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Stats, Volume 2, Issue 3 (September 2019) – 4 articles

Cover Story (view full-size image): Linear correlation is a common traditional statistic quantitative analysts study. Its classical version quantifies two attributes’ value pairing trends for a set of observations, whose nature can be negative, none, or positive. Researchers rarely focus on the few advantageous qualities negative correlation displays. Extending this statistic to geographic data quantifies the relationship between neighboring value pairs of a single attribute (i.e., spatial autocorrelation). Researchers rarely treat negative spatial autocorrelation, sometimes arguing that it seldom characterizes georeferenced data, making it one of the most neglected spatial statistics/econometrics concepts. This paper redresses this situation, furnishing concrete examples of it, and demonstrating its frequent coexistence as a mixture with positive spatial autocorrelation. View this paper.
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28 pages, 5284 KiB  
Article
Negative Spatial Autocorrelation: One of the Most Neglected Concepts in Spatial Statistics
by Daniel A. Griffith
Stats 2019, 2(3), 388-415; https://doi.org/10.3390/stats2030027 - 15 Aug 2019
Cited by 21 | Viewed by 7849
Abstract
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 [...] Read more.
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. Full article
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17 pages, 1920 KiB  
Article
On Generalized Slash Distributions: Representation by Hypergeometric Functions
by Peter Zörnig
Stats 2019, 2(3), 371-387; https://doi.org/10.3390/stats2030026 - 19 Jul 2019
Cited by 4 | Viewed by 2688
Abstract
The popular concept of slash distribution is generalized by considering the quotient Z = X/Y of independent random variables X and Y, where X is any continuous random variable and Y has a general beta distribution. The density of Z can usually be [...] Read more.
The popular concept of slash distribution is generalized by considering the quotient Z = X/Y of independent random variables X and Y, where X is any continuous random variable and Y has a general beta distribution. The density of Z can usually be expressed by means of generalized hypergeometric functions. We study the distribution of Z for various parent distributions of X and indicate a possible application in finance. Full article
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24 pages, 11414 KiB  
Article
Computing Happiness from Textual Data
by Emad Mohamed and Sayed A. Mostafa
Stats 2019, 2(3), 347-370; https://doi.org/10.3390/stats2030025 - 03 Jul 2019
Cited by 2 | Viewed by 3792
Abstract
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, [...] Read more.
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 in a machine learning document classification approach. The classification algorithms used include logistic regression, gradient boosting, and fastText. Our results show that textual data expressing moments of happiness can be quite beneficial in understanding the “causes of happiness” for different social groups, and that social characteristics like gender, marital status, parenthood status, and, to some extent age, can be successfully predicted form such textual data. This research aims to bring together elements from philosophy and psychology to be examined by computational corpus linguistics methods in a way that promotes the use of Natural Language Processing for the Humanities. Full article
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15 pages, 401 KiB  
Article
Confidence Sets for Statistical Classification
by Wei Liu, Frank Bretz, Natchalee Srimaneekarn, Jianan Peng and Anthony J. Hayter
Stats 2019, 2(3), 332-346; https://doi.org/10.3390/stats2030024 - 30 Jun 2019
Cited by 2 | Viewed by 2821
Abstract
Classification has applications in a wide range of fields including medicine, engineering, computer science and social sciences among others. In statistical terms, classification is inference about the unknown parameters, i.e., the true classes of future objects. Hence, various standard statistical approaches can be [...] Read more.
Classification has applications in a wide range of fields including medicine, engineering, computer science and social sciences among others. In statistical terms, classification is inference about the unknown parameters, i.e., the true classes of future objects. Hence, various standard statistical approaches can be used, such as point estimators, confidence sets and decision theoretic approaches. For example, a classifier that classifies a future object as belonging to only one of several known classes is a point estimator. The purpose of this paper is to propose a confidence-set-based classifier that classifies a future object into a single class only when there is enough evidence to warrant this, and into several classes otherwise. By allowing classification of an object into possibly more than one class, this classifier guarantees a pre-specified proportion of correct classification among all future objects. An example is provided to illustrate the method, and a simulation study is included to highlight the desirable feature of the method. Full article
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