In clinical trials with multiple visits, dropouts often occur and the population of patients who dropped out may be different from the population of patients who completed the study. To assess treatment effects over the population of all randomized patients, which is called the intention-to-treat analysis and is required by regulatory agencies, last observation analysis (LOAN) focuses on the la...

MOTIVATION To improve the understanding of molecular regulation events, various approaches have been developed for deducing gene regulatory networks from mRNA expression data. RESULTS We present a new score for network inference, η(2), that is derived from an analysis of variance. Candidate transcription factor:target gene (TF:TG) relationships are assumed more likely if the expression of TF ...

Extended Linear Models, Multivariate Splines and ANOVA by Mark Henry Hansen Doctor of Philosophy in Statistics University of California at Berkeley Professor Charles J. Stone, Chair In this dissertation, we pursue a theoretical investigation into several aspects of multivariate function estimation. In general, we con ne ourselves to estimators that are smooth, piecewise polynomial functions, or...

Ito processes are the most common form of continuous semimartingales, and include diffusion processes. The paper is concerned with the nonparametric regression relationship between two such Ito processes. We are interested in the quadratic variation (integrated volatility) of the residual in this regression, over a unit of time (such as a day). A main conceptual finding is that this quadratic v...

Piecewise linear convex functions arise as integrands in stochastic programs. They are Lipschitz continuous on their domain, but do not belong to tensor product Sobolev spaces. Motivated by applying Quasi-Monte Carlo methods we show that all terms of their ANOVA decomposition, except the one of highest order, are smooth if the underlying densities are smooth and a certain geometric condition is...

We focus on the analysis of variance (ANOVA) method for high dimensional approximations employing the Dirac measure. This anchored-ANOVA representation converges exponentially fast for certain classes of functions but the error depends strongly on the anchor points. We employ the concept of “weights per dimension” to construct a theory that leads to the optimal anchor points. We then present ex...

Ecological studies typically involve comparison of biological responses among a variety of environmental conditions. When the response variables have continuous distributions and the conditions are discrete, whether inherently or by design, then it is appropriate to analyze the data using analysis of variance (ANOVA). When data conform to a complete. balanced design (equal numbers of observatio...

Here x is a numeric vector of data values and y is an optional numeric vector of data values. If y is excluded, the function performs a one-sample t-test on the data contained in x, if it is included it performs a two-sample t-tests using both x and y. The option mu provides a number indicating the true value of the mean (or difference in means if you are performing a two sample test) under the...

The analysis of variance is now often applied to functions defined on the unit cube, where it serves as a tool for the exploratory analysis of functions. The mean dimension of a function, defined as a natural weighted combination of its ANOVA mean squares, provides one measure of how hard or easy the function is to integrate by quasi-Monte Carlo sampling. This paper presents some new identities...

In this paper, we introduce an alternative to Yuen's test for the comparison of several population trimmed means. This nonparametric ANOVA type test is based on the empirical likelihood (EL) approach and extends the results for one population trimmed mean from Qin and Tsao (2002). The results of our simulation study indicate that for skewed distributions, with and without variance heterogeneity...