On “A mutual information estimator with exponentially decaying bias” by Zhang and Zheng

2018 ◽  
Vol 17 (2) ◽  
Author(s):  
Jialin Zhang ◽  
Chen Chen
Keyword(s):  
Mutual Information ◽  
Asymptotic Normality ◽  
Ratio Test ◽  
Nonparametric Estimator ◽  
Chi Square ◽  
Testing Independence ◽  
Log Likelihood ◽  
Random Elements ◽  
Chi Square Test ◽  
Do So

Abstract Zhang, Z. and Zheng, L. (2015): “A mutual information estimator with exponentially decaying bias,” Stat. Appl. Genet. Mol. Biol., 14, 243–252, proposed a nonparametric estimator of mutual information developed in entropic perspective, and demonstrated that it has much smaller bias than the plugin estimator yet with the same asymptotic normality under certain conditions. However it is incorrectly suggested in their article that the asymptotic normality could be used for testing independence between two random elements on a joint alphabet. When two random elements are independent, the asymptotic distribution of $\sqrt{n}$-normed estimator degenerates and therefore the claimed normality does not hold. This article complements Zhang and Zheng by establishing a new chi-square test using the same entropic statistics for mutual information being zero. The three examples in Zhang and Zheng are re-worked using the new test. The results turn out to be much more sensible and further illustrate the advantage of the entropic perspective in statistical inference on alphabets. More specifically in Example 2, when a positive mutual information is known to exist, the new test detects it but the log likelihood ratio test fails to do so.

scholarly journals Confronting Theories of Firm Growth in Light of Degrees-of-Freedom Analysis

2015 ◽  
Vol 22 (74) ◽  
pp. 385-404
Author(s):  
Sérgio Fernando Loureiro Rezende ◽  
Ricardo Salera ◽  
José Márcio de Castro
Keyword(s):  
Degrees Of Freedom ◽  
Firm Growth ◽  
Dynamic Capabilities ◽  
Statistical Tests ◽  
Explanatory Power ◽  
Stage Theory ◽  
Chi Square ◽  
Growth Optimum ◽  
Chi Square Test ◽  
Do So

This article aims to confront four theories of firm growth – Optimum Firm Size, Stage Theory of Growth, The Theory of the Growth of the Firm and Dynamic Capabilities – with empirical data derived from a backward-looking longitudinal qualitative case of the growth trajectory of a Brazilian capital goods firm. To do so, we employed Degree of Freedom-Analysis for data analysis. This technique aims to test the empirical strengths of competing theories using statistical tests, in particular Chi-square test. Our results suggest that none of the four theories fully explained the growth of the firm we chose as empirical case. Nevertheless, Dynamic Capabilities was regarded as providing a more satisfactory explanatory power.

scholarly journals Clinical versus Dental Laboratory Survey Regarding Modern Fixed Implant Supported Prosthetic in Romania

2022 ◽  
Vol 12 (1) ◽  
pp. 472
Author(s):  
Luminita Oancea ◽  
Eugenia Panaitescu ◽  
Mihai Burlibasa ◽  
Catalin Gagiu
Keyword(s):  
Treatment Plan ◽  
Ratio Test ◽  
Multiple Choice Questions ◽  
Online Questionnaire ◽  
Chi Square ◽  
Exact Test ◽  
Leading Role ◽  
Chi Square Test ◽  
Training Courses ◽  
Laboratory Survey

(1) Background: The success of prosthetic treatment with implant support depends on the combined effort of the team doctor-technician, each of them being responsible for the validation of execution stages. (2) Methods: we composed an online questionnaire with 18 multiple choice questions, using the Google Forms application. It was filled out by an equal number of prosthodontic specialists and dental technicians. Differences and associations were evaluated by Likelihood Ratio test, Linear by Linear association test, Kruskal-Wallis H test, Pearson Chi-Square test and the Fisher’s Exact test. (3) Results: Differences and similarities were found between the statements of prosthodontic specialists and dental technicians. Years of experience are correlated with the number of restorations, impression techniques and types of restoration (p ≤ 0.05). Similar answers for both groups were registered for preferred screw retained type of prosthetic abutment and most frequently reported complications. (4) Conclusions: The different perspectives of the two members of the prosthodontic team regarding the leading role in the treatment plan, type of abutment, impression technique and prosthetic design of implant fixed restorations has been revealed in our study. Similar education curricula and standards for continuing training courses after graduation are necessary for prosthodontic specialists and technicians in Romania.

scholarly journals Assessment of the links between awareness about MI and behavior related to vaccination

2019 ◽  
Vol 29 (Supplement_4) ◽  
Author(s):  
V Jasiukaitienė ◽  
I Stankutė ◽  
L Miščikienė
Keyword(s):  
Categorical Variables ◽  
Educational Institutions ◽  
Morbidity Rate ◽  
Meningococcal Infection ◽  
The European Union ◽  
Chi Square ◽  
Significant Difference ◽  
Chi Square Test ◽  
And Behavior ◽  
Do So

Abstract Backgrounds In Lithuania, the morbidity rate of meningococcal infection (MI) is one of the highest in the European Union. In year 2017 - 81 MI cases were reported (2.9 cases / 100 thousand inhabitants). The aim of the study - to assess the links between awareness of parents of pre-school children about meningococcal infection and behavior related to vaccination. Methods Anonymous questionnaire survey was carried out in pre-school educational institutions of Kaunas city in 2019. 165 questionnaires were presented to parents (response rate 91.52%). Associations between categorical variables were measured using Chi square test. A statistically significant difference was defined when p < 0.05. Z criterion was used for evaluating hypothesis of variable dependence. Results 55.0% of respondents know that MI is caused by bacteria and it is spread by air (84.8%). 40.1% of parents indicated that they have vaccinated their children or are planning to do so. 38.0% of respondents chose not to have their children vaccinated and did not plan vaccination in the future. Answers of parents, who have vaccinated or are planning vaccination of their children, showed a statistically significant increase of awareness of the risk of MI spreading by air (44.4% and 0.0%, p < 0.05) and that in order to avoid the risk of MI (42.3% and 0.0%, p < 0.05) children need to be vaccinated following recommended vaccination plan (53.4% and 25.0%, p < 0.05), as well that in Lithuania MI vaccine has been included in the recommended vaccination plan in 2018 (43.7% and 12.5%, p < 0.05). Conclusions More than half of the respondents know the pathogen of the MI, the way of it spreading, but less than half of them have vaccinated or are planning to vaccinate their children. Links have been identified between the vaccination of children and awareness of the ways of MI spreading and prevention of it. Key messages The behavior of parents with better awareness is related to decision of vaccination. Parents with better awareness have vaccinated or are planning to vaccinate their children from MI.

scholarly journals Class-Based Probability Estimation Using a Semantic Hierarchy

2002 ◽  
Vol 28 (2) ◽  
pp. 187-206 ◽  
Author(s):  
Stephen Clark ◽  
David Weir
Keyword(s):  
Minimum Description Length ◽  
Estimation Method ◽  
Estimation Methods ◽  
Minimum Description Length Principle ◽  
Chi Square ◽  
Semantic Hierarchy ◽  
Log Likelihood ◽  
Data Problem ◽  
Chi Square Test ◽  
Sparse Data Problem

This article concerns the estimation of a particular kind of probability, namely, the probability of a noun sense appearing as a particular argument of a predicate. In order to overcome the accompanying sparse-data problem, the proposal here is to define the probabilities in terms of senses from a semantic hierarchy and exploit the fact that the senses can be grouped into classes consisting of semantically similar senses. There is a particular focus on the problem of how to determine a suitable class for a given sense, or, alternatively, how to determine a suitable level of generalization in the hierarchy. A procedure is developed that uses a chi-square test to determine a suitable level of generalization. In order to test the performance of the estimation method, a pseudo-disambiguation task is used, together with two alternative estimation methods. Each method uses a different generalization procedure; the first alternative uses the minimum description length principle, and the second uses Resnik's measure of selectional preference. In addition, the performance of our method is investigated using both the standard Pearson chi-square statistic and the log-likelihood chi-square statistic.

scholarly journals Effects of the intervention of the Multicenter Study IDEFICS on the prevalence of caries in Spanish children

2021 ◽  
Vol 20 ◽  
pp. e211359
Author(s):  
Vinícius Aguiar Lages ◽  
Maria Paula Rando Meirelles ◽  
Marília Jesus Batista ◽  
Carolina Matteussi Lino ◽  
Andréa Moscardini da Costa ◽  
...  
Keyword(s):  
Assessment System ◽  
Caries Detection ◽  
Chi Square ◽  
White Spots ◽  
Two Cities ◽  
Chi Square Test ◽  
Untreated Caries ◽  
Permanent Molars ◽  
Age Range ◽  
Do So

Aim: To evaluate the effects of an intervention for the prevention of obesity on the prevalence of dental caries disease in Spanish children. Methods: Two cities participated intervention study nested in a cohort IDEFICS (Identification and prevention of dietary and lifestyle induced health effects in children and infants): Huesca, where there was a 2-year intervention, which encouraged less sugar consumption; and Zaragoza (control). The prevalence of caries was evaluated by examining the 1st permanent molars in the 7-11 age range, using the ICDAS (International Caries Detection and Assessment System). These teeth erupt at 6 years of age and at the baseline (2007-2008) were free of caries because they were not present in the oral cavity. As outcomes, white spots were selected, combining the ICDAS criteria 1 and 2, and untreated caries, combining criteria 4, 5 and 6. Their association with socioeconomic variables, BMI (Body Mass Index), frequency of sugar intake, sex and parents’ perceptions of their children, was investigated. To do so, the chi-square test was applied (p<0.05). Results: The sample consisted of 281 children. The prevalence of white spots and untreated caries was higher in Huesca, despite the intervention. There was no association between the outcomes and the variables studied (p>0.05). Conclusion: The intervention for the prevention of obesity did not exert any association with the prevalence of caries in Spanish children.

scholarly journals Metode Linking Butir False Positive pada Pendeteksi DIF berdasarkan Teori Responsi Butir

2010 ◽  
Vol 14 (1) ◽  
Author(s):  
Wardani Rahayu
Keyword(s):  
Likelihood Ratio ◽  
Likelihood Ratio Test ◽  
False Positive ◽  
Ratio Test ◽  
Chi Square ◽  
Chi Square Test

Tujuan dari peneiitian ini adalah untuk mengetahui pengaruh metode linking pada sejumlah butir false positif dalam pendeteksian DIF berdasarkan teori response butir. Metode linking yang digunakan adalah metode rerata dan sigma (RS), metode tegar rerata dan sigma (TRS), metode kurva karakteristik (KK). Pendeteksian DIF dilakukan dengan menggunakan metode Lord's Chi-Square Test. Hasil pendeteksian DIF melalui metode Lord's Chi-Square ini didasarkan pada banyaknya butir false positive (FP) yang mempengaruhi keakuratan metode linking. Jumlah butir false positif dihitung dari butir yang sebelumnya diperkirakan tidak DIF berdasarkan Likelihood Ratio Test, akan tetapi setelah pendeteksian DIF menggunakan Lord's Chi-Square Test, ternyata ditemukan bahwa item mengandung DIF. Hasil peneiitian menunjukkan bahwa metode kurva karakteristik, metode rerata dan metode sigma adalah lebih akurat daripada metode tegar rerata dan metode sigma. Namun, metode kurva karakteristik memiliki akurasi yang sama dengan metode rerata dan metode sigma. Kata kunci: metode Unking, butir false positive, DIF

scholarly journals Two Studies in Automobile Insurance Ratemaking

1960 ◽  
Vol 1 (4) ◽  
pp. 192-217 ◽  
Author(s):  
Robert A. Bailey ◽  
LeRoy J. Simon
Keyword(s):  
The Other ◽  
Actual Data ◽  
Automobile Insurance ◽  
Chi Square ◽  
Canadian Experience ◽  
Multiple Classification ◽  
Chi Square Test ◽  
Best Fit ◽  
Improved Methods ◽  
Do So

Section A of this paper uses the Canadian experience for private passenger automobiles to show (1) that merit rating is almost as effective as the class plan in separating the better risks from the poorer risks, (2) that both merit rating and class rating leave unanalyzed a considerable amount of variation among risks and (3) that certain available evidence supports the conclusion that annual mileage, which has long been felt to be an important measure of hazard, is a very significant cause of this unanalyzed variation among risks.Section B presents a method for obtaining relativities among groups on which a multiple classification system has been imposed. The customary method of calculating class relativities uses the total experience for each class with all subdivisions within the classes added together. With the customary method it is difficult to make a completely accurate adjustment for different distributions by territory or merit rating, because any change in the class relativities disturbs the other sets of relativities and conversely. It is shown that even if such an adjustment were made, the customary method of calculating relativities one set at a time does not reflect the relative credibility of each subgroup and does not produce the best fit to the actual data. Moreover it produces differences between the actual data and the fitted values which are far too large to be caused by chance. In addition, for private passenger automobile insurance in Canada, it is shown that two sets of relativities which are multiplied together cannot produce the best fit to the actual data, and some of the consequences of trying to do so are explained. Some methods are advanced whereby all sets of relativities for classes, merit ratings, territories, and so forth, can be calculated simultaneously, which will overcome all the deficiencies in the customary method. These improved methods use the technique of minimizing a measure (technically known as the chi-square test) of the differences between the actual data and the fitted values. Some applications to other lines of insurance are mentioned.

scholarly journals Getting rid of the Chi-square and Log-likelihood tests for analysing vocabulary differences between corpora

2018 ◽  
Vol 22 (22) ◽  
pp. 33 ◽  
Author(s):  
Yves Bestgen
Keyword(s):  
Corpus Linguistics ◽  
Statistical Tests ◽  
Statistical Test ◽  
Corpus Analysis ◽  
Chi Square ◽  
Statistical Software ◽  
British English ◽  
Log Likelihood ◽  
Chi Square Test ◽  
Chi Square Tests

Log-likelihood and Chi-square tests are probably the most popular statistical tests used in corpus linguistics, especially when the research is aiming to describe the lexical variations between corpora. However, because this specific use of the Chi-square test is not valid, it produces far too many significant results. This paper explains the source of the problem (i.e., the non-independence of the observations), the reasons for which the usual solutions are not acceptable and which kinds of statistical test should be used instead. A corpus analysis conducted on the lexical differences between American and British English is then reported, in order to demonstrate the problem and to confirm the adequacy of the proposed solution. The last section presents the commands that can be used with WordSmith Tools, a very popular software for corpus processing, to obtain the necessary data for the adequate tests, as well as a very easy-to-use procedure in R, a free and easy to install statistical software, that performs these tests.

A mutual information estimator with exponentially decaying bias

2015 ◽  
Vol 14 (3) ◽  
Author(s):  
Zhiyi Zhang ◽  
Lukun Zheng
Keyword(s):  
Maximum Likelihood ◽  
Mutual Information ◽  
Asymptotic Normality ◽  
Sample Size ◽  
Maximum Likelihood Estimator ◽  
Simulation Study ◽  
Type I Error ◽  
Type I ◽  
Nonparametric Estimator ◽  
Likelihood Estimator

AbstractA nonparametric estimator of mutual information is proposed and is shown to have asymptotic normality and efficiency, and a bias decaying exponentially in sample size. The asymptotic normality and the rapidly decaying bias together offer a viable inferential tool for assessing mutual information between two random elements on finite alphabets where the maximum likelihood estimator of mutual information greatly inflates the probability of type I error. The proposed estimator is illustrated by three examples in which the association between a pair of genes is assessed based on their expression levels. Several results of simulation study are also provided.

Testing Independence in 2 × 2 Contingency Tables

1989 ◽  
Vol 14 (1) ◽  
pp. 47-79 ◽  
Author(s):  
Neal E. A. Kroll
Keyword(s):  
Statistical Tests ◽  
Comparative Trial ◽  
Chi Square ◽  
Potential Models ◽  
Exact Test ◽  
Multinomial Models ◽  
Testing Independence ◽  
Chi Square Test ◽  
Conservative Approximation ◽  
Critical Regions

Three of the potential models for the 2 × 2 contingency table are discussed: the hyper geometric Independence Trial, the double-binomial Comparative Trial, and the multinomial Double Dichotomy Trial. Then the critical regions of seven statistical tests are evaluated within each of these models. The uncorrected Pearson’s Chi-Square test and Upton’s correction are found to be overly liberal in all three models, particularly for the hypergeometric. A continuity correction, when properly applied, is shown to be an extremely good approximation to Fisher’s Exact test, which employs the hypergeometric distribution to evaluate outcome probabilities—but is an extremely conservative approximation to the double binomial and multinomial models. Haber’s test is recommended for these two cases, but the amount of work required may be prohibitive for many investigators.

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