The statistical difficulties of estimating cancer risks from low doses of a carcinogen are illustrated by examples from radiation carcinogenesis. Although more is known about dose-response relationships for ionizing radiation than for any other environmental carcinogen, estimates of cancer risk from low radiation doses have been extremely controversial; disagreements by factors of 100 or more a...

This is a statisticalmodel (the “multiple logistic model”) for pooling data from many variables into a single probability estimate that a person examined in a health screening system requires medical care. Because discrete variables are frequently studied in health screening programs, the required assumption of multivariate normality of the predictor variables related to many statistical techni...

In this paper, we prove uniform Morrey-Campanato type estimates for this equation, using a multiplier method borrowed from [9]. These bounds encode in the optimal way the decay: |u(x)| ∼ 1/|x| d−1 2 at infinity of the solution u. They imply weighted L-estimates for the solution u. We also prove a uniform L-estimate without weight for the trace of the solution on the interface, which states that...

3.1 Maximum likelihood estimates — in exponential families. Let (X, B) be a measurable space and {P θ , θ ∈ Θ} a measurable family of laws on (X, B), dominated by a σ-finite measure v. Let f (θ, x) be a jointly measurable version of the density (dP θ /dv)(x) by Theorem 1.3.3. For each x ∈ X, a maximum likelihood estimate (MLE) of θ is any θ ˆ = θ ˆ (x) such that f (ˆ θ, x) = sup{f (φ, x) : φ ∈ ...

We suggest an iterative approach to computing K-step maximum likelihood estimates (MLE) of the parametric components in semiparametric models based on their profile likelihoods. The higher order convergence rate of K-step MLE mainly depends on the precision of its initial estimate and the convergence rate of the nuisance functional parameter in the semiparametric model. Moreover, we can show th...

Point estimation for the selected treatment in a two-stage drop-the-loser trial is not straightforward because a substantial bias can be induced in the standard maximum likelihood estimate (MLE) through the first stage selection process. Research has generally focused on alternative estimation strategies that apply a bias correction to the MLE; however, such estimators can have a large mean squ...