scholarly journals Comparing Calibration Product Type Estimators of Population Mean In Stratified Sampling under Two Constraints Using Different Distance Measures

2021 ◽  
pp. 1-16
Author(s):  
D. N. Ojua ◽  
J. A. Abuchu ◽  
E. O. Ojua ◽  
E. I. Enang
Keyword(s):  
Sample Size ◽  
Distance Measure ◽  
Real Life ◽  
Product Type ◽  
The Other ◽  
Distance Measures ◽  
Exponential Distributions ◽  
Chi Square ◽  
Life Data ◽  
Real Life Data

Calibration approach adjusts the original design weights by incorporating an auxiliary variable into it, to make the estimator be in the form of a regression estimator. This method was employed to propose calibration product type estimators using three distance measures namely; chi-square distance measure, the minimum entropy distance measure and the modified chi-square distance measure using double constraints. The estimators of variances of the proposed estimators were also obtained. An empirical study to ascertain the performance of these estimators using a secondary data set and simulated data under underlying distributional assumptions of Gamma, Normal and Exponential distributions with varying sample sizes of 10%, 15%, 20% and 25% were carried out. The result with the real life data showed that the calibration product type estimator from chi-square distance measure estimated the population mean with minimum bias than and obtained from the other distance measures. The result from real life data also revealed that the estimator obtained from chi-square distance measure under two constraints was more efficient than the other three estimators. The result from simulation studies showed that the proposed calibration product type estimators outperform the conventional product type estimator in term of efficiency, consistency and reliability under the Gamma and Exponential distributions with the exponential distribution taking the lead. The conventional product type estimator however was found to be better under normal distribution. It was also observed that as sample size increases there was no significant change in the performance of these proposed estimators which justifies the preference with small sample size.

scholarly journals Calibration Approach Product Type Estimators of Population Mean in Stratified Sampling with Single Constraint: A Comparison of Three Distance Measures

2021 ◽  
pp. 41-58
Author(s):  
Enang, Ekaette Inyang ◽  
Ojua, Doris Nkan ◽  
T. T. Ojewale
Keyword(s):  
Distance Measure ◽  
Real Life ◽  
High Gain ◽  
Product Type ◽  
Distance Measures ◽  
Minimum Entropy ◽  
Chi Square ◽  
Data Set ◽  
Population Mean ◽  
Single Constraint

This study employed the method of calibration on product type estimator to propose calibration product type estimators using three distance measures namely; chi-square distance measure, the minimum entropy distance measure and the modified chi-square distance measure for single constraint. The estimators of variances of the proposed estimators were also obtained. An empirical study to ascertain the performance of these estimators was carried out using real life and stimulated data set. The result with the real life data showed that the proposed calibration product type estimator  produced better estimates of the population mean  compared to   and . Results from the simulation study showed that the proposed calibration product type estimators had a high gain in efficiency as compared to the product type estimator. The simulation result also showed that the proposed estimators were more consistent and reliable under the Gamma and Exponential distributions with the exponential distribution taking the lead. The conventional product type estimator however was found to be better if the underlying distributional assumption is normal in nature.

scholarly journals Calibration-Based Estimators using Different Distance Measures under Two Auxiliary Variables: A Comparative Study

2021 ◽  
Vol 19 (1) ◽  
pp. 2-20
Author(s):  
Piyush Kant Rai ◽  
Alka Singh ◽  
Muhammad Qasim
Keyword(s):  
Mean Squared Error ◽  
Real Life ◽  
Distance Functions ◽  
Distance Measures ◽  
Auxiliary Variables ◽  
Data Set ◽  
Life Data ◽  
Squared Error ◽  
Real Life Data ◽  
Relative Root

This article introduces calibration estimators under different distance measures based on two auxiliary variables in stratified sampling. The theory of the calibration estimator is presented. The calibrated weights based on different distance functions are also derived. A simulation study has been carried out to judge the performance of the proposed estimators based on the minimum relative root mean squared error criterion. A real-life data set is also used to confirm the supremacy of the proposed method.

scholarly journals ENHANCING EFFICIENCY OF RATIO ESTIMATOR OF POPULATION MEDIAN BY CALIBRATION TECHNIQUES

2020 ◽  
Vol 9 (8) ◽  
pp. 14-23
Keyword(s):  
Real Life ◽  
Auxiliary Variable ◽  
Survey Sampling ◽  
Ratio Estimator ◽  
Chi Square ◽  
Life Data ◽  
Real Life Data ◽  
Efficiency Comparison ◽  
Calibration Techniques ◽  
Better Than

The use of calibration estimation techniques in survey sampling have been found to improve the precision of estimators. This paper adopts the calibration approach with the assumption that the population median of the auxiliary variable is known to obtain a more efficient ratio-type estimator in estimating population median in stratified sampling. Conditions necessary for efficiency comparison have been obtained which show that the proposed estimator will always perform better than the existing asymptotically unbiased separate estimators in stratified random sampling. Numerical evaluations have been carried out through simulation and real-life data to compliment the theoretical claims. Results from the simulation study carried out under three distributional assumptions, namely the chi square, lognormal and Cauchy distributions with different sample settings showed that the new estimator provided better estimate of the median with greater gain in efficiency. In addition, result from the real-life data further supports the superiority of the proposed estimator over the existing ones considered in this study.

scholarly journals Two stage adaptive cluster sampling based on ordered statistics

2019 ◽  
Vol 16 (1) ◽  
Author(s):  
Girish Chandra ◽  
Neeraj Tiwari ◽  
Raman Nautiyal
Keyword(s):  
Random Sampling ◽  
Real Life ◽  
Simple Random Sampling ◽  
The Other ◽  
Cluster Sampling ◽  
Adaptive Cluster Sampling ◽  
Two Stage ◽  
Life Data ◽  
Real Life Data ◽  
Ordered Statistics

The estimation problem on sparsely distributed populations using adaptive cluster sampling (ACS) is discussed. In the first phase of ACS, two stage sampling is used in which primary and secondary sampling units are selected using simple random sampling without replacement. The idea of Thompson (1996) is introduced in order to choose an appropriate fixed value of pre-specified condition, which might represent the number of rare species, before conducting the survey by the use of order statistics. Different estimators of the population mean under the two possible schemes (open and closed boundaries of primary sampling units) are studied and the Rao-Blackwell theorem for improving these estimators is also used. Numerical illustrations, one on real life data and the other based on simulation study, are discussed for these two schemes. This design may be quite useful in environmental, forestry and other areas of research dealing with rare, endangered or threatened species.

scholarly journals Distance Learning in Discriminative Vector Quantization

2009 ◽  
Vol 21 (10) ◽  
pp. 2942-2969 ◽  
Author(s):  
Petra Schneider ◽  
Michael Biehl ◽  
Barbara Hammer
Keyword(s):  
Vector Quantization ◽  
Euclidean Distance ◽  
Distance Measure ◽  
Real Life ◽  
Data Driven ◽  
Data Sets ◽  
Life Data ◽  
Real Life Data ◽  
Metric Structures ◽  
The Given

Discriminative vector quantization schemes such as learning vector quantization (LVQ) and extensions thereof offer efficient and intuitive classifiers based on the representation of classes by prototypes. The original methods, however, rely on the Euclidean distance corresponding to the assumption that the data can be represented by isotropic clusters. For this reason, extensions of the methods to more general metric structures have been proposed, such as relevance adaptation in generalized LVQ (GLVQ) and matrix learning in GLVQ. In these approaches, metric parameters are learned based on the given classification task such that a data-driven distance measure is found. In this letter, we consider full matrix adaptation in advanced LVQ schemes. In particular, we introduce matrix learning to a recent statistical formalization of LVQ, robust soft LVQ, and we compare the results on several artificial and real-life data sets to matrix learning in GLVQ, a derivation of LVQ-like learning based on a (heuristic) cost function. In all cases, matrix adaptation allows a significant improvement of the classification accuracy. Interestingly, however, the principled behavior of the models with respect to prototype locations and extracted matrix dimensions shows several characteristic differences depending on the data sets.

scholarly journals On the Mistaken Use of the Chi-Square Test in Benford’s Law

Stats ◽  
2021 ◽  
Vol 4 (2) ◽  
pp. 419-453
Author(s):  
Alex Ely Kossovsky
Keyword(s):  
Research Question ◽  
Real Life ◽  
Benford’S Law ◽  
Data Sets ◽  
Chi Square ◽  
Data Set ◽  
Life Data ◽  
Real Life Data ◽  
Benford's Law ◽  
Chi Square Test

Benford’s Law predicts that the first significant digit on the leftmost side of numbers in real-life data is distributed between all possible 1 to 9 digits approximately as in LOG(1 + 1/digit), so that low digits occur much more frequently than high digits in the first place. Typically researchers, data analysts, and statisticians, rush to apply the chi-square test in order to verify compliance or deviation from this statistical law. In almost all cases of real-life data this approach is mistaken and without mathematical-statistics basis, yet it had become a dogma or rather an impulsive ritual in the field of Benford’s Law to apply the chi-square test for whatever data set the researcher is considering, regardless of its true applicability. The mistaken use of the chi-square test has led to much confusion and many errors, and has done a lot in general to undermine trust and confidence in the whole discipline of Benford’s Law. This article is an attempt to correct course and bring rationality and order to a field which had demonstrated harmony and consistency in all of its results, manifestations, and explanations. The first research question of this article demonstrates that real-life data sets typically do not arise from random and independent selections of data points from some larger universe of parental data as the chi-square approach supposes, and this conclusion is arrived at by examining how several real-life data sets are formed and obtained. The second research question demonstrates that the chi-square approach is actually all about the reasonableness of the random selection process and the Benford status of that parental universe of data and not solely about the Benford status of the data set under consideration, since the focus of the chi-square test is exclusively on whether the entire process of data selection was probable or too rare. In addition, a comparison of the chi-square statistic with the Sum of Squared Deviations (SSD) measure of distance from Benford is explored in this article, pitting one measure against the other, and concluding with a strong preference for the SSD measure.

Neuropsychology in the Real World

2014 ◽  
Vol 25 (4) ◽  
pp. 233-238 ◽  
Author(s):  
Martin Peper ◽  
Simone N. Loeffler
Keyword(s):  
Neuropsychological Assessment ◽  
Real World ◽  
Ecological Validity ◽  
Real Life ◽  
Emotional States ◽  
Context Sensitive ◽  
Traditional Assessment ◽  
Life Data ◽  
Real Life Data ◽  
Assessment And Treatment

Current ambulatory technologies are highly relevant for neuropsychological assessment and treatment as they provide a gateway to real life data. Ambulatory assessment of cognitive complaints, skills and emotional states in natural contexts provides information that has a greater ecological validity than traditional assessment approaches. This issue presents an overview of current technological and methodological innovations, opportunities, problems and limitations of these methods designed for the context-sensitive measurement of cognitive, emotional and behavioral function. The usefulness of selected ambulatory approaches is demonstrated and their relevance for an ecologically valid neuropsychology is highlighted.

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