Seminar Katedre za verovatnoću i statistiku, 23. maj 2023.

Naredni sastanak Seminara biće održan onlajn u utorak, 23. maja 2023. sa početkom u 16.15.

Predavač: dr Abid Hussain, Department of Statistics Govt. Mian Shahbaz Sharif College, Rawalpindi, Pakistan
Many of the more useful and powerful non-parametric procedures may be presented unified bytreating them as rank transformation procedures. But on the other hand, if we have only ranks for analysis, we do not know the magnitudes of the difference between measurements that were ranked because the ranks procedures are treated all the differences between values equally. For example, three students taking an examination may be ranked first, second, and third on the basis of the order in which they complete the examination. This does not mean, however, that the time elapsing between completion by number 1 and by number 2 is the same as that between number 2 and number 3. For example, the student finishing first may finish five minutes before the second student, who, in turn, may finish eight minutes before the third. In this example, if we use only ranks for further investigation, we will lose the actual time difference information between finishing the test among competitors.
We need an alternative rank transformation that works as an ordinary ranking scheme as well as behaves relatively with its original data format. We put our effort to resolve this issue by proposing a new relative rank-based scheme. The ordinary ranks are functionalized by incorporating data range and quantile coverage simultaneously in the proposed formula. This dual use of additional information is found to enhance the sensitivity of the devised scheme toward offering more competent weights of competing observations. Some key mathematical properties of the proposed functionalization are highlighted. The performance is also investigated under a set of diverse parametric settings involving different stochastic formulations, sample sizes, degrees of correlation, etc. In the second part of this seminar, I will present a rank correlation coefficient based on the differences of the ranks only (not the squared difference of ranks). This method was discussed in the seminal work of Spearman (1904). He mentioned this method on pager number 86 with some merits and drawbacks. Best of my knowledge, this approach has never been used in the literature, because of maybe unavailability of sampling properties and critical values. After almost 120 years, I have solved the sampling properties and determined the critical values for this method. Based on the results, we can use this approach parallel with the Spearman’s correlation coefficient (ρ) and Kendall’s correlation coefficient (τ).

Spearman, C. (1904). The proof and measurement of association between two things. The American Journal of Psychology, 15:72–101.

Link za pristup predavanju:
Meeting ID: 948 5940 4654
Passcode: 231282

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