Consistency properties for the wavelet estimator in nonparametric regression model with dependent errors

In this paper, we establish the pth mean consistency, complete consistency, and the rate of complete consistency for the wavelet estimator in a nonparametric regression model with m-extended negatively dependent random errors. We show that the best rates can be nearly $O(n^{-1/3})$ O ( n − 1 / 3 ) under some general conditions. The results obtained in the paper markedly improve and extend some corresponding ones to a much more general setting.

ALTERNATIVE COEFFICIENT OF CONCORDANCE IN CASE OF CONNECTED RANKS

Рассматривается оценка согласованности мнений экспертов при проведении экспертного опроса. Наиболее часто в качестве такой оценки применяется коэффициент конкордации Кендалла. Однако этот коэффициент не может в полной мере применяться для установления хорошей согласованности мнений экспертов, поскольку он показывает только отклонение от случаев полной несогласованности. Для устранения данного недостатка может рассматриваться альтернативный коэффициент конкордации, оценивающий близость сумм рангов альтернатив к случаю полной согласованности. Здесь дается определение этого коэффициента при наличии связанных рангов. Сложность определения заключается в том, что в этом случае наблюдается несколько случаев полной согласованности с различными суммами рангов. Определение альтернативного коэффициента конкордации при наличии связанных рангов проводится в два этапа. Сначала вводится его определение для упорядоченных таблиц специального вида и показывается его совпадение с коэффициентом конкордации Кендалла в этом случае. После дается определение альтернативного коэффициента конкордации в общем случае и показывается более простая формула его вычисления. Далее приводятся некоторые примеры сравнений значений рассматриваемых коэффициентов конкордации, их статистических характеристик и гистограмм The article considers evaluation of expert opinion consistency when conducting an expert survey. The most commonly used score is Kendall's coefficient of concordance. However, this coefficient cannot be fully applied to establish good agreement of expert opinions, as it only shows deviations from cases of complete inconsistency. To eliminate this drawback, an alternative concordance coefficient can be considered, which estimates the proximity of the sums of the ranks of the alternatives to the case of complete consistency. The article gives the definition of this coefficient in the presence of connected ranks. The difficulty of this definition lies in the fact that in this case there are several cases of complete consistency with different sums of ranks. Definition of the alternative coefficient of concordance in the presence of tied ranks is carried out in two stages. First, its definition for ordered tables of a special kind is introduced and its coincidence with Kendall's coefficient of concordance in this case is shown. After that, the definition of the alternative coefficient of concordance in the general case is given and a simpler formula for its calculation is shown. Below are some examples of comparisons of the values of the considered concordance coefficients, their statistical characteristics, and histograms

Evaluation of Coordinate Points Consistency in Medieval Geographical Manuscripts (the case of Ibn Sa'id's Data on the Southern and Eastern Mediterranean)

The article develops a technique for analyzing mathematical data (longitude and latitude) characterizing the location of cities in medieval Arabic geographical manuscripts. The calculations made at the coordinates of 19 points given by the Arab-Spanish traveler of the 13th century Ibn Sa'id. These data are taken from his text and from the book of Abu-l-Fida referring to Ibn Sa'id. With the help of the Python - PostgreSQL technological stack for each pair of cities a set of spheroids was determined that fit for placement them in the corresponding coordinates. Then the options for intersecting the sets in all possible combinations are analyzed. The consistent exclusion of all possible combinations of cities from the entire set allows these cities to be arranged according to the degree of consistency of coordinates for any number of withdrawn points. The results tell us that most of the coordinates were not the result of astronomical observations. One of the tasks was to test a hypothesis that some of the cities the coordinates of which were determined more accurately served as “reference” points serving the basis for calculating coordinates of the rest of the cities. Complete consistency of coordinates was achieved with the exclusion of 14 cities from the set in the first version and 13 cities in the second one. However, the geography of the rest cities in Ibn Sa’id’s version does not support the “reference points” hypothesis. Abu-l-Fida’s version can boast a result that is more close to the hypothes, but to prove it one has to solve the problem of data origin used by Abu-l-Fida to correct coordinates. The technique described can be applied to any other set of coordinates of ancient geographical descriptions to evaluate the degree of their consistency and search for “reference” points.

Complete consistency for the estimator of nonparametric regression model based on m-END errors

In this paper, we study the complete consistency for the estimator of nonparametric regression model based on m-END errors and obtain the convergence rates of the complete consistency under more general conditions. Finally, some simulations are illustrated to verify the validity of our results.

The Appendix

Readers of the Treatise have long been perplexed by the appendix, in which Hume seems to recant his position on personal identity. Hume himself, while expressing some reservations about the arguments he advances in Book I of the Treatise, never rebuts or withdraws any of these arguments; he only doubts their conclusion. Second, he never replaces the account with any other. These facts at best suggest his ambivalence. Moreover, were he to recant these arguments, given the complete consistency in method in the Treatise as a whole, it is not at all clear that he would be entitled to any of the principal arguments or conclusions of the Treatise, inasmuch as all proceed from the same foundations via analogous reasoning. This chapter shows that this volume’s reading of the Treatise allows Hume a reply to his second thoughts, even if it is a reply he himself did not consider.

Complete consistency for recursive probability density estimator of widely orthant dependent samples

In this paper, we will study the recursive density estimators of the probability density function for widely orthant dependent WOD random variables. The complete consistency and complete convergence rate are established under some general conditions.