Pub Date : 2024-03-28DOI: 10.3329/ijss.v24i1.72023
T. J. Rao
Prof. CR Rao has been awarded the prestigious 2023 International Prize in Statistics. The citation reads: “In his remarkable 1945 paper published in the Bulletin of the Calcutta Mathematical Society, Calyampudi Radhakrishna (C.R.) Rao demonstrated three fundamental results that paved the way for the modern field of Statistics and provided statistical tools heavily used in science today……”. These three results are ‘Cramer-Rao Lower Bound’ (CRLB), ‘Rao- Blackwellization’ (RB) and the third one now flourished as ‘Information Geometry’. In this paper, we shall discuss two offshoots from his work over the eight decades. Several articles have appeared on his life and work (see for example, T. J. Rao (2019 and 2023a, 2023b) and Kumar (2023)). The first offshoot is based on one of the three breakthrough results, namely, Rao–Blackwell Theorem, first proved by C.R. Rao in 1945, when he was just 25 years old and also by Blackwell later in 1947. The second one is on Association Rule Mining (ARM), which he developed when he was 96 years old. These two papers reveal the transition of statistical methodologies from Fisherian concepts to recent applications of AI and ML. In this paper we shall pose some questions which need further study. International Journal of Statistical Sciences, Vol.24(1), March, 2024, pp 85-89
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Pub Date : 2024-03-28DOI: 10.3329/ijss.v24i1.72025
E. P. Clement, E. I. Enang
This study introduces the concept of inverse exponentiation in formulating calibration weights in stratified double sampling and proposes a more improved calibration estimator based on Koyuncu and Kadilar (2014) calibration estimator. The variance of the proposed logarithmic calibration estimator has been derived under large sample approximation. Calibration asymptotic optimum estimator and its approximate variance estimator are derived for the proposed logarithmic calibration estimator. Results of empirical study showed that the proposed logarithmic calibration estimator performs better than the Koyuncu and Kadilar (2014) calibration estimator with appreciable gains in efficiency. Also, simulation study for the comparison of the proposed logarithmic estimator with a Global estimator [Generalized Regression (GREG) estimator ] proved the robustness of the proposed logarithmic calibration estimator and by extension the efficacy of inverse exponentiation in calibration weightings. Analysis and evaluation are presented. International Journal of Statistical Sciences, Vol.24(1), March, 2024, pp 91-102
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