scholarly journals On Improving Ratio/Product Estimator by Ratio/Product-cum-Mean-per-Unit Estimator Targeting More Efficient Use of Auxiliary Information

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Angela Shirley ◽  
Ashok Sahai ◽  
Isaac Dialsingh
Keyword(s):  
Auxiliary Information ◽  
Simple Random Sample ◽  
Sample Mean ◽  
Parameter Ratio ◽  
Large Sample Approximation ◽  
Product Estimator ◽  
Sample Approximation ◽  
The Mean ◽  
Classical Linear Regression ◽  
Linear Regression Estimator

To achieve a more efficient use of auxiliary information we propose single-parameter ratio/product-cum-mean-per-unit estimators for a finite population mean in a simple random sample without replacement when the magnitude of the correlation coefficient is not very high (less than or equal to 0.7). The first order large sample approximation to the bias and the mean square error of our proposed estimators are obtained. We use simulation to compare our estimators with the well-known sample mean, ratio, and product estimators, as well as the classical linear regression estimator for efficient use of auxiliary information. The results are conforming to our motivating aim behind our proposition.

scholarly journals Finite Population Mean Estimation through a Two-Parameter Ratio Estimator Using Auxiliary Information in Presence of Non-Response

2016 ◽  
Vol 12 (2) ◽  
pp. 5-39 ◽  
Author(s):  
S. K. Pal ◽  
H. P. Singh
Keyword(s):  
Auxiliary Information ◽  
Auxiliary Variable ◽  
Human Populations ◽  
Ratio Estimator ◽  
Population Mean ◽  
Parameter Ratio ◽  
Mean Estimation ◽  
Large Sample Approximation ◽  
Respondent Group ◽  
Sample Approximation

Abstract In surveys covering human populations it is observed that information in most cases are not obtained at the first attempt even after some callbacks. Such problems come under the category of non-response. Surveys suffer with non-response in various ways. It depends on the nature of required information, either surveys is concerned with general or sensitive issues of a society. Hansen and Hurwitz (1946) have considered the problem of non-response while estimating the population mean by taking a subsample from the non-respondent group with the help of extra efforts and an estimator was suggested by combining the information available from the response and nonresponse groups. We also mention that in survey sampling auxiliary information is commonly used to improve the performance of an estimator of a quantity of interest. For estimating the population mean using auxiliary information in presence of non-response has been discussed by various authors. In this paper, we have developed estimators for estimating the population mean of the variable under interest when there is non-response error in the study as well as in the auxiliary variable. We have studied properties of the suggested estimators under large sample approximation. Comparison of the suggested estimators with usual unbiased estimator reported by Hansen and Hurwitz (1946) and the ratio estimator due to Rao (1986) have been made. The results obtained are illustrated with aid of an empirical study.

scholarly journals A Two-Parameter Ratio-Product-Ratio Estimator Using Auxiliary Information

2012 ◽  
Vol 2012 ◽  
pp. 1-15 ◽  
Author(s):  
Peter S. Chami ◽  
Bernd Sing ◽  
Doneal Thomas
Keyword(s):  
Mean Squared Error ◽  
Auxiliary Information ◽  
Degree Of Approximation ◽  
Simple Random Sample ◽  
Ratio Estimator ◽  
Sample Mean ◽  
Product Ratio ◽  
Squared Error ◽  
Parameter Ratio ◽  
Two Parameter

We propose a two-parameter ratio-product-ratio estimator for a finite population mean in a simple random sample without replacement following the methodology in the studies of Ray and Sahai (1980), Sahai and Ray (1980), A. Sahai and A. Sahai (1985), and Singh and Espejo (2003).The bias and mean squared error of our proposed estimator are obtained to the first degree of approximation. We derive conditions for the parameters under which the proposed estimator has smaller mean squared error than the sample mean, ratio, and product estimators. We carry out an application showing that the proposed estimator outperforms the traditional estimators using groundwater data taken from a geological site in the state of Florida.

scholarly journals A Class of Ratio-Type Estimator Using Two Auxiliary Variables for Estimating The Population Mean With Some Known Population Parameters

2019 ◽  
pp. 329-340 ◽  
Author(s):  
Toluwalase Janet Akingbade ◽  
Fabian C. Okafor
Keyword(s):  
Mean Square ◽  
Population Parameters ◽  
Auxiliary Variables ◽  
Study Variable ◽  
Sample Mean ◽  
Population Mean ◽  
The Mean ◽  
Classical Linear Regression ◽  
Linear Regression Estimator ◽  
Better Than

In this paper, we have suggested a class of ratio type estimators with a linear combination using two auxiliary variables with some known population mean of the study variable. The bias and the mean square error of the proposed estimators are derived. We identified sub-members of the class of ratio type estimators. The condition for which the the proposed the proposed estimators perform better than the sample mean per unit, Olkin (1958) multivariate ratio, classical linear regression estimator, Singh(1965), Mohanty (1967) and Swain (2012) are derived. From the analysis, it is observed that the proposed estimators perform better than the sample mean per unit and other existing ratio type estimators considered in this study.

scholarly journals An Improved Family of Estimators of Finite Population Mean Using Information on an Auxiliary Variable in Sample Surveys

2017 ◽  
Vol 13 (2) ◽  
pp. 77-108
Author(s):  
H. P. Singh ◽  
A. Yadav
Keyword(s):  
Mean Squared Error ◽  
Auxiliary Information ◽  
Auxiliary Variable ◽  
Sample Surveys ◽  
Sample Mean ◽  
Population Mean ◽  
Squared Error ◽  
Parameter Ratio ◽  
Large Sample Approximation ◽  
Class Of Estimators

Abstract In this paper we have suggested a family of estimators of the population mean using auxiliary information in sample surveys. The bias and mean squared error of the proposed class of estimators have been obtained under large sample approximation. We have derived the conditions for the parameters under which the proposed class of estimators has smaller mean squared error than the sample mean, ratio, product, regression estimator and the two parameter ratio-product-ratio estimators envisaged by Chami et al (2012). An empirical study is carried out to demonstrate the performance of the proposed class of estimators over other existing estimators.

scholarly journals A New Exponential Approach for Reducing the Mean Squared Errors of the Estimators of Population Mean Using Conventional and Non-Conventional Location Parameters

2020 ◽  
Vol 18 (1) ◽  
Author(s):  
Housila P. Singh ◽  
Anita Yadav
Keyword(s):  
Large Sample ◽  
Population Mean ◽  
Mean Squared Errors ◽  
Large Sample Approximation ◽  
Location Parameters ◽  
Sample Approximation ◽  
The Mean

Classes of ratio-type estimators t (say) and ratio-type exponential estimators te (say) of the population mean are proposed, and their biases and mean squared errors under large sample approximation are presented. It is the class of ratio-type exponential estimators te provides estimators more efficient than the ratio-type estimators.

scholarly journals Generalized Ratio-cum-Product Estimator for Finite Population Mean under Two-Phase Sampling Scheme

2021 ◽  
Vol 19 (1) ◽  
pp. 2-16
Author(s):  
Gajendra Kumar Vishwakarma ◽  
Sayed Mohammed Zeeshan
Keyword(s):  
Sampling Scheme ◽  
Two Phase ◽  
Phase Sampling ◽  
Product Estimator ◽  
The Mean ◽  
Set Up ◽  
Mean Square Errors ◽  
Linear Regression Estimator ◽  
The Given ◽  
Two Phase Sampling

A method to lower the MSE of a proposed estimator relative to the MSE of the linear regression estimator under two-phase sampling scheme is developed. Estimators are developed to estimate the mean of the variate under study with the help of auxiliary variate (which are unknown but it can be accessed conveniently and economically). The mean square errors equations are obtained for the proposed estimators. In addition, optimal sample sizes are obtained under the given cost function. The comparison study has been done to set up conditions for which developed estimators are more effective than other estimators with novelty. The empirical study is also performed to supplement the claim that the developed estimators are more efficient.

scholarly journals Neutrosophic ratio-type estimators for estimating the population mean

2021 ◽  
Author(s):  
Zaigham Tahir ◽  
Hina Khan ◽  
Muhammad Aslam ◽  
Javid Shabbir ◽  
Yasar Mahmood ◽  
...  
Keyword(s):  
Minimum Mean Square Error ◽  
Auxiliary Information ◽  
Population Parameter ◽  
Uncertain Information ◽  
Population Mean ◽  
Classical Statistics ◽  
Neutrosophic Statistics ◽  
The Mean ◽  
Type Data ◽  
First Time

AbstractAll researches, under classical statistics, are based on determinate, crisp data to estimate the mean of the population when auxiliary information is available. Such estimates often are biased. The goal is to find the best estimates for the unknown value of the population mean with minimum mean square error (MSE). The neutrosophic statistics, generalization of classical statistics tackles vague, indeterminate, uncertain information. Thus, for the first time under neutrosophic statistics, to overcome the issues of estimation of the population mean of neutrosophic data, we have developed the neutrosophic ratio-type estimators for estimating the mean of the finite population utilizing auxiliary information. The neutrosophic observation is of the form $${Z}_{N}={Z}_{L}+{Z}_{U}{I}_{N}\, {\rm where}\, {I}_{N}\in \left[{I}_{L}, {I}_{U}\right], {Z}_{N}\in [{Z}_{l}, {Z}_{u}]$$ Z N = Z L + Z U I N where I N ∈ I L , I U , Z N ∈ [ Z l , Z u ] . The proposed estimators are very helpful to compute results when dealing with ambiguous, vague, and neutrosophic-type data. The results of these estimators are not single-valued but provide an interval form in which our population parameter may have more chance to lie. It increases the efficiency of the estimators, since we have an estimated interval that contains the unknown value of the population mean provided a minimum MSE. The efficiency of the proposed neutrosophic ratio-type estimators is also discussed using neutrosophic data of temperature and also by using simulation. A comparison is also conducted to illustrate the usefulness of Neutrosophic Ratio-type estimators over the classical estimators.

scholarly journals Modeling of temporal groundwater level variations based on a Kalman filter adaptation algorithm with exogenous inputs

2016 ◽  
Vol 19 (2) ◽  
pp. 191-206 ◽  
Author(s):  
Emmanouil A. Varouchakis
Keyword(s):  
Kalman Filter ◽  
Groundwater Level ◽  
Auxiliary Information ◽  
Model Parameters ◽  
Adaptation Algorithm ◽  
Arx Model ◽  
Resources Management ◽  
Temporal Modelling ◽  
The Mean ◽  
First Time

Reliable temporal modelling of groundwater level is significant for efficient water resources management in hydrological basins and for the prevention of possible desertification effects. In this work we propose a stochastic method of temporal monitoring and prediction that can incorporate auxiliary information. More specifically, we model the temporal (mean annual and biannual) variation of groundwater level by means of a discrete time autoregressive exogenous variable (ARX) model. The ARX model parameters and its predictions are estimated by means of the Kalman filter adaptation algorithm (KFAA) which, to our knowledge, is applied for the first time in hydrology. KFAA is suitable for sparsely monitored basins that do not allow for an independent estimation of the ARX model parameters. We apply KFAA to time series of groundwater level values from the Mires basin in the island of Crete. In addition to precipitation measurements, we use pumping data as exogenous variables. We calibrate the ARX model based on the groundwater level for the years 1981 to 2006 and use it to predict the mean annual and biannual groundwater level for recent years (2007–2010). The predictions are validated with the available annual averages reported by the local authorities.

The Content of IMF Staff Reports for Euro Area Countries

2014 ◽  
pp. 272-292
Author(s):  
Lena Golubovskaja
Keyword(s):  
Standard Deviation ◽  
Euro Area ◽  
Mean Value ◽  
Systematic Bias ◽  
Executive Board ◽  
Sample Mean ◽  
Warning Tone ◽  
The Mean ◽  
Run Up ◽  
The Imf

This chapter analyzes the tone and information content of the two external policy reports of the Internal Monetary Fund (IMF), the IMF Article IV Staff Reports, and Executive Board Assessments for Euro area countries. In particular, the researchers create a tone measure denoted WARNING based on the existing DICTION 5.0 Hardship dictionary. This study finds that in the run-up to the current credit crises, average WARNING tone levels of Staff Reports for Slovenia, Luxembourg, Greece, and Malta are one standard deviation above the EMU sample mean; and for Spain and Belgium, they are one standard deviation below the mean value. Furthermore, on average for Staff Reports over the period 2005-2007, there are insignificant differences between the EMU sample mean and Staff Reports’ yearly averages. Researchers find the presence of a significantly increased level of WARNING tone in 2006 (compared to the previous year) for the IMF Article IV Staff Reports. There is also a systematic bias of WARNING scores for Executive Board Assessments versus WARNING scores for the Staff Reports.

scholarly journals Credibility Approximations for Bayesian Prediction of Second Moments

1985 ◽  
Vol 15 (2) ◽  
pp. 103-121 ◽  
Author(s):  
William S. Jewell ◽  
Rene Schnieper
Keyword(s):  
Least Squares ◽  
Linear Functions ◽  
Quadratic Functions ◽  
Sample Variance ◽  
Credibility Theory ◽  
Sample Mean ◽  
Second Moment ◽  
Second Moments ◽  
Special Cases ◽  
The Mean

AbstractCredibility theory refers to the use of linear least-squares theory to approximate the Bayesian forecast of the mean of a future observation; families are known where the credibility formula is exact Bayesian. Second-moment forecasts are also of interest, for example, in assessing the precision of the mean estimate. For some of these same families, the second-moment forecast is exact in linear and quadratic functions of the sample mean. On the other hand, for the normal distribution with normal-gamma prior on the mean and variance, the exact forecast of the variance is a linear function of the sample variance and the squared deviation of the sample mean from the prior mean. Bühlmann has given a credibility approximation to the variance in terms of the sample mean and sample variance.In this paper, we present a unified approach to estimating both first and second moments of future observations using linear functions of the sample mean and two sample second moments; the resulting least-squares analysis requires the solution of a 3 × 3 linear system, using 11 prior moments from the collective and giving joint predictions of all moments of interest. Previously developed special cases follow immediately. For many analytic models of interest, 3-dimensional joint prediction is significantly better than independent forecasts using the “natural” statistics for each moment when the number of samples is small. However, the expected squared-errors of the forecasts become comparable as the sample size increases.

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