Bias-corrected Maximum Likelihood Estimator Research Articles

Is the minimum chi-square estimator the winner in logit regression?

Abstract Amemiya (1980) showed that the bias-corrected maximum likelihood estimator has a smaller n−2-order MSE matrix than minimum chi-square in a general logit model. In this paper the exact MSE is calculated for both estimators for Berkson's (1995) examples. The bias-corrected maximum likelihood has a smaller exact MSE provided that Berkson's 2n-rule is used in the calculation of the exact results. The margin by which the exact MSE of minimum chi-square exceeds that of bias-corrected maximum likelihood is small, and hence there may be no practical advantage in using the latter estimator.

Bias-corrected maximum likelihood estimator of a log common odds ratio

SUMMARY A bias-correction factor for the maximum likelihood estimator of the log common odds ratio for sparse data is derived, which is applicable when the design is balanced and/or when the number of strata is large. The corrected maximum likelihood estimator is practically unbiased and its mean squared error is smaller than that of the uncorrected maximum likelihood estimator. The correction factor for the maximum likelihood estimator approaches one as strata sizes increase. Examples demonstrate that the corrected maximum likelihood estimator and the exact conditional maximum likelihood estimator are essentially identical although the standard error of the former tends to be slightly smaller than that of the latter. It is also demonstrated that a simple version of the correction factor is a satisfactory approximation. The bias-corrected maximum likelihood estimator proposed in this paper is the extension of Breslow's (1981) and it can be useful particularly when the computational burden of the exact conditional method is excessive.

Failure-Censored Variables-Sampling Plans for Lognormal and Weibull Distributions

Variables-sampling plans arc more efficient than attributes-sampling plans. If the quality characteristic is the life of a product. however, variables sampling can be very time consuming and expensive. To save time and money, tests can be terminated before all test units have failed. This article discusses the design of variables-sampling plans based on failure-censored samples. This method of design can be applied to lognormal-distributed and Wcibull-distributed lifetimes. An example for lognormal-distributed lifetimes will be given. Although the method is based on asymptotic results, Monte Carlo simulations for lognormal and Weibull lifetimes show that the sampling plans meet the required risks when bias corrected maximum likelihood estimators for the location and scale parameters are used. The advantage of failurecensored sampling plans is that they require a much smaller sample size than attributes-sampling plans and a greatly reduced test time when compared to complete variables-sampling plans.

Failure-Censored Variables-Sampling Plans for Lognormal and Weibull Distributions

Variables-sampling plans arc more efficient than attributes-sampling plans. If the quality characteristic is the life of a product. however, variables sampling can be very time consuming and expensive. To save time and money, tests can be terminated before all test units have failed. This article discusses the design of variables-sampling plans based on failure-censored samples. This method of design can be applied to lognormal-distributed and Wcibull-distributed lifetimes. An example for lognormal-distributed lifetimes will be given. Although the method is based on asymptotic results, Monte Carlo simulations for lognormal and Weibull lifetimes show that the sampling plans meet the required risks when bias corrected maximum likelihood estimators for the location and scale parameters are used. The advantage of failurecensored sampling plans is that they require a much smaller sample size than attributes-sampling plans and a greatly reduced test time when compared to complete variables-sampling plans.