A Unified Approach for Analysis of Randomized Response Surveys

2010 ◽  
Vol 143-144 ◽  
pp. 1259-1263
Author(s):  
Zhi Min Hong ◽  
Zai Zai Yan
Keyword(s):  
Privacy Protection ◽  
Simple Random Sampling ◽  
Auxiliary Variable ◽  
Unified Approach ◽  
Variance Bound ◽  
Randomization Scheme ◽  
Class Of Estimators ◽  
The Mean ◽  
Best Estimator ◽  
Sensitive Variable

In this paper, we propose a class of estimators for the population mean of a sensitive variable, taking account into a generic randomization scheme, under the simple random sampling with replacement (SRSWR), when the mean of a supplementary non-sensitive variable is known. The minimum attainable variance bound of the class is obtained and the best estimator is also defined. We prove that the best estimator acts as a regression estimator which is at least as efficient as the corresponding estimator without the auxiliary variable. A new measure of privacy protection is built, and some models can be compared from the perspective of efficiency and privacy protection.

A Class of Estimators of the Population Mean Using Multi­Auxiliary Information

1983 ◽  
Vol 32 (1-2) ◽  
pp. 47-56 ◽  
Author(s):  
S. K. Srivastava ◽  
H. S. Jhajj
Keyword(s):  
Mean Squared Error ◽  
Broad Class ◽  
Auxiliary Variable ◽  
Population Parameters ◽  
Auxiliary Variables ◽  
Sample Mean ◽  
Squared Error ◽  
Class Of Estimators ◽  
The Mean ◽  
Asymptotic Mean Squared Error

For estimating the mean of a finite population, Srivastava and Jhajj (1981) defined a broad class of estimators which we information of the sample mean as well as the sample variance of an auxiliary variable. In this paper we extend this class of estimators to the case when such information on p(> 1) auxiliary variables is available. The estimators of the class involve unknown constants whose optimum values depend on unknown population parameters. When these population parameters are replaced by their consistent estimates, the resulting estimators are shown to have the same asymptotic mean squared error. An expression by which the mean squared error of such estimators is smaller than those which use only the population means of the auxiliary variables, is obtained.

scholarly journals Restructured class of estimators for population mean using an auxiliary variable under simple random sampling scheme

2020 ◽  
Vol 16 (1) ◽  
pp. 61-75
Author(s):  
S. Baghel ◽  
S. K. Yadav
Keyword(s):  
Random Sampling ◽  
Simple Random Sampling ◽  
Auxiliary Variable ◽  
Sampling Scheme ◽  
Order Of Approximation ◽  
Study Variable ◽  
Population Mean ◽  
First Order ◽  
New Class ◽  
Class Of Estimators

AbstractThe present paper provides a remedy for improved estimation of population mean of a study variable, using the information related to an auxiliary variable in the situations under Simple Random Sampling Scheme. We suggest a new class of estimators of population mean and the Bias and MSE of the class are derived upto the first order of approximation. The least value of the MSE for the suggested class of estimators is also obtained for the optimum value of the characterizing scaler. The MSE has also been compared with the considered existing competing estimators both theoretically and empirically. The theoretical conditions for the increased efficiency of the proposed class, compared to the competing estimators, is verified using a natural population.

scholarly journals Regression Estimator Using Double Ranked Set Sampling

2002 ◽  
Vol 7 (2) ◽  
pp. 311
Author(s):  
Hani M. Samawi ◽  
Eman M. Tawalbeh
Keyword(s):  
Correlation Coefficient ◽  
Real Data ◽  
Simple Random Sampling ◽  
Auxiliary Variable ◽  
Ranked Set Sampling ◽  
Regression Estimator ◽  
Primary Analysis ◽  
Data Set ◽  
Population Mean ◽  
The Mean

The performance of a regression estimator based on the double ranked set sample (DRSS) scheme, introduced by Al-Saleh and Al-Kadiri (2000), is investigated when the mean of the auxiliary variable X is unknown. Our primary analysis and simulation indicates that using the DRSS regression estimator for estimating the population mean substantially increases relative efficiency compared to using regression estimator based on simple random sampling (SRS) or ranked set sampling (RSS) (Yu and Lam, 1997) regression estimator.  Moreover, the regression estimator using DRSS is also more efficient than the naïve estimators of the population mean using SRS, RSS (when the correlation coefficient is at least 0.4) and DRSS for high correlation coefficient (at least 0.91.) The theory is illustrated using a real data set of trees.  

scholarly journals Restructured class of estimators for population mean using an auxiliary variable under simple random sampling scheme

2021 ◽  
Vol 17 (2) ◽  
pp. 75-90
Author(s):  
B. Prashanth ◽  
K. Nagendra Naik ◽  
R. Salestina M
Keyword(s):  
Characteristic Polynomial ◽  
Random Sampling ◽  
Simple Random Sampling ◽  
Auxiliary Variable ◽  
Sampling Scheme ◽  
Signed Graph ◽  
Population Mean ◽  
Class Of Estimators

Abstract With this article in mind, we have found some results using eigenvalues of graph with sign. It is intriguing to note that these results help us to find the determinant of Normalized Laplacian matrix of signed graph and their coe cients of characteristic polynomial using the number of vertices. Also we found bounds for the lowest value of eigenvalue.

scholarly journals Estimation of Population Median under Robust Measures of an Auxiliary Variable

2021 ◽  
Vol 2021 ◽  
pp. 1-14
Author(s):  
Muhammad Irfan ◽  
Maria Javed ◽  
Sandile C. Shongwe ◽  
Muhammad Zohaib ◽  
Sajjad Haider Bhatti
Keyword(s):  
Random Sampling ◽  
Mean Squared Error ◽  
Real Life ◽  
Simple Random Sampling ◽  
Auxiliary Variable ◽  
First Order ◽  
Mathematical Properties ◽  
Squared Error ◽  
Class Of Estimators ◽  
Robust Measures

In this paper, a generalized class of estimators for the estimation of population median are proposed under simple random sampling without replacement (SRSWOR) through robust measures of the auxiliary variable. Three robust measures, decile mean, Hodges–Lehmann estimator, and trimean of an auxiliary variable, are used. Mathematical properties of the proposed estimators such as bias, mean squared error (MSE), and minimum MSE are derived up to first order of approximation. We considered various real-life datasets and a simulation study to check the potentiality of the proposed estimators over the competitors. Robustness is also examined through a real dataset. Based on the fascinating results, the researchers are encouraged to use the proposed estimators for population median under SRSWOR.

scholarly journals AVERAGING OF AN INCREASING NUMBER OF MOMENT CONDITION ESTIMATORS

2014 ◽  
Vol 32 (1) ◽  
pp. 30-70 ◽  
Author(s):  
Xiaohong Chen ◽  
David T. Jacho-Chávez ◽  
Oliver Linton
Keyword(s):  
Moment Condition ◽  
Moment Conditions ◽  
Parameter Heterogeneity ◽  
Class Of Estimators ◽  
Optimal Weighting ◽  
The Mean ◽  
The Moment ◽  
Image Position ◽  
Nonlinear Estimators ◽  
Available Information

We establish the consistency and asymptotic normality for a class of estimators that are linear combinations of a set of$\sqrt n$-consistent nonlinear estimators whose cardinality increases with sample size. The method can be compared with the usual approaches of combining the moment conditions (GMM) and combining the instruments (IV), and achieves similar objectives of aggregating the available information. One advantage of aggregating the estimators rather than the moment conditions is that it yields robustness to certain types of parameter heterogeneity in the sense that it delivers consistent estimates of the mean effect in that case. We discuss the question of optimal weighting of the estimators.

A MODIFIED RATIO TYPE ESTIMATOR OF FINITE POPULATION MEAN UNDER STRATIFIED RANDOM SAMPLING SCHEME

2021 ◽  
pp. 58-60
Author(s):  
Naziru Fadisanku Haruna ◽  
Ran Vijay Kumar Singh ◽  
Samsudeen Dahiru
Keyword(s):  
Mean Square Error ◽  
Random Sampling ◽  
Minimum Mean Square Error ◽  
Real Life ◽  
Population Data ◽  
Auxiliary Variable ◽  
Mean Square ◽  
Data Set ◽  
Population Mean ◽  
The Mean

In This paper a modied ratio-type estimator for nite population mean under stratied random sampling using single auxiliary variable has been proposed. The expression for mean square error and bias of the proposed estimator are derived up to the rst order of approximation. The expression for minimum mean square error of proposed estimator is also obtained. The mean square error the proposed estimator is compared with other existing estimators theoretically and condition are obtained under which proposed estimator performed better. A real life population data set has been considered to compare the efciency of the proposed estimator numerically.

scholarly journals EFFECTIVENESS OF HANDS OFF VERSUS HANDS ON TECHNIQUES ON PERINEAL TRAUMA AND PERINEAL PAIN AMONG PARTURIENT MOTHERS

2016 ◽  
Vol 9 (6) ◽  
pp. 179 ◽  
Author(s):  
Jayabharathi Bhaskaran
Keyword(s):  
Sampling Technique ◽  
Simple Random Sampling ◽  
Perineal Trauma ◽  
Perineal Pain ◽  
Study Group ◽  
Perineal Tear ◽  
Group I ◽  
Significant Difference ◽  
Hands On ◽  
The Mean

Background:  Labor is the process by which the fetus and the placenta leave the uterus. Delivery can occur in two ways, vaginally or by a cesarean delivery. The majority of women who have a vaginal birth will sustain perineal trauma from a spontaneous perineal tear or episiotomy or both.Aim: This study aims to assess the effectiveness of hands off versus hands on techniques on perineal trauma and perineal pain among parturient mothers in selected hospitals, Kerala.Methods: The research design adopted in this study was true experimental post test only design. The study was conducted in 3 hospitals at Kerala such as Karothukuzhiyil hospital Pvt, Lakshmi hospital Pvt and Carmal hospital Pvt. Sample size was computed by power analysis based on the previous studies and it would be a total of 90 samples, with 30 parturient mothers in each groups. Simple random sampling technique (Lottery method) was adopted for the selection of parturient mothers into the study. Perineal trauma was assessed by the scale given by Royal College of Obstetrics and Gynaecology (RCOG), 2001, and visual analogue scale (Combined numerical and categorical pain scale) was used to assess the perineal pain of parturient mothers.Results:  The results showed that, there was extremely significant difference found in perineal trauma and perineal pain of parturient mothers between study group I and study II at  p=0.000 level. The mean scores of study group I was lesser than the mean scores of study group II. Conclusion: Different perineal techniques and interventions such as hands on technique, hands off technique, perineal massage, warm compresses etc can be widely used by midwives and birth attendants to prevent perineal trauma during labour.  Key words:  hands off  technique, hands on technique, perineal trauma and perineal pain

scholarly journals Quantifying the closeness to a set of random curves via the mean marginal likelihood

2020 ◽  
Author(s):  
Cédric Rommel ◽  
Joseph Frédéric Bonnans ◽  
Baptiste Gregorutti ◽  
Pierre Martinon
Keyword(s):  
Marginal Likelihood ◽  
Marginal Density ◽  
Random Curves ◽  
Practical Applications ◽  
Random Functions ◽  
Practical Usefulness ◽  
Class Of Estimators ◽  
The Mean ◽  
Multivariate Density ◽  
Aircraft Trajectories

In this paper, we tackle the problem of quantifying the closeness of a newly observed curve to a given sample of random functions, supposed to have been sampled from the same distribution. We define a probabilistic criterion for such a purpose, based on the marginal density functions of an underlying random process. For practical applications, a class of estimators based on the aggregation of multivariate density estimators is introduced and proved to be consistent. We illustrate the effectiveness of our estimators, as well as the practical usefulness of the proposed criterion, by applying our method to a dataset of real aircraft trajectories.

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