was used to assess the association between various predictors and different infestation levels. Specifically, an ordered Bayesian Severity Hierarchical (OBSH) categorical model was obtained. This model was categorical based on the Counties (1-Nyeri, 2-Murang'a and 3-Kiambu). Results from this model showed that for a one-unit decrease in the poverty index at level 1 (individuals categorized as poor) there was about a 69% increase in the severity of jigger infestation. A one-unit increase in the percentage of clay in the soil increased the odds ratio of the severity of jigger infestation by a factor of 11.21 while a high percentage of nitrogen in the soil lowered the severity of infestation. Severity of jigger infestation reduced from the baseline, Nyeri County to Kiambu County. It also increased with increasing altitude due to a decrease in nitrogen levels. PubDate: Sat, 21 Aug 2021 05:25:23 +000

Abstract: Maximum likelihood and proportion estimators of the parameters of the discrete Weibull type II distribution with type I censored data are discussed. A simulation study is performed to generate data from this distribution for suggested values of its parameters and to get the Maximum likelihood estimates of the parameters numerically. The method of proportions suggested by Khan et al. (1989) is also used to estimate the model's parameters. Numerical examples are used to perform a comparison study between the two method results according the values of the estimates and their corresponding mean squared errors. PubDate: Sat, 21 Aug 2021 04:56:59 +000

Abstract: The purpose of this article is to improve Hoeffding's lemma and consequently Hoeffding's tail bounds. The improvement pertains to left skewed zero mean random variables X\in[a,b], where ab. The proof of Hoeffding's improved lemma uses Taylor's expansion, the convexity of \exp(sx), s\in \RR, and an unnoticed observation since Hoeffding's publication in 1963 that for -a>b the maximum of the intermediate function \tau(1-\tau) appearing in Hoeffding's proof is attained at an endpoint rather than at \tau=0.5 as in the case b>-a. Using Hoeffding's improved lemma we obtain one sided and two sided tail bounds for \PP(S_n\ge t) and \PP( S_n \ge t), respectively, where S_n=\sum_{i=1}^nX_i and the X_i\in[a_i,b_i],i=1,...,n are independent zero mean random variables (not necessarily identically distributed). It is interesting to note that we could also improve Hoeffding's two sided bound for all \{X_i: -a_i\ne b_i,i=1,...,n\}. This is so because here the one sided bound should be increased by \PP(-S_n\ge t), wherein the left skewed intervals become right skewed and vice versa. PubDate: Sat, 21 Aug 2021 04:56:59 +000

Abstract: We propose a new iterative algorithm for finding a minimum point of f_*:X \subset \mathbb{R}^d \rightarrow \mathbb{R}, when f_* is known to be convex, but only noisy observations of f_*(\textbf{x}) are available at \textbf{x} \in X for a finite set X. At each iteration of the proposed algorithm, we estimate the probability of each point \textbf{x} \in X being a minimum point of f_* using the fact that f_* is convex, and sample r points from X according to these probabilities. We then make observations at the sampled points and use these observations to update the probability of each point \textbf{x} \in X being a minimum point of f_*. Therefore, the proposed algorithm not only estimates the minimum point of f_* but also provides the probability of each point in X being a minimum point of f_*. Numerical results indicate the proposed algorithm converges to a minimum point of f_* as the number of iterations increases and shows fast convergence, especially in the early stage of the iterations. PubDate: Sat, 21 Aug 2021 04:56:59 +000