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 ∈ ...

Abstract Product advertising captures the attention not only of consumers but also investors. Constructing a measure local investment interest in stocks from Google searches and using Super Bowl as an experiment, we study effects expenses on investor attention. We find that post‐game Monday investors areas with high viewership increases significantly for both non‐local companies air commercials...

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...

dioxin-related compounds are associated with teratogenic and mutagenic risks in laboratory animals, and result in adverse pregnancy outcomes. however, there were inconsistent results in epidemiology studies. in view of this difference, we conducted a systematic review and meta-analysis to examine this association and to assess the heterogeneity among studies. comprehensive literature searches w...

OBJECTIVES Expert judgement of exposure levels is often only poorly or moderately correlated with directly measured levels. For a follow-up of a historical cohort study at a Söderberg aluminum smelter we updated an expert-based semiquantitative job exposure matrix of coal tar pitch volatiles (CTPV) to quantitative estimates of CTPV and benzo(a)pyrene (BaP). METHODS Mixed effects models to pre...

OBJECTIVES To address questions surrounding noise-induced hearing loss (NIHL) from variable noise, we have been evaluating noise exposures and changes in hearing in a prospective cohort of construction workers (representing eight trades) and controls. In this paper, we develop and explore several long-term exposure estimates for cohort members. METHODS We followed cohort members between 1999 ...

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).