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2 edition of Comparison of the separate and combined ratio estimators found in the catalog.

Comparison of the separate and combined ratio estimators

J. N. K. Rao

# Comparison of the separate and combined ratio estimators

## by J. N. K. Rao

• 76 Want to read
• 3 Currently reading

Published by Department of Mathematics, Carleton University in Ottawa .
Written in English

Subjects:
• Estimation theory.,
• Sampling (Statistics)

• Edition Notes

Bibliography: leaf [17].

Classifications The Physical Object Statement by J. N. K. Rao and V. Ramachandran. Series Carleton mathematical series ;, no. 98 Contributions Ramachandran, V., 1934- joint author. LC Classifications QA276.8 .R36 Pagination [17] l. ; Number of Pages 17 Open Library OL5254487M LC Control Number 75327536

In an earlier paper [Rao ] an exact expression for the variance of the ratio estimator under theMidzuno-Sen sampling scheme is obtained and here we study some of the interesting properties of the coefficients involved in this expression which Cited by: 5. Contributions to ratio method of estimation Isidoro Pineda David Iowa State University Follow this and additional works at: Part of theStatistics and Probability Commons This Dissertation is brought to you for free and open access by the Iowa State University Capstones, Theses and Dissertations at Iowa State University.

The ratio estimator is a statistical parameter and is defined to be the ratio of means of two random variables. Ratio estimates are biased and corrections must be made when they are used in experimental or survey work. The ratio estimates are asymmetrical and symmetrical tests such as the t test should not be used to generate confidence intervals.   To estimate the finite population mean, $$\bar Y$$, a two-phase sample may be selected.A simple random sample of sizen′ is chosen, and a concomitant variable,X, is measured for all , a simple random subsample of sizen (0ratio-type estimators of $$\bar Y$$ are given, and their biases and mean square errors determined toO((n′) −2).Cited by: 4.

At the end of section , a small population example is given to illustrate that the ratio estimate is biased and also to demonstrate that the ratio estimate is indeed better than the expansion estimate when the condition for using the ratio estimate is satisfied. Method 1: The Separate Ratio Estimator The separate ratio estimator is based on calculating Lstratum ratio estimates and then form a weighted average of these separate ratio estimates to form a single estimate of the population ratio B. Suppose we want to estimate the population mean yU. For stratum h, the estimated stratum ratio is Bb.

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### Comparison of the separate and combined ratio estimators by J. N. K. Rao Download PDF EPUB FB2

Using estimators for stratiﬂed random sampling, and then useyst=„x as a ratio estimator of„y=„x. This gives a combined ratio estimator. In a situation with two strata (labeledAandB), the expression for estimat- ing a mean using the separate ratio estimator is: ^„yRS= µ. y„A. „xA. („xA)+ µ.

We find that separate ratio estimators are more efficient than combined ratio estimators for population variance. The theoretical results are supported by a numerical illustration with original data.

A simulation study is also carried out to investigate empirical performance of by: 1. •There are two different methods to construct estimators of a ratio in stratiﬁed sampling. • Separate Ratio Estimator:Estimate the ratio of y to x within each stratum and then form a weighted average of the separated estimates.

• Combined Ratio Estimator:Compute the usual y st and x st, then use their quotient as an estimator of y x. •If the stratum sample sizes Comparison of the separate and combined ratio estimators book large (more than 20) it is better to File Size: KB.

Key Words: Ratio-type estimators; Stratified random sampling; Mean square errors. Introduction A ratio estimate of the population mean Y can be made in two ways.

One is to make a separate ratio estimate of the total of each stratum and add these totals. An alternative estimate is derived from a single combined ratio. From the sample data. However, just to show a counter example, we can compute the variance of the ratio estimate using the following Minitab print out and compare this to the regression estimate.

Note: for the Calculus Scores example we should not use the ratio estimator $$\hat{\mu}_r$$ because the p. Comparison of Some Almost Unbiased Ratio Estimators Priyaranjan Dash Department of Statistics, Tripura University, India***Abstract - A survey sampler is always desperate for designing a best estimator and devotes endless effort to achieve that.

As a result a reasonable number of estimators developed especially for the most urged. stratified ratio estimator would be. (24) Ratio estimators in post-stratification are same as the separate ratio estimators in stratified sampling.

But MSE equations differ in these methods. The estimators given in the Section-1 are combined with post-stratified ratio estimator given in (20), following estimators (are proposed as such. Ratio and Product Methods of Estimation An important objective in any statistical estimation procedure is to obtain the estimators of parameters of interest with more Size: KB.

(), etc. Hansen et al. () defined combined ratio estimator using auxiliary information in stratified random sampling. Many authors including Kadilar and Cingi (,) and Singh et al. () worked out ratio type estimators To see the efficiency of the proposed estimator in comparison to other con.

Book value and market value are two financial metrics used to determine the valuation of a company and whether the stock trades at a discount or premium.

The estimators of totals and their variances under strategies S1 to S4 are described in Arantes (). For strategies S1 to S3, estimators were available in Silva and Moura (). For S4 we developed the Horvitz-Thompson estimator of the total and its variance considering properties described in Cochran (), as: V(Yˆ +,)=   Combined ratio, also called "the combined ratio after policyholder dividends ratio," is a measure of profitability used by insurance companies to gauge how well it is performing in its daily.

sample mean, traditional ratio estimator and the ratio estimators suggested by Singh and Tailor () and Kadilar and Cingi ().

It is well known that under simple random sampling without replacement (SRSWOR) the variance of the sample mean is ()1 2 Sy n f V y −. (17) We first compare the MSE of the proposed estimators, given in (16), with.

Abstract: This study is conducted to compare two ratio estimators that use auxiliary information. The estimators are Olkin average ratio estimator and Kadilar-Cingi estimator. Efficiencies of the estimators are investigated theoretically and using data from Federal Inland Revenue Service Revenue House Store.

The resultAuthor: Ibrahim Bawa, Audu Makada. Regression Estimators. Ratio estimators are especially beneficial when there is a degree of proportionality between the two variables $$Y$$ and $$X$$; the more so the higher the correlation.

Ratio Estimators Using Coefficient of Variation and Coefficient of Correlation. namely combined and separate ratio estimators. The comparison of the efficiency between the proposed. same methodology as in the case of the ratio method of estimation.

Let 00 11 22 22 22 (1) (1) Comparison of ˆ Yreg with ratio estimate and SRS sample mean estimate 22 2 Ysreg is termed as separate regression estimator, 2. Combined regression estimatorFile Size: KB.

THE COMPARISON OF ESTIMATORS OF RATIO FOR A REGRESSION MODEL From the above, we get the following theorem in the setup of section 2. THEOREM Assume that Xl, "', Xn are i.i.d. random variables with a continuous density function w£th mean 1, variance (J'2 and finite }l6, where 0.

To estimate the ratio of two population characteristics. The most common case is the population ratio Bof means or totals: B = 2. To use the relationship between Xand Y to improve estimation of ty or yU.

The sampling plan will be to take a SRS of npairs (x 1;y 1);;(xn;yn) from the population of Npairs. We will use the following notation: xU = XN i=1 xi!File Size: KB.

The ratio-type exponential estimator Re y is better than unbiased estimator y if 4 1 C () and the product-type exponential estimator Pe y is better than the unbiased estimator y if 4 1 − C (1. The ratio calculator performs three types of operations and shows the steps to solve: Simplify ratios or create an equivalent ratio when one side of the ratio is empty.

Solve ratios for the one missing value when comparing ratios or proportions. Compare ratios and evaluate as true or false to answer whether ratios or fractions are equivalent.Comparison of the Sample Median and Weighted Mean as Estimators of the Population Weighted Mean Assessment/Sales Ratio by Robert C.

Denne and Robert J. Gloudemans This is a slightly modified version of a paper prepared for the IAAO Assessment Standards Committee on Ma A. C. Onyeka et al. 29 riable x, is known, we proposed six separate-type estimators of the population ratio R YX= in post strati- fied sampling scheme, following [1] as, 1 () 1 ˆ L h Sh h h hh y R x bx X ω ∗ = = −− ∑ () 2 11 ˆ LL h hh Sh h hh h hh h h y yx R x xX X x ωω ∗ == ∗ == ∑ ∑ () 3.