In this paper, we study adaptive nonparametric regression estimation in the presence of conditional heteroskedastic error terms. We demonstrate that both the conditional mean and conditional variance functions in a nonparametric regression model can be estimated adaptively based on the local profile likelihood principle. Both the one-step Newton-Raphson estimator and the local profile likelihoo...

Under the setting of a case-cohort design, covariate values are ascertained for a smaller subgroup of the original study cohort which typically is a representative sample from a population. Individuals with a specific event outcome are selected to the second stage study group as cases and an additional subsample is selected to act as a control group. We carry out analysis of such a design using...

Estimation methods are proposed for fitting logistic regression in which outcome and covariate variables are missing separately or simultaneously. One of the two proposed estimators is an extension of the validation likelihood estimator of BreslowandCain (1988). The other is a joint conditional likelihood estimator that uses both validation and nonvalidation data. Large sample properties of the...

It is shown empirically that mixed autoregressive moving average regression models with generalized autoregressive conditional heteroskedasticity (Reg-ARMA-GARCH models) can have multimodality in the likelihood that is caused by a dummy variable in the conditional mean. Maximum likelihood estimates at the local and global modes are investigated and turn out to be qualitatively different, leadin...

Analyses of data using Rasch models, including the special case of matched case-control studies, are common applications of conditional likelihood in which the usual inferential procedures are applied only after conditioning on an approximately ancillary statistic. Another common approach to the analysis of Rasch models is to integrate the nuisance parameters over a mixing distribution, using t...

In this paper, the problem of predicting times to failure of units censored in multiple stages of progressively hybrid censoring for the proportional hazards family is considered. We discuss different classical predictors. The best unbiased predictor ($BUP$), the maximum likelihood predictor ($MLP$) and conditional median predictor ($CMP$) are all derived. As an example, the obtained results ar...

Suppose we observe an ergodic Markov chain on the real line, with a parametric model for the autoregression function, i.e. the conditional mean of the transition distribution. If one speciies, in addition, a paramet-ric model for the conditional variance, one can deene a simple estimator for the parameter, the maximum quasi-likelihood estimator. It is robust against misspeciication of the condi...

This paper compares two different ways of estimating statistical language models. Many statistical NLP tagging and parsing models are estimated by maximizing the (joint) likelihood of the fully-observed training data. However, since these applications only require the conditional probability distributions, these distributions can in principle be learnt by maximizing the conditional likelihood o...