This article constructs a consistent robust estimator of mixture complexity based on a random sample of counts distributed according to a probability mass function whose exact form is unknown but is postulated to be close to members of some parametric family of finite mixtures. Following the approach of Woo and Sriram (2004), we develop a robust estimator of mixture complexity using Minimum Hellinger distances, when all the parameters associated with the mixture model are unknown.
Abstract not available.
In multistage models, individuals (or experimental units) move through a succession of "stages" corresponding to distinct states. The resulting data can be considered to be a form of multivariate survival data containing information about the transition times and the stages occupied. Traditional survival analysis is the simplest example of a multistage model, where individuals begin in an initial stage (say, alive) and may move irreversibly to a second stage (death).
Assuming a general linear model with unknown and possibly unequal normal error variances, the interest is to develop a one-sample procedure to handle the hypothesis testing on all, partial, or a subset of regression parameters.
For finite mixtures, consistent estimation of number of components, known as mixture complexity, is considered based on a random sample of counts distributed according to a probability mass function, whose exact form is unknown but is postulated to be close to members of some parametric family of finite mixtures. Following a recent approach of Woo and Sriram (2004), we develop a robust estimator of mixture complexity using Minimum Hellinger distance, when all the parameters associated with the mixture model are unknown. The estimator is shown to be consistent.
This paper studies the ordinary least squares trend estimator in a simple linear regression under the setting of multiple known changepoint times. The error component in the model is allowed to be a general short-memory stationary autocorrelated series. Consistency and asymptotic normality of the estimator is established and its limiting properties are quantified. An example in climatology is given where the multiple changepoint aspect is key.
The asymptotic distribution of the test statistic for testing the dimensionality in the sir-II method is derived and shown to be a linear combination of chi-squared random variables under weak assumptions. This statistic is based on Li's (1991) sequential test statistic for sliced inverse regression (sir). Also presented is a simulation study of the result.
We consider the problem of predicting cancer patient survival time from the gene expression profile of their tumor samples. The partial least squares methodology has been modified to account for right censoring. Performances of three approaches: reweighting, mean imputation and multiple imputation, to handle right censored data, are studied in a detailed simulation study against the benchmark of standard PLS had there been no censoring. It is shown that both imputation schemes perform very similarly and are better than reweighting.
Rogers gives three cases of infinite continued fractions which terminate for certain parameter values. We have analyzed the associated integrals and produced equivalent rational factor ratios.
A simple graphic, the "inverted q-q plot," enables visualization of the monotonic function that transforms data to a desired target distribution. An important special case is use of the Box-Cox family to transform data to a normal distribution. This graphic can be used to develop novel estimates of parameters in a transformation. We describe here the asymptotic properties of these parameter estimates.