# Estimation Of Mean By An Auxiliary Variable

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### On Auxiliary Variables and Models in Estimation in Surveys

The auxiliary variable may introduce bias Fuller and An (1998) enphasize that the level of bias reduction depends on the relations between the auxiliary variable, the variable of interest, and the response probability. In this section we provide a simple example in which a candidate auxiliary variable satisfying

### Effect of Correlation Level on the Use of Auxiliary Variable

efficiency, it was established that the higher the correlation level between the study and auxiliary variable(s) is, the bet- ter the estimator is. Keywords: Correlation Level; Auxiliary Variable; Regression Estimator; Double Sampling and Relative Efficiency of Estimator 1. Introduction In sampling theory, auxiliary information may be utilized

### An Estimator of the Mean Estimation of Study Variable Using

An Estimator of the Mean Estimation of Study Variable Using Median of Auxiliary Variable IASSL ISSN 2424-6271 109 sample of size is draw without replacement from the population

### A New Regression Type Estimator with Two Auxiliary Variables

Aug 12, 2014 highly positively correlated with the study variable. Murthy  used auxiliary information in single -phase sa m-pling to develop the product estimator for estimation of population mean. Singh  gave a multivariate expres-sion of Murthy s  product estimator while Raj  put forward a method for using multi-auxiliary variables

### Estimation of Population Variance Using the Coefficient of

It is notable that the appropriate use of auxiliary information in probability sampling designs yields considerable reduction in the variance of the estimators How to cite this paper: Milton, T.K., Odhiambo, R.O. and Orwa, G.O. (2017) Estimation of Population Variance Using of an Auxiliary Variable under Simple Ran-dom Sampling. Open Journal of

### A simulation study: new optimal estimators for population

ated the dual use of auxiliary variable under a stratified random sampling scheme. Dual use of auxiliary variable consists: (1) the original auxiliary information and (2) the ranked auxiliary information. We proposed new optimal exponential-type estimators for the estimation of the finite population mean.

### Estimation of Mean of Finite Population Using Double Sampling

variable under the situation in which both study and auxiliary variables are suffered from non-response. The expressions for the biases and mean square errors of the proposed estimators up to the ﬁr st order of approximation have been obtained.

### An Estimation of Sensitive Proportion Utilizing Higher Order

An Estimation of Sensitive Proportion Utilizing Higher Order Moments of Auxiliary Variable Zawar Hussain * and Javid Shabbir * *Department of Statistics, Quaid-i-Azam University, Pakistan. Emails: [email protected], [email protected] Abstract To estimate the population proportion of a stigmatizing attribute use of auxiliary information in randomized

### Estimation of Variance Using Known Coefficient of Variation

auxiliary variable to improve the ratio estimators in estimating a population mean. Based on Subramani & Kumarapandiyan (2012a), a modified ratio type variance estimator using a linear combination of known value of a population median and coefficient of variation of an auxiliary variable is proposed. Results

### Generalized Estimators of Population Median using Auxiliary

Median estimation, Auxiliary variable, Mean squared errors, Bias, Simple random sampling, Population Median, Sample Median. 1. Introduction In survey sampling, statisticians have given more attention to the estimation of population mean, total, variance etc. but median is regarded as a more appropriate measure of location than mean

### Estimation of the mean using the rank statistics of an

auxiliary variable to estimate the parameters of the y-variable. We assume that the population mean X of the auxiliary variable is known and a simple random sample of n pairs (x^, y^) is drawn from the popula­ tion. There are two general classes of estimators which are designed to increase precision by utilizing this supplementary information,

### A Note on Estimation of Population Mean in Sample Survey

estimation which yields larger efficiency. Ratio, regression and product methods of estimation are good examples in this context. When the population mean of the auxiliary variable is known a large number of estimators for the population mean of the study variable is available in the literature for instance see Singh, H. P. (1986) and Singh, S

### ISSN: Two phase stratified sampling with regression method of

auxiliary variable z with known population mean In this case it is assumed that the variable z is also correlated with y than x, hence, the need for this regression estimator in two-phase stratified sampling with two auxiliary variables. There are two types of two-phase sampling design. In the first type, the auxiliary variable does

### Estimation of Finite Population Mean using Two Auxiliary

1 be the study and auxiliary variables with respective population means X 0 and X 1. Let X 2 be the additional auxiliary variable with populationmean X 2. The aim of the present research is to estimate the population mean X 0 using the information on the auxiliary variables X 1 and X 2 under the condition that the population mean X

### Chapter 5 Ratio and Product Methods of Estimation

estimation procedure yields better estimators, provided the information is valid and proper. Use of such auxiliary information is made through the ratio method of estimation to obtain an improved estimator of the population mean. In ratio method of estimation, auxiliary information on a variable is available, which

### VARIANCE ESTIMATION USING ARITHMETIC MEAN, GEOMETRIC MEAN AND

Let x be the auxiliary variable, highly correlated to the study variable y. If information on an auxiliary variable is readily available then it is a well-known fact that the ratio-type and regression-type estimators can be used for estimation of parameters of interest, due to increase in efficiency of these estimators.

### Two parameter modified ratio estimators with two auxiliary

Two parameter modified ratio estimators with two auxiliary variables for the estimation of finite population mean 561 Copr 2018 r Citation: Subramani J. Two parameter modified ratio estimators with two auxiliary variables for the estimation of finite population mean. Biom Biostat Int J. 2018;7(6):559‒568. DOI: 10.15406/bbij.2018.07.00259 x =X 1 e

### Estimation of Population Mean Using Known Median and Co

Feb 05, 2012 prior information on auxiliary variable X which is positively correlated with the study variable Y. Over the years the ratio method of estimation has been extensively used because of its intuitive appeal and the computational simplicity. When the population parameters of the auxiliary variable X such as Population Mean, Co-efficient of

### Exponential Type Product Estimator for Finite Population Mean

product estimator for the estimation of the population mean. The proposed estimator possesses the characteristic of a bi-serial negative correlation between the study variable and its auxiliary attribute. Efficiency comparison has been carried out between the proposed estimator and the existing estimators theoretically and numerically.

### Application of Auxiliary Variables in Two-Step Semi

This researchincorporatesthe auxiliary variables in the two-step semi-parametric multiple imputation procedure so as to improve efficiency and reduce the biasedness in estimation of mean. The inclusion ofthe auxiliary variables in the weighted FPBB is done under the assumption of MAR.

### MULTIVARIATE RATIO ESTIMATION WITH KNOWN POPULATION

Prior knowledge about population mean along with coefficient of variation of the population of an auxiliary variable is known to be very useful particularly when the ratio, product and regression estimators are used for estimation of population mean of a variable of interest.

### On Estimation of Population Mean Using Information on

On Estimation of Population Mean Using Information on Auxiliary Attribute Rajesh Singh Department of Statistics BHU, Varanasi (U.P.), India [email protected] Abstract We consider the problem of estimating the finite population mean when some information on auxiliary attribute is available.

### Almost Unbiased Modified Linear Regression Estimators for

auxiliary variable which is correlated with the study variable Over the years the ratio method of estimation has been extensively used because of its intuitive appeal and the computational simplicity. The classical Ratio estimator for the population mean of the study variable is defined as: , where (1)

### A Class of Modified Ratio Estimators Using Deciles of an

Feb 06, 2012 Auxiliary Variable J. Subramani*, G. Kumarapandiyan Department of Statistics, Ramanujan School of Mathematical Sciences, Pondicherry University, R V Nagar, Kalapet, Puducherry, 605014, India Abstract. In the past, a number of modified ratio estimators are suggested for estimation of the population mean of the

### A NEW ESTIMATOR OF MEAN USING DOUBLE SAMPLING

estimation stage. In other words, in the case of single auxiliary variable X, if the population mean X of the auxiliary variable is unknown then we consider taking a preliminary large sample of m units by using simple random and without replacement sampling (SRSWOR) from the population of N units. In the sample s 1 of m units, we observe only

### ON THE GENERALIZED CLASS OF ESTIMATORS FOR ESTIMATION OF

for the estimation of the unknown population mean of the variable of in-terest accompanying the issue of non-response in the study and in the auxiliary variables. The asymptotic bias and the asymptotic variance of the suggested class are acquired, up to the rst degree of approximation and, compared with the linear regression estimator.

### Modified Ratio Estimators for Population Mean Using Function

mean of the study variable and is the sample mean of auxiliary variable X. It is assumed that the population mean of auxiliary variable X is known. Many modified ratio type estimators available in the literature are biased but have minimum mean squared errors compared to that of usual ratio estimator. Some of the modified

### Improved Estimation of the Population Mean Using Known

Using Known Parameters of an Auxiliary Variable Rajesh Tailor Balkishan Sharma Vikram University Ujjain, M.P., India An improved ratio-cum-product type estimator of the finite population mean is

### A robust unbiased dual to product estimator for population

the sample mean as an estimator of population mean. So there is need of another type of estimator which also makes use of information on auxiliary variable x. Product method of estimation is an attempt in this direction. Product-type estima-tors are widely used for estimating population mean when the correlation between

### A note on a difference-type estimator for population mean

When the knowledge of the auxiliary variable is used at the estimation stage, the ratio, product and regression methods of estimation are widely employed in these situations. The most important topic which is widely discussed in the various probability sampling schemes is the estimation of the population mean of the study variable. A large

### ESTIMATION OF POPULATION MEAN USING TWO AUXILIARY VARIABLES

sampling, Mean Squared Error, Efficiency, Bias. Introduction It is widely known in the context of literature of survey sampling that the efficiency of the estimators of the population parameters of the variable of interest can be increased by the use of auxiliary information related to auxiliary variable x which is highly correlated with the

### ESTIMATION OF POPULATION MEAN USING TRANSFORMED AUXILIARY

variance of the study variable and auxiliary variable, respectively. The problem of non-response is common and more widespread in mail surveys than in a personal interview. Hansen and Hurwitz (1946) were the first one to deal with this situation and proposed methodology for the estimation of population mean of the study variable

### Efficient and Unbiased Estimation Procedure of Population

Sample Structure and Some Existing Estimation Procedures Let y k, x k, and z k be the values of the study variable y, first auxiliary variable x, and second auxiliary variable z, respectively, associated with the kth unit of the finite population U = (U 1, U 2, U 3, , U N). The intent is to estimate the population mean

### On Improved Estimation of Population Mean using Qualitative

of study and auxiliary variables respectively to estimate population mean of study variable. Srivenkataramana (1980) first proposed the dual to ratio estimator for estimating population mean. Kadilar and Cingi (2004, 2005) analyzed combinations of regression type estimators in the case of two auxiliary

### Estimation of Population Mean Using Auxiliary Attribute in

Keywords: Auxiliary attribute, Mean square error, Non-response, Study character. 1. INTRODUCTION It is well known that the estimators for population mean using information on auxiliary character give the better estimate in comparison to the usual estimator. Sometimes the auxiliary information is available in the form of attribute.

### Compromise Allocation for Mean Estimation in Stratified

estimators of population mean, under different situations, when some of the observations on either study variable or auxiliary variable or both of the observations are unavailable. In this paper we have assumed the same situation of missing values. We have proposed an estimator which is based on all observations either available or missing

### USE OF AUXILIARY INFORMATION IN SAMPLING

with respect to the study variable. In this chapter we consider the problem of optimum stratification when the information on the auxiliary variable X is used to estimate the populations mean Y of study variable y using ratio and regression method of estimation. Chapter 3 deals with the problem of ratio estimate in successive sampling.

### Combination of Two Exponential Ratio Type Estimators for

Therefore the proposed estimator should be preferred for the estimation of population mean using auxiliary variable with double sampling in presence of non-response. Figure-1: Relative efficiency (%) with respect to different estimator.

### Difference-Type Estimators for Estimation of Mean in The

of population mean P. y. of study variable using auxiliary information in the presence of measurement errors. Fuller (1995) examined the importance of measurement errors in estimating parameters in sample surveys. His major concerns are estimation of population mean or total and its standard error, quartile estimation and estimation through