Stats

Negative spatial autocorrelation is one of the most neglected concepts in quantitative geography, regional science, and spatial statistics/econometrics in general. This paper focuses on and contributes to the literature in terms of the following three reasons why this neglect exists: Existing spatial autocorrelation quantification, the popular form of georeferenced variables studied, and the presence of both hidden negative spatial autocorrelation, and mixtures of positive and negative spatial autocorrelation in georeferenced variables. This paper also presents details and insights by furnishing concrete empirical examples of negative spatial autocorrelation. These examples include: Multi-locational chain store market areas, the shrinking city of Detroit, Dallas-Fort Worth journey-to-work flows, and county crime data. This paper concludes by enumerating a number of future research topics that would help increase the literature profile of negative spatial autocorrelation.

Lean Six Sigma DMAIC Checklist Templates are a guide to Lean Six Sigma Green Belt, Lean Six Sigma Black Belt, and Lean Six Sigma Master Black Belt Projects. Lean Six Sigma Practitioners use the DMAIC (Define, Measure, Analyze, Improve, and Control) Phases. There are Backup Slides that include the tools and templates of Optional or less often tools. There are guidelines in the notes section. These templates are used to document Lean Six Sigma Projects as they are executed. There are checklists and guides to ensure the DMAIC Phase is completed and approved before moving to the next process improvement phase. I wish you well on your projects. Steven Bonacorsi, Lean Six Sigma Master Black Belt.

The paper reports on both methodological and substantive findings. It presents a method for generating simplified representations for regional urban populations, their geographical sub-populations and communities. the method generates greatly simplified high-resolution socio-economic profiles of populated geographical areas from complex large census data sets.

Benford’s law (BL) specifies the expected digit distributions of data in social sciences, such as demographic or financial data. We focused on the first-digit distribution and hypothesized that it would apply to data on locations of animals freely moving in a natural habitat. We believe that animal movement in natural habitats may differ with respect to BL from movement in more restricted areas (e.g., game preserve). To verify the BL-hypothesis for natural habitats, during 2015–2018, we collected telemetry data of twenty individuals of wild red deer from an alpine region of Austria. For each animal, we recorded the distances between successive position records. Collecting these data for each animal in weekly logbooks resulted in 1132 samples of size 65 on average. The weekly logbook data displayed a BL-like distribution of the leading digits. However, the data did not follow BL perfectly; for 9% (99) of the 1132 weekly logbooks, the chi-square test refuted the BL-hypothesis. A Monte...

The first considers the value of the text from the perspective of service teaching: teaching business and management students about maths/stats/OR. The second considers the value of the text from the perspective of teaching maths/stats/OR students about the role and use of quantitative techniques in wider business decision making. The text is written by two US academics and is clearly aimed at the US market. The text is structured into four – fairly traditional-parts with individual chapters in each part.

The design and analysis of experiments which involve factors each consisting of both fixed and random levels fit into linear mixed models. The assumed linear mixed-model design matrix takes either a full-rank or less-than-full-rank form. The complexity of the data structures of such experiments falls in the model-selection and parameter-estimation process. The fundamental consideration in the estimation process of linear models is the special case in which elements of the error vector are assumed equal and uncorrelated. However, different assumptions on the structure of the variance–covariance matrix of error vector in the estimation of parameters of a linear mixed model may be considered. We conceptualise a repeated-measures design with multiple between-subjects factors, in which each of these factors has both fixed and random levels. We focus on the construction of linear mixed-effects models, the estimation of variance components, and hypothesis testing in which the default covar...

Activation of Stat5 is frequently found in leukemias. To study the mechanism and role of Stat5 activation, we introduced a constitutively activated Stat5a mutant, cS5F, into murine bone marrow (BM) cells. BM transplantation with cS5F-transfected cells caused development of multilineage leukemias in lethally irradiated wild-type or nonirradiated Rag2(-/-) mice. The leukemic cells showed strongly enhanced levels of cS5F tetramers but unchanged cS5F dimer levels in a DNA binding assay. Moreover, Stat5a mutants engineered to form only dimers, but not tetramers, failed to induce leukemias. In addition, Stat5 tetramers were found to accumulate in excess compared to dimers in various human leukemias. These data suggest that Stat5 tetramers are associated with leukemogenesis.

In this paper, we use a corpus of about 100,000 happy moments written by people of different genders, marital statuses, parenthood statuses, and ages to explore the following questions: Are there differences between men and women, married and unmarried individuals, parents and non-parents, and people of different age groups in terms of their causes of happiness and how they express happiness? Can gender, marital status, parenthood status and/or age be predicted from textual data expressing happiness? The first question is tackled in two steps: first, we transform the happy moments into a set of topics, lemmas, part of speech sequences, and dependency relations; then, we use each set as predictors in multi-variable binary and multinomial logistic regressions to rank these predictors in terms of their influence on each outcome variable (gender, marital status, parenthood status and age). For the prediction task, we use character, lexical, grammatical, semantic, and syntactic features ...

A proper understanding and analysis of suitable models involved in forecasting currency exchange rates dynamics is essential to provide reliable information about the economy. This paper deals with model fit and model forecasting of eight time series of historical data about currency exchange rate considering the United States dollar as reference. The time series techniques: classical autoregressive integrated moving average model, the non-parametric univariate and multivariate singular spectrum analysis (SSA), artificial neural network (ANN) algorithms, and a recent prominent hybrid method that combines SSA and ANN, are considered and their performance compared in terms of model fit and model forecasting. Moreover, specific methodological and computational adaptations were conducted to allow for these analyses and comparisons.

Interpolation is procedure that depends on spatial and/or statistical properties of analysed variable(s). It is special challenging task for data that included low number of samples, like dataset with less than 20 data. This problem is especially emphasized in the subsurface geological mapping, i.e. in the cases where data are taken solely from wells. Successful solutions of such mapping problems ask for knowledge about interpolation methods designed primarily for small datasets and dataset itself. Here are compared two methods, namely Inverse Distance Weighting and Modified Shepard’s Method, applied for three variables (porosity, permeability, thickness) measured in the Neogene sandstone hydrocarbon reservoirs (Northern Croatia). The results showed that pure cross-validation is not enough condition for appropriate map selection, but also geometrical features need to be considered, for datasets with less than 20 points.

Missing covariate values are a common problem in survival studies, and the method of choice when handling such incomplete data is often multiple imputation. However, it is not obvious how this can be used most effectively when an incomplete covariate is a function of other covariates. For example, body mass index (BMI) is the ratio of weight and height-squared. In this situation, the following question arises: Should a composite covariate such as BMI be imputed directly, or is it advantageous to impute its constituents, weight and height, first and to construct BMI afterwards? We address this question through a carefully designed simulation study that compares various approaches to multiple imputation of composite covariates in a survival context. We discuss advantages and limitations of these approaches for various types of missingness and imputation models. Our results are a first step towards providing much needed guidance to practitioners for analysing their incomplete survival ...

In this work, we introduce a new Burr XII power series class of distributions, which is obtained by compounding exponentiated Burr XII and power series distributions and has a strong physical motivation. The new distribution contains several important lifetime models. We derive explicit expressions for the ordinary and incomplete moments and generating functions. We discuss the maximum likelihood estimation of the model parameters. The maximum likelihood estimation procedure is presented. We assess the performance of the maximum likelihood estimators in terms of biases, standard deviations, and mean square of errors by means of two simulation studies. The usefulness of the new model is illustrated by means of three real data sets. The new proposed models provide consistently better fits than other competitive models for these data sets.

A description of Likert scales can be given using the multipoles technique known in quantum physics and applied to behavioral sciences data. This paper considers decomposition of Likert scales by the multipoles for the application of decreasing the respondents’ heterogeneity. Due to cultural and language differences, different respondents habitually use the lower end, the mid-scale, or the upper end of the Likert scales which can lead to distortion and inconsistency in data across respondents. A big impact of different kinds of respondent is well known, for instance, in international studies, and it is called the problem of high and low raters. Application of a multipoles technique to the row-data smoothing via prediction of individual rates by the histogram of the Likert scale tiers produces better results than standard row-centering in data. A numerical example by marketing research data shows that the results are encouraging: while a standard row-centering produces a poor outcome...

In this work, we deal with a robust fitting of a wrapped normal model to multivariate circular data. Robust estimation is supposed to mitigate the adverse effects of outliers on inference. Furthermore, the use of a proper robust method leads to the definition of effective outlier detection rules. Robust fitting is achieved by a suitable modification of a classification-expectation-maximization algorithm that has been developed to perform a maximum likelihood estimation of the parameters of a multivariate wrapped normal distribution. The modification concerns the use of complete-data estimating equations that involve a set of data dependent weights aimed to downweight the effect of possible outliers. Several robust techniques are considered to define weights. The finite sample behavior of the resulting proposed methods is investigated by some numerical studies and real data examples.

The forward search (FS) is a general method of robust data fitting that moves smoothly from very robust to maximum likelihood estimation. The regression procedures are included in the MATLAB toolbox FSDA. The work on a SAS version of the FS originates from the need for the analysis of large datasets expressed by law enforcement services operating in the European Union that use our SAS software for detecting data anomalies that may point to fraudulent customs returns. Specific to our SAS implementation, the fsdaSAS package, we describe the approximation used to provide fast analyses of large datasets using an FS which progresses through the inclusion of batches of observations, rather than progressing one observation at a time. We do, however, test for outliers one observation at a time. We demonstrate that our SAS implementation becomes appreciably faster than the MATLAB version as the sample size increases and is also able to analyse larger datasets. The series of fits provided by ...

Functional data analysis techniques, such as penalized splines, have become common tools used in a variety of applied research settings. Penalized spline estimators are frequently used in applied research to estimate unknown functions from noisy data. The success of these estimators depends on choosing a tuning parameter that provides the correct balance between fitting and smoothing the data. Several different smoothing parameter selection methods have been proposed for choosing a reasonable tuning parameter. The proposed methods generally fall into one of three categories: cross-validation methods, information theoretic methods, or maximum likelihood methods. Despite the well-known importance of selecting an ideal smoothing parameter, there is little agreement in the literature regarding which method(s) should be considered when analyzing real data. In this paper, we address this issue by exploring the practical performance of six popular tuning methods under a variety of simulate...

New results on volatility modeling and forecasting are presented based on the NoVaS transformation approach. Our main contribution is that we extend the NoVaS methodology to modeling and forecasting conditional correlation, thus allowing NoVaS to work in a multivariate setting as well. We present exact results on the use of univariate transformations and on their combination for joint modeling of the conditional correlations: we show how the NoVaS transformed series can be combined and the likelihood function of the product can be expressed explicitly, thus allowing for optimization and correlation modeling. While this keeps the original “model-free” spirit of NoVaS it also makes the new multivariate NoVaS approach for correlations “semi-parametric”, which is why we introduce an alternative using cross validation. We also present a number of auxiliary results regarding the empirical implementation of NoVaS based on different criteria for distributional matching. We illustrate our fi...

In this paper, we use a corpus of about 100,000 happy moments written by people of different genders, marital statuses, parenthood statuses, and ages to explore the following questions: Are there differences between men and women, married and unmarried individuals, parents and non-parents, and people of different age groups in terms of their causes of happiness and how they express happiness? Can gender, marital status, parenthood status and/or age be predicted from textual data expressing happiness? The first question is tackled in two steps: first, we transform the happy moments into a set of topics, lemmas, part of speech sequences, and dependency relations; then, we use each set as predictors in multi-variable binary and multinomial logistic regressions to rank these predictors in terms of their influence on each outcome variable (gender, marital status, parenthood status and age). For the prediction task, we use character, lexical, grammatical, semantic, and syntactic features ...

Both historically and in terms of practiced academic organization, the anticipation should be that a flourishing synergistic interface exists between statistics and operations research in general, and between spatial statistics/econometrics and spatial optimization in particular. Unfortunately, for the most part, this expectation is false. The purpose of this paper is to address this existential missing link by focusing on the beneficial contributions of spatial statistics to spatial optimization, via spatial autocorrelation (i.e., dis/similar attribute values tend to cluster together on a map), in order to encourage considerably more future collaboration and interaction between contributors to their two parent bodies of knowledge. The key basic statistical concept in this pursuit is the median in its bivariate form, with special reference to the global and to sets of regional spatial medians. One-dimensional examples illustrate situations that the narrative then extends to two-dime...

This paper presents new perspectives and methodological instruments for verifying the validity of Benford’s law for a large given dataset. To this aim, we first propose new general tests for checking the statistical conformity of a given dataset with a generic target distribution; we also provide the explicit representation of the asymptotic distributions of the relevant test statistics. Then, we discuss the applicability of such novel devices to the case of Benford’s law. We implement extensive Monte Carlo simulations to investigate the size and the power of the introduced tests. Finally, we discuss the challenging theme of interpreting, in a statistically reliable way, the conformity between two distributions in the presence of a large number of observations.

The distance constrained maximum likelihood procedure (DCML) optimally combines a robust estimator with the maximum likelihood estimator with the purpose of improving its small sample efficiency while preserving a good robustness level. It has been published for the linear model and is now extended to the GLM. Monte Carlo experiments are used to explore the performance of this extension in the Poisson regression case. Several published robust candidates for the DCML are compared; the modified conditional maximum likelihood estimator starting with a very robust minimum density power divergence estimator is selected as the best candidate. It is shown empirically that the DCML remarkably improves its small sample efficiency without loss of robustness. An example using real hospital length of stay data fitted by the negative binomial regression model is discussed.

In this work, we propose a new protocol that integrates robust classification and visualization techniques to analyze mixed data. This protocol is based on the combination of the Forward Search Distance-Based (FS-DB) algorithm (Grane, Salini, and Verdolini 2020) and robust clustering. The resulting groups are visualized via MDS maps and characterized through an analysis of several graphical outputs. The methodology is illustrated on a real dataset related to European COVID-19 numerical health data, as well as the policy and restriction measurements of the 2020–2021 COVID-19 pandemic across the EU Member States. The results show similarities among countries in terms of incidence and the management of the emergency across several waves of the disease. With the proposed methodology, new smart visualization tools for analyzing mixed data are provided.

A method for statistical analysis of multimodal and/or highly distorted data is presented. The new methodology combines different clustering methods with the GAMLSS (generalized additive models for location, scale, and shape) framework, and is therefore called c-GAMLSS, for “clustering GAMLSS. ” In this new extended structure, a latent variable (cluster) is created to explain the response-variable (target). Any and all parameters of the distribution for the response variable can also be modeled by functions of the new covariate added to other available resources (features). The method of selecting resources to be used is carried out in stages, a step-based method. A simulation study considering multiple scenarios is presented to compare the c-GAMLSS method with existing Gaussian mixture models. We show by means of four different data applications that in cases where other authentic explanatory variables are or are not available, the c-GAMLSS structure outperforms mixture models, som...

In this paper, we determine treatment effects when the treatment assignment is based on two or more cut-off points of covariates rather than on one cut-off point of one assignment variable. using methods that are referred to as multivariate regression discontinuity designs (MRDD). One major finding of this paper is the discovery of new evidence that both matric points and household income have a huge impact on the probability of eligibility for funding from the National Student Financial Aid Scheme (NSFAS) to study for a bachelor’s degree program at universities in South Africa. This evidence will inform policymakers and educational practitioners on the effects of matric points and household income on the eligibility for NSFAS funding. The availability of the NSFAS grant impacts greatly students’ decisions to attend university or seek other opportunities elsewhere. Using the frontier MRDD analytical results, barely scoring matric points greater than or equal to 25 points compared to...

In this article, we implement a flexible Gibbs sampler to make inferences for two-parameter Birnbaum–Saunders (BS) distribution in the presence of right-censored data. The Gibbs sampler is applied on the fiducial distributions of the BS parameters derived using the maximum likelihood, methods of moments, and their bias-reduced estimates. A Monte-Carlo study is conducted to make comparisons between these estimates for Type-II right censoring with various parameter settings, sample sizes, and censoring percentages. It is concluded that the bias-reduced estimates outperform the rest with increasing precision. Higher sample sizes improve the overall accuracy of all the estimates while the amount of censoring shows a negative effect. Further comparisons are made with existing methods using two real-world examples.

Single-index models are potentially important tools for multivariate non-parametric regression analysis. They generalize linear regression models by replacing the linear combination α0⊤X with a non-parametric component η0α0⊤X, where η0(·) is an unknown univariate link function. In this article, we generalize these models to have a functional component, replacing the generalized partially linear single index models η0α0⊤X+β0⊤Z , where α is a vector in IRd, η0(·) and β0(·) are unknown functions that are to be estimated. We propose estimates of the unknown parameter α0, the unknown functions β0(·) and η0(·) and establish their asymptotic distributions, and furthermore, a simulation study is carried out to evaluate the models and the effectiveness of the proposed estimation methodology.

The assessment of agreement in method comparison and observer variability analysis of quantitative measurements is usually done by the Bland–Altman Limits of Agreement, where the paired differences are implicitly assumed to follow a normal distribution. Whenever this assumption does not hold, the 2.5% and 97.5% percentiles are obtained by quantile estimation. In the literature, empirical quantiles have been used for this purpose. In this simulation study, we applied both sample, subsampling, and kernel quantile estimators, as well as other methods for quantile estimation to sample sizes between 30 and 150 and different distributions of the paired differences. The performance of 15 estimators in generating prediction intervals was measured by their respective coverage probability for one newly generated observation. Our results indicated that sample quantile estimators based on one or two order statistics outperformed all of the other estimators and they can be used for deriving nonp...

The asymptotic distribution is presented for the linear instrumental variables model estimated with a ridge penalty and a prior where the tuning parameter is selected with a holdout sample. The structural parameters and the tuning parameter are estimated jointly by method of moments. A chi-squared statistic permits confidence regions for the structural parameters. The form of the asymptotic distribution provides insights on the optimal way to perform the split between the training and test sample. Results for the linear regression estimated by ridge regression are presented as a special case.