An alternative method of reducing or eliminating the bias in the ratio estimator is to alter the method of sampling.
2.
The common odds ratio estimator is denoted "'? MH "'and can be computed by the following equation:
3.
The accuracy of Sharpe ratio estimators hinges on the statistical properties of returns, and these properties can vary considerably among strategies, portfolios, and over time.
4.
If the ratio estimator is unimodal ( which is frequently the case ) then a conservative estimate of the 95 % confidence intervals can be made with the Vysochanski? Petunin inequality.
5.
Then the ratio of the sum of the " y " variates and the sum of the " x " variates chosen in this fashion is an unbiased estimate of the ratio estimator.
6.
If a linear relationship between the " x " and " y " variates exists and the regression equation passes through the origin then the estimated variance of the regression equation is always less than that of the ratio estimator.
7.
The first known use of the ratio estimator was by John Graunt in England who in 1662 was the first to estimate the ratio " y " / " x " where " y " represented the total population and " x " the known total number of registered births in the same areas during the preceding year.
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