International Journal of Statistical Sciences

Optimum Designs for Optimum Mixtures: An Informative Review

Manisha Pal — Thu, 28 Mar 2024 00:00:00 +0000

In a mixture experiment, the measured response is assumed to depend only on the relative proportions of ingredients or components present in the mixture. Scheffe´ (1958) first systematically considered this problem, and introduced different models and suitable designs. Optimum designs for the estimation of parameters in various mixture models are available in the literature. However, in a mixture experiment, interest is likely to be more on the optimum mixing proportions of the ingredients being used. In this exposition, we take the readers on a journey through the optimum designs developed for estimating the optimum mixture combination as accurately as possible under various mixture models.

International Journal of Statistical Sciences, Vol.24(1), March, 2024, pp 1-14

New Series of D-efficient Covariate Designs under BIBD set-up

Anurup Majumder, Hiranmoy Das, Ankita Dutta, Dikeshwar Nishad — Thu, 28 Mar 2024 00:00:00 +0000

In the present study, an effort has been made to construct D-efficient covariate designs in BIB design (v, b, r, k and λ) set-up when either one of k and r is odd or both k and r are odd numbers and Hadamard matrix of order k i.e., H_k does not exist. For all the developed D-efficient designs, the covariates are mutually orthogonal to each other. The methods of construction of D-efficient covariate designs are developed with the help of a new matrix viz., Special Array (Das et. al., 2020). In this article, the series of developed D-efficient covariate designs are not available in the existing literature.

International Journal of Statistical Sciences, Vol.24(1), March, 2024, pp 15-30

Model Robust Optimal Designs for Kronecker Model for Mixture Experiments

Mahesh Kumar Panda — Thu, 28 Mar 2024 00:00:00 +0000

In comparison to Scheffè’s canonical polynomial models (S-models), the Kronecker models (K-models) for mixture experiments are symmetric, compact in notation, and based on the Kronecker algebra of vectors and matrices. Further, there is a corresponding transition from S-models to K-models in the form of model re-parameterization. In the literature, it has been recommended to use second-degree K-models in practice compared to the widely used second-degree S-models especially when the moment matrix is of an ill-conditioning type. The motivation of the present article is to discriminate between K-models and S-models in terms of the model-robust D- and A-optimality criteria. These optimality criteria are discussed when there is uncertainty in selecting an appropriate model out of two rival models for a mixture experiment.

International Journal of Statistical Sciences, Vol.24(1), March, 2024, pp 31-48

Crafting Disaster-Driven Statistics: A Strategic Sampling Model

Syed Shahadat Hossain, Md Rafiqul Islam — Thu, 28 Mar 2024 00:00:00 +0000

This article details the development and implementation of a strategic sampling methodology aimed at enhancing disaster-related statistics in Bangladesh. The study focuses on creating a specialized sampling frame by conducting a comprehensive census of enumeration areas (mouzas) affected by natural disasters. Employing a two-stage random sampling technique, the methodology incorporates stratification at district and disaster-type levels to capture diverse disaster occurrences. The Kish allocation method is utilized for sample allocation, addressing disparities in district sizes. Through meticulous trial and error simulations, the study ensures minimum sample sizes within each domain while employing inverse probability weights to estimate parameters. This strategic approach adopts robust estimations, enriching insights into disaster-related statistics.

International Journal of Statistical Sciences, Vol.24(1), March, 2024, pp 49-64

Study of Covariates’ Effects in the Presence of Neighbor Effects : An Informative Review

Sobita Sapam, Bikas K Sinha, KK Singh Meitei — Thu, 28 Mar 2024 00:00:00 +0000

With reference to a Gauss-Markov Model, Analysis of Covariance (ANCOVA) is a standard exercise in the study of differential treatment effects in the presence of covariates. Again in the presence of ‘Neighbor Effects’, we carry out necessary data analysis in a routine manner. In this paper we present a review of this area of research, encompassing both covariates’ effects and neighbor effects.

International Journal of Statistical Sciences, Vol.24(1), March, 2024, pp 65-73

Estimating Gain in Efficiency in Complicated Randomized Response Surveys versus Simpler Alternatives

Arijit Chaudhuri, Dipika Patra — Thu, 28 Mar 2024 00:00:00 +0000

Hartley and Ross’s (1954) ratio-type unbiased estimator for a finite population total based on a Simple Random Sample taken Without Replacement (SRSWOR) is examined for its performance versus the expansion estimator from the sample data at hand by Chaudhuri and Samaddar (2022). They also examined how Des Raj (1956) estimator based on PPSWOR performs against SRSWOR combined with expansion estimator using PPSWOR sample values. Here we study the expansion of them to Randomized Response survey data.

International Journal of Statistical Sciences, Vol.24(1), March, 2024, pp 75-84

Some Questions Related to Rao-Blackwellization and Association Rule Mining

T J Rao — Thu, 28 Mar 2024 00:00:00 +0000

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

On the Use of Inverse Exponentiation to Improve the Efficiency of Calibration Estimators in Stratified Double Sampling

Etebong P Clement, Ekaette I Enang — Thu, 28 Mar 2024 00:00:00 +0000

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

Ratio Type Estimator for Balanced Sampling Plan excluding Adjacent Units

Neeraj Tiwari, Jharna Banerjie, Girish Chandra, Shailja Bhari — Thu, 28 Mar 2024 00:00:00 +0000

The study variables are usually correlated with the auxiliary variables and therefore their correlation could easily be computed. In this paper, the correlation coefficient is used for the estimation procedure, and therefore, we proposed a Horvitz-Thompson ratio-type estimator using correlation coefficient for Balanced Sampling plan excluding Adjacent units (BSA plan). It has been illustrated theoretically and empirically that the proposed Horvitz-Thompson ratio-type estimator is more precise than the Horvitz-Thompson estimator based on BSA plan. The proposed estimator provides an opportunity to utilise the auxiliary information for the estimation of population mean for BSA plan and useful for many real-life experiments.

International Journal of Statistical Sciences, Vol.24(1), March, 2024, pp 103-114

On the Sample Size Determination based on the Randomized Response Surveys

Kajal Dihidar — Thu, 28 Mar 2024 00:00:00 +0000

In general, the well known Chebyshev’s inequality is used to determine the sample size in order to conduct a survey using direct responses. The same technique intending to cover for sensitive variables are attempted recently by many statisticians. However it has been observed that in many cases the acceptable sample sizes are hard to be obtained, mainly because of appearance of some easily non-controllable part. Chaudhuri and Sen (2020), Chaudhuri and Patra (2023) and others have illustrated different situations and solutions are proposed therein. In this paper, following Chaudhuri, Bose and Dihidar (2011), we have made an attempt to deterimine the sample size corresponding to the estimators of sensitive population proportion using multiple randomized responses from distinct persons sampled. Along with the theoretical derivations, some numerical illustrations are presented. Based on the important extractions of our numerical illustration results, the recommendable sample size in practical real survey situations are observed.

International Journal of Statistical Sciences, Vol. 24(1) March, 2024, pp 115-132

Understanding Chao (Biometrika, 1982) [Paper on ΠPS Sampling Schemes]

Y Menon Singh, G Sandweep Sharma, Opendra Salam, B K Sinha — Thu, 28 Mar 2024 00:00:00 +0000

Chao's (1982) sampling scheme offers a systematic approach to select samples based on probability proportional to size (PPS) sampling without replacement but it might be difficult to grasp, particularly for entry-level researchers. In response, this study revisits Chao's method with the aim of providing a simplified and more intuitive understanding. Drawing inspiration from efforts by Dr. Tommy Wright and subsequent group discussions with BKS, we present a step-by-step breakdown of Chao's scheme with illustrative examples, emphasizing its elegance and practicality. This study showcases the value of making complex statistical methods accessible for broader engagement in research and practice.

International Journal of Statistical Sciences, Vol.24(1), March, 2024, pp 133-154

Indirect Questioning Technique Related to Sensitive Quantitative Variables with Options for Direct, Randomized and Item Count Responses

Purnima Shaw, Sanghamitra Pal — Thu, 28 Mar 2024 00:00:00 +0000

Randomized Response (RR) Technique (RRT) pioneered by Warner (1965) is a useful tool to elicit responses on sensitive characteristics, such as induced abortions, drug abuse, drunken driving, total amount of counterfeit notes of a particular denomination held by individuals in the population, etc. There exists a huge literature on Randomized Response (RR) devices for estimation of finite population mean of quantitative variables, sensitive in nature mostly based on Eichhorn and Hayre (1983). Device-I and Device-II vide Chaudhuri and Christofides (2013) allow estimation of population mean of sensitive quantitative variables using sample chosen by a general sampling design. On the other hand, Item Count Technique (ICT), described elaborately in Chaudhuri and Christofides (2013), is an alternative to RRT for respondents who do not choose to provide RRs. While some respondents may find a variable as sensitive, others may find it innocuous enough to provide a direct response (DR) about his/her true value. In such a case, Optional Randomized Response (ORR) Technique (ORRT) with options for DR and RR was introduced by Chaudhuri and Mukherjee (1985). Pal (2007) proposed an ORR device which offers choices for RR and ICT to the respondents for giving their answers. A new ORRT with options for DR, RR and ICT was provided by Shaw and Pal (2021) for eliciting indirect responses on sensitive characteristics. As this device relates to estimation of population proportion of sensitive characteristics, an attempt has been made to extend it for sensitive quantitative variables. Further, to take care of individuals’ varying choices for DR, RR and ICT and to protect the privacy of the respondents’ choices, this paper develops an ORR device allowing the respondents chosen by a general sampling design, to choose any one of the three options according to their choices.

International Journal of Statistical Sciences, Vol.24(1), March, 2024, pp 155-170