We consider solutions to the equation detDφ = μ when μ has a doubling property. We prove new geometric characterizations for this doubling property (by means of the so-called engulfing property) and deduce the quantitative behaviour of φ. Also, a constructive approach to the celebrated C-estimates proved by L. Caffarelli is presented, settling one of the open questions posed by C. Villani in [11].

in the early stages of a construction project, the reliability and accuracy of conceptual cost estimates are major concerns for clients and cost engineers. previous studies applied scoring methods and established common rules or mathematical methods to assess the quality of cost estimates. however, those approaches have some limitations in adapting to real-world projects or require understandin...

When studying a prevalent outcome, it is often of interest to estimate the prevalence ratio instead of the odds ratio. In SAS one can use PROC GENMOD with the binomial distribution and the log link function. Unlike the logistic model, the log-binomial model places restrictions on the parameter space, and the maximum likelihood estimate (MLE) might occur on the boundary of the parameter space, i...

In this paper, the range-spread target detection in compound Gaussian clutter with reciprocal of the square root of gamma (RSRG) texture is investigated. The RSRG distribution has been proved to be a good model for texture component of extremely heterogeneous radar clutter. Taking this compound Gaussian model as a spherically invariant random process (SIRP), the Neyman-Pearson optimal detector ...

The fractal dimension estimate for two-variable fractional Brownian motion using the maximum likelihood estimate (MLE) is developed. We formulate a model to describe the two-variable fractional Brownian motion, then derive the likelihood function for that model and estimate the fractal dimension by maximizing the likelihood function. We then compare the MLE with the box-dimension estimation met...

We describe a Monte Carlo method to approximate the maximum likelihood estimate (MLE), when there are missing data and the observed data likelihood is not available in closed form. This method uses simulated missing data that are independent and identically distributed and independent of the observed data. Our Monte Carlo approximation to the MLE is a consistent and asymptotically normal estima...