Statistical Theory Commons^™

Balancing Score Adjusted Targeted Minimum Loss-Based Estimation, Samuel D. Lendle, Bruce Fireman, Mark J. Van Der Laan

U.C. Berkeley Division of Biostatistics Working Paper Series

Adjusting for a balancing score is sufficient for bias reduction when estimating causal effects including the average treatment effect and effect among the treated. Estimators that adjust for the propensity score in a nonparametric way, such as matching on an estimate of the propensity score, can be consistent when the estimated propensity score is not consistent for the true propensity score but converges to some other balancing score. We call this property the balancing score property, and discuss a class of estimators that have this property. We introduce a targeted minimum loss-based estimator (TMLE) for a treatment specific mean with ...

Analysis Of Spatial Data, Xiang Zhang

Theses and Dissertations--Statistics

In many areas of the agriculture, biological, physical and social sciences, spatial lattice data are becoming increasingly common. In addition, a large amount of lattice data shows not only visible spatial pattern but also temporal pattern (see, Zhu et al. 2005). An interesting problem is to develop a model to systematically model the relationship between the response variable and possible explanatory variable, while accounting for space and time effect simultaneously.

Spatial-temporal linear model and the corresponding likelihood-based statistical inference are important tools for the analysis of spatial-temporal lattice data. We propose a general asymptotic framework for spatial-temporal linear models and ...

Estimating Effects On Rare Outcomes: Knowledge Is Power, Laura B. Balzer, Mark J. Van Der Laan

U.C. Berkeley Division of Biostatistics Working Paper Series

Understanding the etiology of rare cancers, perinatal mortality, international conflicts or natural disasters can have profound impacts on population health and well-being. However, when the outcome of interest occurs in 5% or less of the population, effect estimation can be particularly challenging. To increase statistical power and the stability of results, researchers commonly oversample cases or events. However, the study of rare outcomes need not be limited to case-control settings. Building on the work of Gruber and van der Laan (2010), we construct a new targeted minimum loss-based estimator (TMLE) for estimating the effect of an exposure or treatment on ...

Optimal Tests Of Treatment Effects For The Overall Population And Two Subpopulations In Randomized Trials, Using Sparse Linear Programming, Michael Rosenblum, Han Liu, En-Hsu Yen

Johns Hopkins University, Dept. of Biostatistics Working Papers

We propose new, optimal methods for analyzing randomized trials, when it is suspected that treatment effects may differ in two predefined subpopulations. Such sub-populations could be defined by a biomarker or risk factor measured at baseline. The goal is to simultaneously learn which subpopulations benefit from an experimental treatment, while providing strong control of the familywise Type I error rate. We formalize this as a multiple testing problem and show it is computationally infeasible to solve using existing techniques. Our solution involves a novel approach, in which we first transform the original multiple testing problem into a large, sparse linear ...

Minimax Sparse Principal Subspace Estimation In High Dimensions, Vincent Q. Vu, Jing Lei

Department of Statistics

We study sparse principal components analysis in high dimensions, where p (the number of variables) can be much larger than n (the number of observations), and analyze the problem of estimating the subspace spanned by the principal eigenvectors of the population covariance matrix. We prove optimal, non-asymptotic lower and upper bounds on the minimax subspace estimation error under two different, but related notions of ℓ_q subspace sparsity for 0 ≤ q ≤ 1. Our upper bounds apply to general classes of covariance matrices, and they show that ℓ_q constrained estimates can achieve optimal minimax rates without restrictive spiked covariance conditions.

Asymmetric Empirical Similarity, Joshua C. Teitelbaum

Georgetown Law Faculty Publications and Other Works

The paper suggests a similarity function for applications of empirical similarity theory in which the notion of similarity is asymmetric. I propose defining similarity in terms of a quasimetric. I suggest a particular quasimetric and explore the properties of the empirical similarity model given this function. The proposed function belongs to the class of quasimetrics induced by skewed norms. Finally, I provide a skewness axiom that, when imposed in lieu of the symmetry axiom in the main result of Billot et al. (2008), characterizes an exponential similarity function based on a skewed norm.

Exact Likelihood Inference For Multiple Exponential Populations Under Joint Censoring, Feng Su

Open Access Dissertations and Theses

The joint censoring scheme is of practical significance while conducting comparative life-tests of products from different units within the same facility. In this thesis, we derive the exact distributions of the maximum likelihood estimators (MLEs) of the unknown parameters when joint censoring of some form is present among the multiple samples, and then discuss the construction of exact confidence intervals for the parameters.

We develop inferential methods based on four different joint censoring schemes. The first one is when a jointly Type-II censored sample arising from $k$ independent exponential populations is available. The second one is when a jointly progressively ...

A Prior-Free Framework Of Coherent Inference And Its Derivation Of Simple Shrinkage Estimators, David R. Bickel

COBRA Preprint Series

The reasoning behind uses of confidence intervals and p-values in scientific practice may be made coherent by modeling the inferring statistician or scientist as an idealized intelligent agent. With other things equal, such an agent regards a hypothesis coinciding with a confidence interval of a higher confidence level as more certain than a hypothesis coinciding with a confidence interval of a lower confidence level. The agent uses different methods of confidence intervals conditional on what information is available. The coherence requirement means all levels of certainty of hypotheses about the parameter agree with the same distribution of certainty over parameter ...

Adaptive Randomization Designs, Jenna Colavincenzo

Statistics

Adaptive design methodologies use prior information to develop a clinical trial design. The goal of an adaptive design is to maintain the integrity and validity of the study while giving the researcher flexibility in identifying the optimal treatment. An example of an adaptive design can be seen in a basic pharmaceutical trial. There are three phases of the overall trial to compare treatments and experimenters use the information from the previous phase to make changes to the subsequent phase before it begins.

Adaptive design methods have been in practice since the 1970s, but have become increasingly complex ever since. One ...

On Penalized Likelihood Estimation For A Non-Proportional Hazards Regression Model, Karthik Devarajan, Nader Ebrahimi

COBRA Preprint Series

The fundamental assumption of proportionality of hazards in the Cox
model sometimes does not hold in practice. In this paper, a semi-parametric generalization of the Cox model that permits crossing hazard curves is described. This model allows the interaction between covariates and the baseline hazard, and has been the subject of recent investigation. It includes, for the two sample problem, the case of two Weibull distributions and two extreme value distributions differing in both scale and shape parameters. The partial likelihood approach cannot be applied here to estimate the model parameters, and flexible methods based on splines and sieves for ...

Tests That Reject At Least One Subpopulation Null Hypothesis After Rejecting For Overall Population, Michael Rosenblum

Johns Hopkins University, Dept. of Biostatistics Working Papers

It is often of interest to determine treatment effects in the overall study population, as well as in certain subpopulations. These subpopulations could be defined by a risk factor, such as a biomarker, measured at baseline. We consider situations where the overall population is
partitioned into two subpopulations of interest.
If the null hypothesis of no treatment effect in the overall population is rejected, a natural question is what can be said about these subpopulations.
Whenever there is a treatment effect in the overall population, it follows logically that there must be a treatment effect in at least one of ...