The traditional three-step procedure for correcting for heteroskedasticity uses a consistent but biased estimator for the variances 2 t in enacting the second step. An estimator is developed here that is unbiased in the presence of heteroskedasticity. Its behavior is examined along with the traditional estimator and another known to be unbiased in the absence of heteroskedasticity. The behavior...

Schaefer et al. [15] proposed a ridge logistic estimator in logistic regression model. In this paper a new estimator based on the ridge logistic estimator is introduced in logistic regression model and we call it as almost unbiased ridge logistic estimator. The performance of the new estimator over the ridge logistic estimator and the maximum likelihood estimator in scalar mean squared error cr...

We derive Monte Carlo-amenable solutions to the problem of unbiased estimation of a nonlinear function of the mean of a normal distribution. For most nonlinear functions the maximum likelihood estimator is biased. Our method yields a Monte Carlo approximation to the uniformly minimum variance unbiased estimator for a wide class of nonlinear functions. Applications to problems arising in the ana...

We handle two major issues in applying extreme value analysis to financial time series, bias and serial dependence, jointly. This is achieved by studying bias correction method when observations exhibit weakly serial dependence, namely the β−mixing series. For estimating the extreme value index, we propose an asymptotically unbiased estimator and prove its asymptotic normality under the β−mixin...

Stochastic neurons can be useful for a number of reasons in deep learning models, but in many cases they pose a challenging problem: how to estimate the gradient of a loss function with respect to the input of such stochastic neurons, i.e., can we “back-propagate” through these stochastic neurons? We examine this question, existing approaches, and present two novel families of solutions, applic...

Let X1,X2, . . . ,Xn be a random sample from a normal N(θ,σ2) distribution with an unknown mean θ = 0,±1,±2, . . . . Hammersley (1950) proposed the maximum likelihood estimator (MLE) d = [Xn], nearest integer to the sample mean, as an unbiased estimator of θ and extended the Cramér-Rao inequality. The Hammersley lower bound for the variance of any unbiased estimator of θ is significantly improv...

Random samples are extensively used to summarize massive data sets and facilitate scalable analytics. Coordinated sampling, where samples of different data sets “share” the randomization, is a powerful method which facilitates more accurate estimation of many aggregates and similarity measures. We recently formulated a model of Monotone Estimation Problems (MEP), which can be applied to coordin...