The phenomenon of separation or monotone likelihood is observed in the fitting process of a logistic model if the likelihood converges while at least one parameter estimate diverges to +/- infinity. Separation primarily occurs in small samples with several unbalanced and highly predictive risk factors. A procedure by Firth originally developed to reduce the bias of maximum likelihood estimates ...

The characteristic function of the folded normal distribution and its moment function are derived. The entropy of the folded normal distribution and the Kullback–Leibler from the normal and half normal distributions are approximated using Taylor series. The accuracy of the results are also assessed using different criteria. The maximum likelihood estimates and confidence intervals for the param...

using quarterly data from 2002:1 to 2013:2 we study the persistence in the inflation rates in iran based on the total cpi and the cpi in 12 subgroups. the persistence is investigated using two different tools: (i) the adf unit root test and (ii) bootstrap confidence intervals. we calculate a 90% confidence interval for the sum of the autoregressive coefficients, as a measure of persistence, usi...

Abstract: In this paper the geometric process is used for the analysis of accelerated life testing for Marshall-Olkin Extended Exponential (MOEE) distribution using Type I censored data. Assuming that the lifetimes under increasing stress levels form a geometric process, the parameters are estimated by using the maximum likelihood method and the original parameters instead of the developing inf...

Optimization methods have been widely applied in statistics. Among them, capability measuring techniques are widely applied in industries. Process Capability Indices (PCIs) have been proposed for measuring process production capability. This paper concentrates, the lower and upper confidence limits for the PCIs are obtained from generalized pivotal quantity of random model and also, use this co...

We construct bootstrap confidence intervals for smoothing spline and smoothing spline ANOVA estimates based on Gaussian data, and penalized likelihood smoothing spline estimates based on data from exponential families. Several variations of bootstrap confidence intervals are considered and compared. We find that the commonly used bootstrap percentile intervals are inferior to the T intervals an...

This paper focuses on different methods of estimation and forecasting in first-order integer-valued autoregressive processes with Poisson-Lindley (PLINAR(1)) marginal distribution. For this purpose, the parameters of the model are estimated using Whittle, maximum empirical likelihood and sieve bootstrap methods. Moreover, Bayesian and sieve bootstrap forecasting methods are proposed and predict...

Recently, there has been a lot of interest in statistical methods for analyzing data with surrogate endpoints. In this article, we consider parameter estimation from a model that relates a variable Y to a set of covariates, X, in the presence of a surrogate, S. We assume that the data are made up of two random samples from the population, a validation set where (Y,X,S) are observed on every sub...

The use of parameter-rich substitution models in molecular phylogenetics has been criticized on the basis that these models can cause a reduction both in accuracy and in the ability to discriminate among competing topologies. We have explored the relationship between nucleotide substitution model complexity and nonparametric bootstrap support under maximum likelihood (ML) for six data sets for ...