scholarly journals Admissibility of the Sample Mean as Estimate of the Mean of a Finite Population

1968 ◽  
Vol 39 (2) ◽  
pp. 606-620 ◽  
Author(s):  
V. M. Joshi
Keyword(s):  
Finite Population ◽  
Sample Mean ◽  
The Mean

scholarly journals A comparison of two methods for predicting changes in the distribution of gene frequency when selection is applied repeatedly to a finite population

1969 ◽  
Vol 13 (2) ◽  
pp. 117-126 ◽  
Author(s):  
Derek J. Pike
Keyword(s):  
Iterative Procedure ◽  
Gene Frequency ◽  
Finite Population ◽  
Transition Matrices ◽  
Single Cycle ◽  
Gene Frequencies ◽  
Mean And Variance ◽  
The Mean ◽  
The One ◽  
Selection Of

Robertson (1960) used probability transition matrices to estimate changes in gene frequency when sampling and selection are applied to a finite population. Curnow & Baker (1968) used Kojima's (1961) approximate formulae for the mean and variance of the change in gene frequency from a single cycle of selection applied to a finite population to develop an iterative procedure for studying the effects of repeated cycles of selection and regeneration. To do this they assumed a beta distribution for the unfixed gene frequencies at each generation.These two methods are discussed and a result used in Kojima's paper is proved. A number of sets of calculations are carried out using both methods and the results are compared to assess the accuracy of Curnow & Baker's method in relation to Robertson's approach.It is found that the one real fault in the Curnow-Baker method is its tendency to fix too high a proportion of the genes, particularly when the initial gene frequency is near to a fixation point. This fault is largely overcome when more individuals are selected. For selection of eight or more individuals the Curnow-Baker method is very accurate and appreciably faster than the transition matrix method.

scholarly journals On sojourn times at particular gene frequencies

1975 ◽  
Vol 25 (2) ◽  
pp. 89-94 ◽  
Author(s):  
Edward Pollak ◽  
Barry C. Arnold
Keyword(s):  
Markov Chains ◽  
Gene Frequency ◽  
Overlapping Generations ◽  
Finite Population ◽  
Diffusion Method ◽  
Gene Frequencies ◽  
Sojourn Times ◽  
The Mean ◽  
Number Of Visits ◽  
Finite Markov Chains

SUMMARYThe distribution of visits to a particular gene frequency in a finite population of size N with non-overlapping generations is derived. It is shown, by using well-known results from the theory of finite Markov chains, that all such distributions are geometric, with parameters dependent only on the set of bij's, where bij is the mean number of visits to frequency j/2N, given initial frequency i/2N. The variance of such a distribution does not agree with the value suggested by the diffusion method. An improved approximation is derived.

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.

scholarly journals A Note on Nonlinearity Bias and Dichotomous Choice CVM: Implications for Aggregate Benefits Estimation

1996 ◽  
Vol 25 (1) ◽  
pp. 54-59 ◽  
Author(s):  
R.A. Souter ◽  
J.M. Bowker
Keyword(s):  
Logit Model ◽  
Nonlinear Models ◽  
Nonlinear Function ◽  
Dichotomous Choice ◽  
Sample Mean ◽  
Mean Values ◽  
Concomitant Variables ◽  
The Mean ◽  
Using Data ◽  
Single Response

It is a generally known statistical fact that the mean of a nonlinear function of a set of random variables is not equivalent to the function evaluated at the means of the variables. However, in dichotomous choice contingent valuation studies a common practice is to calculate an overall mean (or median) by integrating over offer space (numerically or analytically) an estimated logit or probit function in which sample mean values for the concomitant variables are used. We demonstrate this procedure to be incorrect and we statistically test the procedure against the correct method for nonlinear models. Using data resulting in a well-behaved logit model, we reject the hypothesis of congruence between the two means. Such a finding should be considered in future single response dichotomous choice CVM studies, particularly when aggregation is of interest.

scholarly journals A Study on the Chain Ratio-Type Estimator of Finite Population Variance

2014 ◽  
Vol 2014 ◽  
pp. 1-5 ◽  
Author(s):  
Yunusa Olufadi ◽  
Cem Kadilar
Keyword(s):  
Finite Population ◽  
Numerical Comparison ◽  
Mean Square ◽  
Auxiliary Variables ◽  
Population Variance ◽  
Two Phase ◽  
First Order ◽  
Phase Sampling ◽  
The Mean ◽  
Two Phase Sampling

We suggest an estimator using two auxiliary variables for the estimation of the unknown population variance. The bias and the mean square error of the proposed estimator are obtained to the first order of approximations. In addition, the problem is extended to two-phase sampling scheme. After theoretical comparisons, as an illustration, a numerical comparison is carried out to examine the performance of the suggested estimator with several estimators.

scholarly journals Estimation of Population Mean in Chain Ratio-Type Estimator under Systematic Sampling

2015 ◽  
Vol 2015 ◽  
pp. 1-5 ◽  
Author(s):  
Mursala Khan ◽  
Rajesh Singh
Keyword(s):  
Finite Population ◽  
Real Data ◽  
Survey Sampling ◽  
Systematic Sampling ◽  
Auxiliary Variables ◽  
Data Set ◽  
Population Mean ◽  
First Order ◽  
The Mean ◽  
A Chain

A chain ratio-type estimator is proposed for the estimation of finite population mean under systematic sampling scheme using two auxiliary variables. The mean square error of the proposed estimator is derived up to the first order of approximation and is compared with other relevant existing estimators. To illustrate the performances of the different estimators in comparison with the usual simple estimator, we have taken a real data set from the literature of survey sampling.

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