Note on the existence and modulus of continuity of the {\textit{SLE}}_8 curve

We review one method for estimating the modulus of continuity of a Schramm–Loewner evolution (SLE) curve in terms of the inverse Loewner map. Then we prove estimates about the distribution of the inverse Loewner map, which underpin the difficulty in bounding the modulus of continuity of SLE for $\kappa =8$ . The main idea in the proof of these estimates is applying the Girsanov theorem to reduce the problem to estimates about one-dimensional Brownian motion.     

Akaike-type criteria and the reliability of inference: Model selection versus statistical model specification

Since the 1990s, the Akaike Information Criterion (AIC) and its various modifications/extensions, including BIC, have found wide applicability in econometrics as objective procedures that can be used to select parsimonious statistical models. The aim of this paper is to argue that these model selection procedures invariably give rise to unreliable inferences, primarily because their choice within a prespecified family of models (a) assumes away the problem of model validation, and (b) ignores the relevant error probabilities. This paper argues for a return to the original statistical model specification problem, as envisaged by Fisher (1922), where the task is understood as one of selecting a statistical model in such a way as to render the particular data a truly typical realization of the stochastic process specified by the model in question. The key to addressing this problem is to replace trading goodness-of-fit against parsimony with statistical adequacy as the sole criterion for when a fitted model accounts for the regularities in the data.     

Estimation of P[Y < X] for generalized exponential distribution

This paper deals with the estimation of P[Y < X] when X and Y are two independent generalized exponential distributions with different shape parameters but having the same scale parameters. The maximum likelihood estimator and its asymptotic distribution is obtained. The asymptotic distribution is used to construct an asymptotic confidence interval of P[Y < X]. Assuming that the common scale parameter is known, the maximum likelihood estimator, uniformly minimum variance unbiased estimator and Bayes estimator of P[Y < X] are obtained. Different confidence intervals are proposed. Monte Carlo simulations are performed to compare the different proposed methods. Analysis of a simulated data set has also been presented for illustrative purposes.Part of the work was supported by a grant from the Natural Sciences and Engineering Research Council     

An information theoretic argument for the validity of the exponential model

Based on the Cramér-Rao inequality (in the multiparameter case) the lower bound of Fisher information matrix is achieved if and only if the underlying distribution is ther-parameter exponential family. This family and the lower bound of Fisher information matrix are characterized when some constraints in the form of expected values of some statistics are available. If we combine the previous results we can find the class of parametric functions and the corresponding UMVU estimators via Cramér-Rao inequality.     

Likelihood ratio tests for model selection of stochastic frontier models

An important issue when conducting stochastic frontier analysis is how to choose a proper parametric model, which includes choices of the functional form of the frontier function, distributions of the composite errors, and also the exogenous variables. In this paper, we extend the likelihood ratio test of Vuong, Econometrica 57(2):307–333, (1989) and Takeuchi’s, Suri-Kagaku (Math Sci) 153:12–18, (1976) model selection criterion to the stochastic frontier models. The most attractive feature of this test is that it can not only be used for testing a non-nested model, but also still be applicable even when the general model is misspecified. Finally, we also demonstrate how to apply this test to the Indian farm data used by Battese and Coelli, J Prod Anal 3:153–169, (1992), Empir Econ 20(2):325–332, (1995) and Alvarez et al., J Prod Anal 25:201–212, (2006).     

A multiobjective model for the selection and timing of public enterprise projects

In theory, a public utility company improves the quality of community life through its projects and actions. However, project selection and prioritization by these companies are highly complex processes. To assist company planning managers in such processes, we propose a mixed integer programming model that selects, from a bank of projects, which are worthy of investment. The question of timing is also addressed. The model maximizes a weighted sum of normalized economic and financial net present values and a social impact index. It simultaneously satisfies a set of precedence relations among projects, the earliest and latest project start dates, exogenous budget limits, and endogenous project cash flow generation. We illustrate the model's effectiveness using an example constructed from a case study of a major Latin American water and sewage company.     

A finite selection model for experimental design of the health insurance study

This paper is concerned with the problem of estimating the parameters of the standard linear model from grouped data, or more generally from aggregated data. A number of alternative solutions are suggested and compared.     

Use of a Markov decision process model for treatment selection in an asymptomatic disease with consideration of risk sensitivity

Some potentially dangerous diseases are completely asymptomatic. Their diagnosis as incidental findings of ever-more-sensitive medical imaging can leave patients and physicians in something of a quandary. The patient feels well, and potential interventions to stave off long-term deterioration or death bring with them immediate risks. We discuss the use of a Markov Decision Process (MDP) model (rather than Monte Carlo simulation of a Markov Model) to create a tool for analyzing individual treatment decisions for asymptomatic chronic diseases where a patient’s condition cannot improve. We formulate a finite-horizon MDP model to determine optimal treatment plans and discuss three distinct optimality criteria: (a) maximizing expected quality-adjusted-life years with and without discounting, (b) maximizing the expected number of life years in good health, and (c) maximizing the expected utility for number of years in good health. In (c) we assume exponential utility and consider different risk aversion factors reported in the medical literature. We illustrate the model’s use by considering asymptomatic intracranial aneurysm. Our model builds on a simulation model [19] created to examine treatment recommendations based on cost-effectiveness. We demonstrate that incorporating risk aversion leads to “no treatment” recommendations for some types of aneurysm. Furthermore, the use of alternate patient-selected criteria leads to recommendations that vary from [19] in several scenarios. We also discuss the use of the software as a decision support tool to help make individualized treatment recommendations and demonstrate that the computational performance of the algorithm makes its use feasible during a short office visit.