Confidence Intervals for Stereological Estimators with Infinite Variance

Consistent Confidence Intervals for Maximum Pseudolikelihood Estimators

Maximum pseudolikelihood estimation (MPLE) constitutes a computationally efficient and easily implemented alternative to maximum likelihood and simulationbased methods. The MPLE has been shown to be consistent and asymptotically normally distributed in a number of interesting cases. However, the coverage probability of the conventional confidence interval for the MPLE is biased downward. We pro...

Explicit Nonparametric Confidence Intervals for the Variance with Guaranteed Coverage

_________________________________________________________________ In this paper, we provide a method for constructing confidence intervals for the variance that exhibit guaranteed coverage probability for any sample size, uniformly over a wide class of probability distributions. In contrast, standard methods achieve guaranteed coverage only in the limit for a fixed distribution or for any sampl...

Consistency for Least Squares Regression Estimators with Infinite Variance Data

The least squares estimators are discussed for the linear regression model with random predictors. Both predictors and errors may have infinite variance. Under the condition that the predictors are in a stable domain of attraction, we determine necessary and sufficient conditions for weak consistency of the least squares estimators in the simple linear model. The conditions vary, depending on w...

Confidence Intervals Based on Robust Estimators

Honest Confidence Intervals for the Error Variance in Stepwise Regression

An honest confidence interval for the error variance in a stepwise regression is a one-sided interval that adjusts for the effects of variable selection. The endpoint of this interval may be many times larger than the usual endpoint. Such adjustments are most important when selecting variables from a large number of available predictors, particularly in situations with more available predictors...