In this paper, we introduce a new multivariate Weibull (MVW) distribution with many interesting properties. We obtain the maximum likelihood estimate (MLE) of the parameters and their asymptotic multivariate normal (AMVN) distribution in MVWmodel. We propose large sample studentized tests for testing multivariate exponentiality and also tests for independence and identical marginals of the comp...

The maximum likelihood approach to jointly model the survival time and its longitudinal covariates has been successful to model both processes in longitudinal studies. Random effects in the longitudinal process are often used to model the survival times through a proportional hazards model, and this invokes an EM algorithm to search for the maximum likelihood estimates (MLEs). Several intriguin...

A general simulation procedure is described to validate model fitting algorithms for complex likelihood functions that are utilized in periodic cancer screening trials. Although screening programs have existed for a few decades, there are still many unsolved problems, such as how age or hormone affects the screening sensitivity, the sojourn time in the preclinical state, and the transition prob...

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...

The classical Schauder type results on C-regularity of solutions are exposed for linear second order elliptic equations with Hölder coefficients. Our approach is based on equivalent seminorms in Hölder spaces C, which are similar to seminorms introduced by S. Campanato [1]. Under this approach, the C-estimates for solutions are derived from the maximum principle and the interior smoothness of h...

In this paper, we study the maximum likelihood estimates (MLEs) of expected frequencies under a loop order restriction in an I × J contingency table. Some properties of the MLEs are given and an algorithm for computing the MLEs is detailed. The proposed methods are illustrated by using the data from Wing (1962).