Multistage estimation of the difference of locations of two negative exponential populations under a modified Linex loss function: Real data illustrations from cancer studies and reliability analysis
Bibliographic record
Abstract
We have designed modified two-stage and purely sequential strategies to estimate the difference of location parameters from two independent negative exponential populations having unknown but proportional scale parameters under a modified Linex loss function. This article extends one-sample methodologies of Mukhopadhyay and Bapat (2016 Mukhopadhyay, N. and Bapat, S. R. (2016). Multistage Point Estimation Methodologies for a Negative Exponential Location under a Modified Linex Loss Function: Illustrations with Infant Mortality and Bone Marrow Data, Sequential Analysis 35: 175–206. http://dx.doi.org/10.1080/07474946.2016.1165532.[Taylor & Francis Online], [Web of Science ®] , [Google Scholar], Sequential Analysis). Some preliminary results are established along the lines of Mukhopadhyay and Hamdy (1984 Mukhopadhyay, N. and Hamdy, H. I. (1984). On Estimating the Difference of Location Parameters of Two Negative Exponential Distributions, Canadian Journal of Statistics 12: 67–76.[Crossref] , [Google Scholar], Canadian Journal of Statistics) and Mukhopadhyay and Darmanto (1988 Mukhopadhyay, N. and Darmanto, S. (1988). Sequential Estimation of the Difference of Means of Two Negative Exponential Populations, Sequential Analysis 7: 165–190.[Taylor & Francis Online] , [Google Scholar], Sequential Analysis). We have resorted to Mukhopadhyay and Duggan (1997 Mukhopadhyay, N. and Duggan, W. T. (1997). Can a Two-Stage Procedure Enjoy Second Order Properties? Sankhya, Series A 59: 435–448. [Google Scholar], Sankhya, Series A) in developing asymptotic second-order properties for the modified two-stage methodology and to nonlinear renewal theory of Lai and Siegmund (1977 Lai, T. L. and Siegmund, D. (1977). A Nonlinear Renewal Theory with Applications to Sequential Analysis I, Annals of Statistics 5: 946–954.[Crossref], [Web of Science ®] , [Google Scholar], 1979 Lai, T. L. and Siegmund, D. (1979). A Nonlinear Renewal Theory with Applications to Sequential Analysis II, Annals of Statistics 7: 60–76.[Crossref], [Web of Science ®] , [Google Scholar], Annals of Statistics) and Woodroofe (1977 Woodroofe, M. (1977). Second Order Approximation for Sequential Point and Interval Estimation, Annals of Statistics 5: 984–995.[Crossref], [Web of Science ®] , [Google Scholar], Annals of Statistics) in addressing analogous properties under the purely sequential methodology. Then, we supplement with extensive sets of data analysis via computer simulations validating that both modified two-stage and purely sequential methods perform very well. Both methodologies are also illustrated and implemented using real datasets from cancer studies and reliability analysis.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.021 | 0.045 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.002 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.002 | 0.002 |
| Insufficient payload (model declined to judge) | 0.002 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".