Ralph Bradley's contributions to the world of statistics fall under two headings: his statistical research (especially the Bradley-Terry Test used extensively in taste testing experiments) and his professional leadership role in statistical science, as evidenced by his development of statistical programs, by his Presidency (1981) of the American Statistical Association and by his editorial efforts. The conversation in Statistical Science (5) provides more details of his views and life.
A general class of Markovian non-Gaussian bifurcating models for cell lineage data is presented. Examples include bifurcating autoregression, random coefficient autoregression, bivariate exponential, bivariate gamma, and bivariate Poisson models. Quasilikelihood estimation for the model parameters and large-sample properties of the estimates are discussed.
Testing a constant mean (no trend) null hypothesis against an increasing alternative is frequently of interest to the time series analyst. Often a linear function is imposed as the alternative trend, sometimes by default as merely the simplest nonconstant function. This paper studies tests for trends with more general shape-restricted alternatives, which include nondecreasing and convex functions. Shape-restricted alternatives comprise a broad range of trends and may be appropriate when the alternative trend structure is not well understood.
Motivation: Detection of differentially expressed genes is one of the major goals of microarray experiments. Pairwise comparison for each gene is not appropriate without controlling the overall (experimentwise) type 1 error rate. Dudoit et al. have advocated use of permutation-based step-down P-value adjustments to correct the observed significance levels for the individual (i.e., for each gene) two sample t-tests.
This article introduces threshold GARCH (1,1) processes to which Box-Cox transformations are applied. This class of processes included nonlinear ARCH and GARCH models as special cases. The model accommodates asymmetries in conditional variances through a "threshold". The stationary solution is explicitly obtained and moment structures are investigated. Estimation for parameters is also discussed.
This paper studies estimation issues for shot noise processes from a process history taken on a discrete-tie lattice. Optimal estimating equation methods are constructed for the case when the impulse response function of the shot process is interval similar; moment-type methods are explored for compactly supported impulse responses. Asymptotic normality of the proposed estimates are established and the limiting covariance of the estimates is derived.
Finite mixtures of generalized linear mixed effect models are presented to handle situations where within-cluster correlation and heterogeneity (subpopulations) exist simultaneously. For this class of models, we consider maximum likelihood (ML) as our main approach to estimation. Due to the complexity of the marginal loglikelihood of this model, the EM algorithm is employed to facilitate computation. The major obstacle in this procedure is to integrate over the random effects' distribution to evaluation the expectation of the E-step.
Over the last decade or so, there has been increasing interest in "zero-inflated" (ZI) regression models to account for "excess" zeros in data. Examples include ZI-Poisson, ZI-Binomial, ZI-Negative Binomial, and ZI-Tobit models. Recently, extensions of these models to the clustered data case have begun to appear. For example, Hall (2000, Biometrics) considered ZI-Poisson and ZI-Binomial models with cluster-specific random effects. In this paper, we consider an alternative approach based on marginal models and generalized estimating equation (GEE) methodology.
In this paper, a single-sample procedure is proposed for obtaining an optimal confidence interval for the largest or smallest mean of several independent normal populations, where the common variance is unknown. It has been found that the optimal confidence interval in the sense of a reducing interval width. This optimal confidence interval is obtained by maximizing the coverage probability with the expected confidence width being fixed at a least favorable configuration of means. Tables of the critical values are given for the optimal confidence interval.
Exact and asymptotic distributions of the maximum likelihood estimator of the autoregressive parameter in a first-order bifurcating autoregressive process with exponential innovations are derived. The limit distributions for the stationary, critical and explosive cases are unified via a single pivot, using a random normalization. The pivot is shown to be asymptotically exponential for all values of the autoregressive parameter.