Academic literature on the topic 'Unbiased interval estimates'

Varoquaux, Gael, and Olivier Colliot. "Evaluating Machine Learning Models and Their Diagnostic Value." In Machine Learning for Brain Disorders. Springer US, 2012. http://dx.doi.org/10.1007/978-1-0716-3195-9_20.

Kuznetsov Nickolay. "Evaluation of the Reliability of Repairable s — t Networks by Fast Simulation Method." In NATO Science for Peace and Security Series - D: Information and Communication Security. IOS Press, 2014. https://doi.org/10.3233/978-1-61499-391-9-120.

Hankin, David G., Michael S. Mohr, and Ken B. Newman. "Equal probability sampling." In Sampling Theory. Oxford University Press, 2019. http://dx.doi.org/10.1093/oso/9780198815792.003.0003.

Hankin, David G., Michael S. Mohr, and Ken B. Newman. "Systematic sampling." In Sampling Theory. Oxford University Press, 2019. http://dx.doi.org/10.1093/oso/9780198815792.003.0004.

"and Var[νˆ ] = 4σ + l ) (l −2(1 + c . Similarly, when σˆ ≤ 0.04, νˆ = δˆ + σˆ − 0.04(c ) (7.12) is an estimate for the constant-scaled metric in accordance with FDA Guidance (2001) using a REML UN model. This estimate is asymptoti-cally normally distributed and unbiased with E[νˆ ] = δ +σ −σ − 0.04(c ) and Var[νˆ ] = 4σ . To assess PBE we ‘plug-in’ estimates of δ and the variance components and calculate the upper bound of an asymptotic 90% confidence interval. If this upper bound is below zero we declare that PBE has been shown. Using the code in Appendix B and the data in Section 7.2, we obtain the value −1.90 for log(AUC) and the value −0.95 for log(Cmax). As both of these are below zero, we can declare that T and R are PBE. 7.5.2 PBE using a replicate design Here we fit the same REML UN model as defined in Section 7.4. Let νˆ = δˆ + σˆ + σˆ − (1 + c )(σˆ + σˆ ) (7.13) be an estimate for the reference-scaled metric in accordance with FDA Guidance (2001) when (σˆ + σˆ > 0.04 and using a REML UN model. Then, this estimate is asymptotically normally distributed, un-biased with E[νˆ ] = δ +σ − (1 + c ) and has variance of Var[νˆ ] = 4σ + l + (1 + c ) (l )+ 2l −2(1+c −2(1 + c + 2(1 + c ) (l ) When σˆ + σˆ ≤ 0.04, let νˆ = δˆ + σˆ + σˆ − (σˆ + σˆ )− 0.04(c ) (7.14) be an estimate for the constant-scaled metric in accordance with FDA." In Design and Analysis of Cross-Over Trials. Chapman and Hall/CRC, 2003. http://dx.doi.org/10.1201/9781420036091-24.

"Guidance FDA (2001) using a REML UN model. Then, this estimate is asymptotically normally distributed, unbiased with E[νˆ ] = δ +σ − (σ )− 0.04(c ) and has variance of Var[νˆ ] = 4σ δ + l + 2l − 2l + 2l To assess PBE we ‘plug-in’ estimates of δ and the variance components and calculate the upper bound of an asymptotic 90% confidence interval. If this upper bound is below zero we declare that PBE has been shown. Using the code in Appendix B and the data in Section 7.4, we obtain the value −0.24 for log(AUC) and the value −0.19 for log(Cmax). As both of these are below zero, we can declare that T and R are PBE. 7.6 ABE for a replicate design Although ABE can be assessed using a 2× 2 design, it can also be as-sessed using a replicate design. If a replicate design is used the number of subjects can be reduced to up to half that required for a 2 × 2 de-sign. In addition it permits the estimation of σ and σ . The SAS code to assess ABE for a replicate design is given in Appendix B. Using the data from Section 7.4, the 90% confidence interval for µ is (−0.1697,−0.0155) for log(AUC) and (−0.2474,−0.0505) for log(Cmax). Exponentiating the limits to obtain confidence limits for exp(µ ), gives (0.8439,0.9846) for AUC and (0.7808,0.9508) for Cmax. Only the first of these intervals is contained within the limits of 0.8 to 1.25, there-fore T cannot be considered average bioequivalent to R. To calculate the power for a replicate design with four periods and with a total of n subjects we can still use the SAS code given in Section 7.3, if we alter the formula for the variance of a difference of two obser-vations from the same subject. This will now be σ +σ instead of σ , where σ is the subject-by-formulation interaction. Note the use of σ rather than 2σ as used in the RT/TR design. This is a result of the estimator using the average of two measurements on each treatment on each subject. One advantage of using a replicate design is that the number of sub-jects needed can be much smaller than that needed for a 2×2 design. As an example, suppose that σ = 0, and we take σ = 0.355 and α = 0.05, as done in Section 7.3. Then a power of 90.5% can be achieved with only 30 subjects, which is about half the number (58) needed for the 2 × 2 design." In Design and Analysis of Cross-Over Trials. Chapman and Hall/CRC, 2003. http://dx.doi.org/10.1201/9781420036091-25.

"ances and covariances obtained from REML are normally distributed with expectation vector and variance-covariance matrix equal to the fol-low  ing, r  espectiv    ely,   When σˆ > 0.04, let νˆ = δˆ + σˆ + σˆ − 2ωˆ + σˆ − (1 + c (7.6) be an estimate for the (7.3) reference-scaled metric in accordance with FDA Guidance (2001) and using a REML UN model. Then (Patter-son, 2003; Patterson and Jones, 2002b), this estimate is asymptotically normally distributed and unbiased with E[νˆ ] = δ +σ − (1 + c and Var[νˆ ] = 4σ + l + 4l + (1 + c ) (l )+ 2l −2(1+c − 2(1+c +4(1+c −2(1+c . Similarly, for the constant-scaled metric, when σˆ ≤ 0.04, νˆ = δˆ + σˆ + σˆ − 2ωˆ + σˆ − σˆ − 0.04(c ) (7.7) E[νˆ ] = δ +σ − 0.04(c ) Var[νˆ ] = 4σ + l + 4l + 2l − 2l − 4l + 4l − 2l . The required asymptotic upper bound √ of the 90% confidence interval can √ then be calculated as νˆ + 1.645× V̂ ar[νˆ ] or νˆ + 1.645× V̂ ar[νˆ ], where the variances are obtained by ‘plugging in’ the estimated values of the variances and covariances obtained from SAS proc mixed into the formulae for Var[νˆ ] or Var[νˆ ]. The necessary SAS code to do this is given in Appendix B. The output reveals that σˆ = 0.0714 and the upper bound is−0.060 for log(AUC). For log(Cmax), σˆ = 0.1060 and the upper bound is −0.055. As both of these upper bounds are below zero, IBE can be claimed." In Design and Analysis of Cross-Over Trials. Chapman and Hall/CRC, 2003. http://dx.doi.org/10.1201/9781420036091-22.

"strate IBE the upper bound of a 90% confidence interval for the above aggregate metric must fall below 2.49. The required upper bound can be calculated in at least three different ways: (1) method-of-moments estimation with a Cornish-Fisher approx-imation (Hyslop et al., 2000; FDA Guidance, 2001), (2) bootstrapping (FDA Guidance, 1997), and (3) by asymptotic approximations to the mean and variance of ν and ν (Patterson, 2003; Patterson and Jones, 2002b,c). Method (1) derives from theory that assumes the inde-pendence of chi-squared variables and is more appropriate to the analysis of a parallel group design. Hence it does not fully account for the within-subject correlation that is present in data obtained from cross-over tri-als. Moreover, the approach is potentially sensitive to bias introduced by missing data and imbalance in the study data (Patterson and Jones, 2002c). Method (2), which uses the nonparametric percentile bootstrap method (Efron and Tibshirani, 1993), was the earliest suggested method of calculating the upper bound (FDA Guidance, 1997), but it has sev-eral disadvantages. Among these are that it is computationally intensive and it introduces randomness into the final calculated upper bound. Re-cent modifications to ensure consistency of the bootstrap (Shao et al., 2000) do not appear to protect the Type I error rate (Patterson and Jones, 2002c) around the mixed-scaling cut-off (0.04) unless calibration (Efron and Tibshirani, 1993) is used. Use of such a calibration technique is questionable if one is making a regulatory submission. Hence, we pre-fer to use method (3) and will illustrate its use shortly. We note that this method appears to protect against inflation of the Type I error rate in IBE and PBE testing, and the use of REML ensures unbiased esti-mates (Patterson and Jones, 2002c) in data sets with missing data and imbalance, a common occurrence in cross-over designs, (Patterson and Jones, 2002a,b). In general (Patterson and Jones, 2002a), cross-over tri-als that have been used to test for IBE and PBE have used sample sizes in excess of 20 to 30 subjects, so asymptotic testing is not unreasonable, and there is a precedent for the use of such procedures in the study of pharmacokinetics (Machado et al., 1999). We present findings here based on asymptotic normal theory using REML and not taking into account shrinkage (Patterson and Jones, 2002b,c). It is possible to account for this factor using the approach of Harville and Jeske (1992); see also Ken-ward and Roger (1997). However, this approach is not considered here in the interests of space and as the approach described below appears to control the Type I error rate for sample sizes as low as 16 (Patterson and Jones, 2002c). In a 2 × 2 cross-over trial it is not possible to estimate separately the within-and between-subject variances and hence a replicate design, where subjects receiving each formulation more than once is required." In Design and Analysis of Cross-Over Trials. Chapman and Hall/CRC, 2003. http://dx.doi.org/10.1201/9781420036091-19.

Zhang, Yunong, and Kaisi Huang. "Unbiased Estimators for Uniform Distribution Applied to Interval Estimation of Transition or Beginning Year About World Reserve Currency." In 2024 20th International Conference on Natural Computation, Fuzzy Systems and Knowledge Discovery (ICNC-FSKD). IEEE, 2024. http://dx.doi.org/10.1109/icnc-fskd64080.2024.10702315.

Laeri, Franco, and André Noack. "Maximum Entropy Analysis of Dynamic Light Scattering Signals." In Optical Fabrication and Testing. Optica Publishing Group, 1988. http://dx.doi.org/10.1364/oft.1988.tha11.

Munoz-diaz, Jorge, and Oscar Ibarra-manzano. "Determining optimum sampling intervals for the local clock states estimated with an unbiased fir algorithm: an applied software." In 2006 Multiconference on Electronics and Photonics. IEEE, 2006. http://dx.doi.org/10.1109/mep.2006.335645.

Passano, Elizabeth, and Philippe Mainc¸on. "Estimating Long-Term Distributions of Extreme Response of a Catenary Riser." In ASME 2011 30th International Conference on Ocean, Offshore and Arctic Engineering. ASMEDC, 2011. http://dx.doi.org/10.1115/omae2011-50151.

Grosu, Corina, and Marta Grosu. "FAKE WARNING: PLAYING WITH IMPRECISE PREDICTIONS." In eLSE 2018. ADL Romania, 2018. http://dx.doi.org/10.12753/2066-026x-18-037.

Kevin, D. A., V. J. Aimikhe, and C. C. Ikeokwu. "A Machine Learning Approach to Determining the CO2 Adsorption Capacity of Coconut Shell-Derived Activated Carbon." In SPE Nigeria Annual International Conference and Exhibition. SPE, 2024. http://dx.doi.org/10.2118/221740-ms.

Sviridov, Mikhail, Dmitry Kushnir, Anton Mosin, Danil Nemuschenko, and Michael Rabinovich. "High-Performance Stochastic Inversion for Real-Time Processing of LWD Ultradeep Azimuthal Resistivity Data." In 2023 SPWLA 64th Annual Symposium. Society of Petrophysicists and Well Log Analysts, 2023. http://dx.doi.org/10.30632/spwla-2023-0082.

Sudev, L. J., and H. V. Ravindra. "Tool Wear Estimation in Drilling Using Acoustic Emission Signal by Multiple Regression and GMDH." In ASME 2008 International Mechanical Engineering Congress and Exposition. ASMEDC, 2008. http://dx.doi.org/10.1115/imece2008-66756.

Sviridov, Mikhail, Anton Mosin, Sergey Lebedev, and Ron Thompson. "VENDOR-NEUTRAL STOCHASTIC INVERSION OF LWD DEEP AZIMUTHAL RESISTIVITY DATA AS A STEP TOWARD EFFICIENCY STANDARDIZATION OF GEOSTEERING SERVICES." In 2021 SPWLA 62nd Annual Logging Symposium Online. Society of Petrophysicists and Well Log Analysts, 2021. http://dx.doi.org/10.30632/spwla-2021-0103.

Zhang, Junjing, Manabu Nozaki, Nola R. Zwarich, et al. "Improved Evaluation Methodology of Fractured Horizontal Well Performance: New Method to Measure the Effect of Gel Damage and Cyclic Stress on Fracture Conductivity." In SPE Western Regional Meeting. SPE, 2023. http://dx.doi.org/10.2118/212977-ms.

Kott, Phillip S. The Degrees of Freedom of a Variance Estimator in a Probability Sample. RTI Press, 2020. http://dx.doi.org/10.3768/rtipress.2020.mr.0043.2008.

Weller, Joel I., Ignacy Misztal, and Micha Ron. Optimization of methodology for genomic selection of moderate and large dairy cattle populations. United States Department of Agriculture, 2015. http://dx.doi.org/10.32747/2015.7594404.bard.