Optimal combination of sampled measurements
First Claim
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1. A method of estimating an attribute of objects, comprising:
- a. obtaining a first sample of said objects based on a first sampling distribution;
b. obtaining a first estimate of said attribute based on said first sample;
c. obtaining a second sample of said objects based on a second sampling distribution, where said second sampling distribution is different from said first sampling distribution;
d. obtaining a second estimate of said attribute based on said second sample;
e. determining a lower bound for a variance based upon each of the first sample and the second sample; and
f. combining the first sample and the second sample using a variance value for each one of the first sample and the second sample that is equal to or larger than the lower bound for the variance for the first sample and second sample.
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Abstract
Two regularized estimators that avoid the pathologies associated with variance estimation are disclosed. The regularized variance estimator adds a contribution to estimated variance representing the likely error, and hence ameliorates the pathologies of estimating small variances while at the same time allowing more reliable estimates to be balanced in the convex combination estimator. The bounded variance estimator employs an upper bound to the variance which avoids estimation pathologies when sampling probabilities are very small.
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Citations
19 Claims
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1. A method of estimating an attribute of objects, comprising:
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a. obtaining a first sample of said objects based on a first sampling distribution; b. obtaining a first estimate of said attribute based on said first sample; c. obtaining a second sample of said objects based on a second sampling distribution, where said second sampling distribution is different from said first sampling distribution; d. obtaining a second estimate of said attribute based on said second sample; e. determining a lower bound for a variance based upon each of the first sample and the second sample; and f. combining the first sample and the second sample using a variance value for each one of the first sample and the second sample that is equal to or larger than the lower bound for the variance for the first sample and second sample. - View Dependent Claims (2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14)
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15. A computer readable medium contained stored instructions which when executed on a computer causes the computer to perform a method of estimating an attribute of objects comprising:
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a. obtaining a first sample of said objects based on a first sampling distribution; b. obtaining a first estimate of said attribute based on said first sample; c. obtaining a second sample of said objects based on a second sampling distribution, where said second sampling distribution is different from said first sampling distribution; d. obtaining a second estimate of said attribute based on said second sample; e. determining a lower bound for a variance based upon each of the first sample and the second sample; and f. combining the first sample and the second sample using a variance value for each one of the first sample and the second sample that is equal to or larger than the lower bound for the variance for the first sample and second sample. - View Dependent Claims (16, 17, 18, 19)
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Specification