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With the availability of high dimensional genetic biomarkers, it is of interest to identify heterogeneous effects of these predictors on patients survival, along with proper statistical inference. Censored quantile regression has emerged as a powerful tool for detecting heterogeneous effects of covariates on survival outcomes. To our knowledge, there is little work available to draw inference on the effects of high dimensional predictors for censored quantile regression. This paper proposes a novel procedure to draw inference on all predictors within the framework of global censored quantile regression, which investigates covariate-response associations over an interval of quantile levels, instead of a few discrete values. The proposed estimator combines a sequence of low dimensional model estimates that are based on multi-sample splittings and variable selection. We show that, under some regularity conditions, the estimator is consistent and asymptotically follows a Gaussian process indexed by the quantile level. Simulation studies indicate that our procedure can properly quantify the uncertainty of the estimates in high dimensional settings. We apply our method to analyze the heterogeneous effects of SNPs residing in lung cancer pathways on patients survival, using the Boston Lung Cancer Survivor Cohort, a cancer epidemiology study on the molecular mechanism of lung cancer.

Presents the author's views on the design and analysis of the clinical trial for Acquired Immune Deficiency Syndrome (AIDS). Information about the complications of trial design for this unique disease; View that the level of discussion in the paper is necessarily non-technical and lacking detail; Discussion on surrogate endpoints in AIDS; View that the authors should give more space to the time urgency of the problems of AIDS.

The article offers a discussion on a novel estimation of the average causal effects of the treatment strategies in the presence of time dependent confounding by indication. Topics discussed include penalized spline of propensity methods in handling missing data to causal inference incorporating a temporal element into consideration; and concludes that different approaches such as modeling and algorithms can be adopted to incorporate the propensity score.

A data set consisting of 143 rankings of 10 occupations from a survey of Goldberg has been analyzed in a number of recent papers. The purpose of this paper is to use so-called "nested orthogonal contrasts" of the occupations to gain further insight into the data. A contrast is a comparison of subsets of the occupations based on their relative ranks, contrasts are orthogonal if the comparisons they represent are not confounded. Various models based on sets of orthogonal contrasts—including contingency table models, models analogous to those of Fligner and Verducci, and latent class models—are applied to the data. It is found that there are three main groups of occupations based on overall prestige, and within each group are distinctions between managerial and technical occupations. [ABSTRACT FROM AUTHOR]

The author comments on the research conducted by Ruth Heller, Tony Cai, Peter Westfall and Armin Schwartzman on the accuracy of summary statistics in large-scale testing in the U.S. The author believes that Cai and Heller wrote authoritatively on the topics. He believes that there are missing discussion on their research regarding the use of ordinary nonparametric bootstrapping to asnwer simple accuracy questions.

The use of high-power industrial equipment, such as large-scale mixing equipment or a hydrocyclone for separation of particles in liquid suspension, demands careful monitoring to ensure correct operation. The fundamental task of state-estimation for the liquid suspension can be posed as a time-evolving inverse problem and solved with Bayesian statistical methods. In this article, we extend Bayesian methods to incorporate statistical models for the error that is incurred in the numerical solution of the physical governing equations. This enables full uncertainty quantification within a principled computation-precision trade-off, in contrast to the over-confident inferences that are obtained when all sources of numerical error are ignored. The method is cast within a sequential Monte Carlo framework and an optimized implementation is provided in Python. [ABSTRACT FROM AUTHOR]

Examines a general class of piecewise stationary processes that allows changes in spectral characteristics of nonstationary time series. Use of process to model natural phenomena; Proposal for an adaptive segmentation method to estimate time-dependent spectrum; Applications of the method to speech signals and earthquake data.

We consider the problem of finding optimal nonsequential designs for a large class of regression models involving polynomials and rational functions with heteroscedastic noise also given by a polynomial or rational weight function. Since the design weights can be found easily by existing methods once the support is known, we concentrate on determining the support of the optimal design. The proposed method treats D-, E-, A-, and Φ p -optimal designs in a unified manner, and generates a polynomial whose zeros are the support points of the optimal approximate design, generalizing a number of previously known results of the same flavor. The method is based on a mathematical optimization model that can incorporate various criteria of optimality and can be solved efficiently by well-established numerical optimization methods. In contrast to optimization-based methods previously proposed for the solution of similar design problems, our method also has theoretical guarantee of its algorithmic efficiency; in concordance with the theory, the actual running times of all numerical examples considered in the paper are negligible. The numerical stability of the method is demonstrated in an example involving high-degree polynomials. As a corollary, an upper bound on the size of the support set of the minimally supported optimal designs is also found. [ABSTRACT FROM AUTHOR]

With the recent availability of high-frequency financial data the long-range dependence of volatility regained researchers' interest and has led to the consideration of long-memory models for volatility. The long-range diagnosis of volatility, however, is usually stated for long sample periods, while for small sample sizes, such as one year, the volatility dynamics appears to be better described by short-memory processes. The ensemble of these seemingly contradictory phenomena point towards short-memory models of volatility with nonstationarities, such as structural breaks or regime switches, that spuriously generate a long memory pattern. In this paper we adopt this view on the dependence structure of volatility and propose a localized procedure for modeling realized volatility. That is at each point in time we determine a past interval over which volatility is approximated by a local linear process. A simulation study shows that long memory processes as well as short memory processes with structural breaks can be well approximated by this local approach. Furthermore, using S&P500 data we find that our local modeling approach outperforms long-memory type models and models with structural breaks in terms of predictability. [ABSTRACT FROM AUTHOR]

Copulas have proven to be very successful tools for the flexible modeling of cross-sectional dependence. In this paper we express the dependence structure of continuous-valued time series data using a sequence of bivariate copulas. This corresponds to a type of decomposition recently called a 'vine' in the graphical models literature, where each copula is entitled a 'pair-copula.' We propose a Bayesian approach for the estimation of this dependence structure for longitudinal data. Bayesian selection ideas are used to identify any independence pair-copulas, with the end result being a parsimonious representation of a time-inhomogeneous Markov process of varying order. Estimates are Bayesian model averages over the distribution of the lag structure of the Markov process. Using a simulation study we show that the selection approach is reliable and can improve the estimates of both conditional and unconditional pairwise dependencies substantially. We also show that a vine with selection outperforms a Gaussian copula with a flexible correlation matrix. The advantage of the pair-copula formulation is further demonstrated using a longitudinal model of intraday electricity load. Using Gaussian, Gumbel, and Clayton pair-copulas we identify parsimonious decompositions of intraday serial dependence, which improve the accuracy of intraday load forecasts. We also propose a new diagnostic for measuring the goodness of fit of high-dimensional multivariate copulas. Overall, the pair-copula model is very general and the Bayesian method generalizes many previous approaches for the analysis of longitudinal data. Supplemental materials for the article are also available online. [ABSTRACT FROM AUTHOR]

In this paper we offer a complete methodology of cumulative slicing estimation to sufficient dimension reduction. In parallel to the classical slicing estimation, we develop three methods that are termed, respectively, as cumulative mean estimation, cumulative variance estimation, and cumulative directional regression. The strong consistency for p= O( n1 / 2 / log n) and the asymptotic normality for p= o( n1 / 2) are established, where p is the dimension of the predictors and n is sample size. Such asymptotic results improve the rate p= o( n1 / 3) in many existing contexts of semiparametric modeling. In addition, we propose a modified BIC-type criterion to estimate the structural dimension of the central subspace. Its consistency is established when p= o( n1 / 2). Extensive simulations are carried out for comparison with existing methods and a real data example is presented for illustration. [ABSTRACT FROM AUTHOR]

In situations where individuals are screened for an infectious disease or other binary characteristic and where resources for testing are limited, group testing can offer substantial benefits. Group testing, where subjects are tested in groups (pools) initially, has been successfully applied to problems in blood bank screening, public health, drug discovery, genetics, and many other areas. In these applications, often the goal is to identify each individual as positive or negative using initial group tests and subsequent retests of individuals within positive groups. Many group testing identification procedures have been proposed; however, the vast majority of them fail to incorporate heterogeneity among the individuals being screened. In this paper, we present a new approach to identify positive individuals when covariate information is available on each. This covariate information is used to structure how retesting is implemented within positive groups; therefore, we call this new approach 'informative retesting.' We derive closed-form expressions and implementation algorithms for the probability mass functions for the number of tests needed to decode positive groups. These informative retesting procedures are illustrated through a number of examples and are applied to chlamydia and gonorrhea testing in Nebraska for the Infertility Prevention Project. Overall, our work shows compelling evidence that informative retesting can dramatically decrease the number of tests while providing accuracy similar to established noninformative retesting procedures. This article has supplementary material online. [ABSTRACT FROM AUTHOR]

Approximate Bayesian Computation is a family of likelihood-free inference techniques that are well suited to models defined in terms of a stochastic generating mechanism. In a nutshell, Approximate Bayesian Computation proceeds by computing summary statistics s obs from the data and simulating summary statistics for different values of the parameter Θ. The posterior distribution is then approximated by an estimator of the conditional density g( Θ| s obs). In this paper, we derive the asymptotic bias and variance of the standard estimators of the posterior distribution which are based on rejection sampling and linear adjustment. Additionally, we introduce an original estimator of the posterior distribution based on quadratic adjustment and we show that its bias contains a fewer number of terms than the estimator with linear adjustment. Although we find that the estimators with adjustment are not universally superior to the estimator based on rejection sampling, we find that they can achieve better performance when there is a nearly homoscedastic relationship between the summary statistics and the parameter of interest. To make this relationship as homoscedastic as possible, we propose to use transformations of the summary statistics. In different examples borrowed from the population genetics and epidemiological literature, we show the potential of the methods with adjustment and of the transformations of the summary statistics. Supplemental materials containing the details of the proofs are available online. [ABSTRACT FROM AUTHOR]

This paper proposes a methodology for combining satellite images with advection-diffusion models for interpolation and prediction of environmental processes. We propose a dynamic state-space model and an ensemble Kalman filter and smoothing algorithm for on-line and retrospective state estimation. Our approach addresses the high dimensionality, measurement bias, and nonlinearities inherent in satellite data. We apply the method to a sequence of SeaWiFS satellite images in Lake Michigan from March 1998, when a large sediment plume was observed in the images following a major storm event. Using our approach, we combine the images with a sediment transport model to produce maps of sediment concentrations and uncertainties over space and time. We show that our approach improves out-of-sample RMSE by 20%-30% relative to standard approaches. This article has supplementary material online. [ABSTRACT FROM AUTHOR]

Multiplicative regression model or accelerated failure time model, which becomes linear regression model after logarithmic transformation, is useful in analyzing data with positive responses, such as stock prices or life times, that are particularly common in economic/financial or biomedical studies. Least squares or least absolute deviation are among the most widely used criterions in statistical estimation for linear regression model. However, in many practical applications, especially in treating, for example, stock price data, the size of relative error, rather than that of error itself, is the central concern of the practitioners. This paper offers an alternative to the traditional estimation methods by considering minimizing the least absolute relative errors for multiplicative regression models. We prove consistency and asymptotic normality and provide an inference approach via random weighting. We also specify the error distribution, with which the proposed least absolute relative errors estimation is efficient. Supportive evidence is shown in simulation studies. Application is illustrated in an analysis of stock returns in Hong Kong Stock Exchange. [ABSTRACT FROM AUTHOR]

The paper proposes two inferential tests for error correlation in the functional linear model, which complement the available graphical goodness-of-fit checks. To construct them, finite dimensional residuals are computed in two different ways, and then their autocorrelations are suitably defined. From these autocorrelation matrices, two quadratic forms are constructed whose limiting distribution are chi-squared with known numbers of degrees of freedom (different for the two forms). The asymptotic approximations are suitable for moderate sample sizes. The test statistics can be relatively easily computed using the package , or similar MATLAB software. Application of the tests is illustrated on magnetometer and financial data. The asymptotic theory emphasizes the differences between the standard vector linear regression and the functional linear regression. To understand the behavior of the residuals obtained from the functional linear model, the interplay of three types of approximation errors must be considered, whose sources are: projection on a finite dimensional subspace, estimation of the optimal subspace, and estimation of the regression kernel. [ABSTRACT FROM AUTHOR]

A longstanding problem in clinical research is distinguishing drug-treated subjects that respond due to specific effects of the drug from those that respond to nonspecific (or placebo) effects of the treatment. Linear mixed effect models are commonly used to model longitudinal clinical trial data. In this paper we present a solution to the problem of identifying placebo responders using an optimal partitioning methodology for linear mixed effects models. Since individual outcomes in a longitudinal study correspond to curves, the optimal partitioning methodology produces a set of prototypical outcome profiles. The optimal partitioning methodology can accommodate both continuous and discrete covariates. The proposed partitioning strategy is compared and contrasted with the growth mixture modeling approach. The methodology is applied to a two-phase depression clinical trial where subjects in a first phase were treated openly for 12 weeks with fluoxetine followed by a double blind discontinuation phase where responders to treatment in the first phase were randomized to either stay on fluoxetine or switched to a placebo. The optimal partitioning methodology is applied to the first phase to identify prototypical outcome profiles. Using time to relapse in the second phase of the study, a survival analysis is performed on the partitioned data. The optimal partitioning results identify prototypical profiles that distinguish whether subjects relapse depending on whether or not they stay on the drug or are randomized to a placebo. [ABSTRACT FROM AUTHOR]

In longitudinal clinical trials, when outcome variables at later time points are only defined for patients who survive to those times, the evaluation of the causal effect of treatment is complicated. In this paper, we describe an approach that can be used to obtain the causal effect of three treatment arms with ordinal outcomes in the presence of death using a principal stratification approach. We introduce a set of flexible assumptions to identify the causal effect and implement a sensitivity analysis for nonidentifiable assumptions which we parameterize parsimoniously. Methods are illustrated on quality of life data from a recent colorectal cancer clinical trial. This article has supplementary material online. [ABSTRACT FROM AUTHOR]

In this paper we develop a nonparametric approach to clustering very high-dimensional data, designed particularly for problems where the mixture nature of a population is expressed through multimodality of its density. Therefore, a technique based implicitly on mode testing can be particularly effective. In principle, several alternative approaches could be used to assess the extent of multimodality, but in the present problem the excess mass method has important advantages. We show that the resulting methodology for determining clusters is particularly effective in cases where the data are relatively heavy tailed or show a moderate to high degree of correlation, or when the number of important components is relatively small. Conversely, in the case of light-tailed, almost-independent components when there are many clusters, clustering in terms of modality can be less reliable than more conventional approaches. This article has supplementary material online. [ABSTRACT FROM AUTHOR]

Multidimensional scaling (MDS) comprises a family of geometric models for the multidimensional representation of data and a corresponding set of methods for fitting such models to actual data. In this paper, we develop a new Bayesian vector MDS model to analyze ordered successive categories preference/dominance data commonly collected in many social science and business studies. A joint spatial representation of the row and column elements of the input data matrix is provided in a reduced dimensionality such that the geometric relationship of the row and column elements renders insight into the utility structure underlying the data. Unlike classical deterministic MDS procedures, the Bayesian method includes a probability based criterion to determine the number of dimensions of the derived joint space map and provides posterior interval as well as point estimates for parameters of interest. Also, our procedure models the raw integer successive categories data which ameliorates the need of any data preprocessing as required for many metric MDS procedures. Furthermore, the proposed Bayesian procedure allows external information in the form of an intractable posterior distribution derived from a related dataset to be incorporated as a prior in deriving the spatial representation of the preference data. An actual commercial application dealing with consumers’ intentions to buy new luxury sport utility vehicles are presented to illustrate the proposed methodology. Favorable comparisons are made with more traditional MDS approaches. [ABSTRACT FROM AUTHOR]

The dynamic hierarchical Dirichlet process (dHDP) is developed to model complex sequential data, with a focus on audio signals from music. The music is represented in terms of a sequence of discrete observations, and the sequence is modeled using a hidden Markov model (HMM) with time-evolving parameters. The dHDP imposes the belief that observations that are temporally proximate are more likely to be drawn from HMMs with similar parameters, while also allowing for “innovation” associated with abrupt changes in the music texture. The sharing mechanisms of the time-evolving model are derived, and for inference a relatively simple Markov chain Monte Carlo sampler is developed. Segmentation of a given musical piece is constituted via the model inference. Detailed examples are presented on several pieces, with comparisons to other models. The dHDP results are also compared with a conventional music-theoretic analysis. All the supplemental materials used by this paper are available online. [ABSTRACT FROM AUTHOR]

Mixture models, or convex combinations of a countable number of probability distributions, offer an elegant framework for inference when the population of interest can be subdivided into latent clusters having random characteristics that are heterogeneous between, but homogeneous within, the clusters. Traditionally, the different kinds of mixture models have been motivated and analyzed from very different perspectives, and their common characteristics have not been fully appreciated. The inferential techniques developed for these models usually necessitate heavy computational burdens that make them difficult, if not impossible, to apply to the massive data sets increasingly encountered in real world studies. This paper introduces a flexible class of models called generalized Pólya urn (GPU) processes. Many common mixture models, including finite mixtures, hidden Markov models, and Dirichlet processes, are obtained as special cases of GPU processes. Other important special cases include finite-dimensional Dirichlet priors, infinite hidden Markov models, analysis of densities models, nested Chinese restaurant processes, hierarchical DP models, nonparametric density models, spatial Dirichlet processes, weighted mixtures of DP priors, and nested Dirichlet processes. An investigation of the theoretical properties of GPU processes offers new insight into asymptotics that form the basis of cost-effective Markov chain Monte Carlo (MCMC) strategies for large datasets. These MCMC techniques have the advantage of providing inferences from the posterior of interest, rather than an approximation, and are applicable to different mixture models. The versatility and impressive gains of the methodology are demonstrated by simulation studies and by a semiparametric Bayesian analysis of high-resolution comparative genomic hybridization data on lung cancer. The appendixes are available online as supplemental material. [ABSTRACT FROM AUTHOR]

While Distance Weighted Discrimination (DWD) is an appealing approach to classification in high dimensions, it was designed for balanced datasets. In the case of unequal costs, biased sampling, or unbalanced data, there are major improvements available, using appropriately weighted versions of DWD (wDWD). A major contribution of this paper is the development of optimal weighting schemes for various nonstandard classification problems. In addition, we discuss several alternative criteria and propose an adaptive weighting scheme (awDWD) and demonstrate its advantages over nonadaptive weighting schemes under some situations. The second major contribution is a theoretical study of weighted DWD. Both high-dimensional low sample-size asymptotics and Fisher consistency of DWD are studied. The performance of weighted DWD is evaluated using simulated examples and two real data examples. The theoretical results are also confirmed by simulations. [ABSTRACT FROM AUTHOR]

State-space models provide an important body of techniques for analyzing time series, but their use requires estimating unobserved states. The optimal estimate of the state is its conditional expectation given the observation histories, and computing this expectation is hard when there are nonlinearities. Existing filtering methods, including sequential Monte Carlo, tend to be either inaccurate or slow. In this paper, we study a nonlinear filter for nonlinear/non-Gaussian state-space models, which uses Laplace’s method, an asymptotic series expansion, to approximate the state’s conditional mean and variance, together with a Gaussian conditional distribution. This Laplace Gaussian filter (LGF) gives fast, recursive, deterministic state estimates, with an error which is set by the stochastic characteristics of the model and is, we show, stable over time. We illustrate the estimation ability of the LGF by applying it to the problem of neural decoding and compare it to sequential Monte Carlo both in simulations and with real data. We find that the LGF can deliver superior results in a small fraction of the computing time. This article has supplementary material online. [ABSTRACT FROM AUTHOR]

In this paper, we extend the LASSO method (Tibshirani 1996) for simultaneously fitting a regression model and identifying important interaction terms. Unlike most of the existing variable selection methods, our method automatically enforces the heredity constraint, that is, an interaction term can be included in the model only if the corresponding main terms are also included in the model. Furthermore, we extend our method to generalized linear models, and show that it performs as well as if the true model were given in advance, that is, the oracle property as in Fan and Li (2001) and Fan and Peng (2004). The proof of the oracle property is given in online supplemental materials. Numerical results on both simulation data and real data indicate that our method tends to remove irrelevant variables more effectively and provide better prediction performance than previous work (Yuan, Joseph, and Lin 2007 and Zhao, Rocha, and Yu 2009 as well as the classical LASSO method). [ABSTRACT FROM AUTHOR]

In this paper, we propose a new dimension reduction method by introducing a nominal regression model with the hazard function as the conditional mean, which naturally retrieves information from complete data and censored data as well. Moreover, without requiring the linearity condition, the new method can estimate the entire central subspace consistently and exhaustively. The method also provides an alternative approach for the analysis of censored data assuming neither the link function nor the distribution. Hence, it exhibits superior robustness properties. Numerical studies show that the method can indeed be readily used to efficiently estimate survival models, explore the data structures and identify important variables. [ABSTRACT FROM AUTHOR]

We apply the nonconcave penalized likelihood approach to obtain variable selections as well as shrinkage estimators. This approach relies heavily on the choice of regularization parameter, which controls the model complexity. In this paper, we propose employing the generalized information criterion, encompassing the commonly used Akaike information criterion (AIC) and Bayesian information criterion (BIC), for selecting the regularization parameter. Our proposal makes a connection between the classical variable selection criteria and the regularization parameter selections for the nonconcave penalized likelihood approaches. We show that the BIC-type selector enables identification of the true model consistently, and the resulting estimator possesses the oracle property in the terminology of Fan and Li (2001). In contrast, however, the AIC-type selector tends to overfit with positive probability. We further show that the AIC-type selector is asymptotically loss efficient, while the BIC-type selector is not. Our simulation results confirm these theoretical findings, and an empirical example is presented. Some technical proofs are given in the online supplementary material. [ABSTRACT FROM AUTHOR]

The technology to harvest electricity from wind energy is now advanced enough to make entire cities powered by it a reality. High-quality, short-term forecasts of wind speed are vital to making this a more reliable energy source. Gneiting et al. (2006) have introduced a model for the average wind speed two hours ahead based on both spatial and temporal information. The forecasts produced by this model are accurate, and subject to accuracy, the predictive distribution is sharp, that is, highly concentrated around its center. However, this model is split into nonunique regimes based on the wind direction at an offsite location. This paper both generalizes and improves upon this model by treating wind direction as a circular variable and including it in the model. It is robust in many experiments, such as predicting wind at other locations. We compare this with the more common approach of modeling wind speeds and directions in the Cartesian space and use a skew- t distribution for the errors. The quality of the predictions from all of these models can be more realistically assessed with a loss measure that depends upon the power curve relating wind speed to power output. This proposed loss measure yields more insight into the true value of each model’s predictions. [ABSTRACT FROM AUTHOR]

This note is based on an invited discussion of the article, “A Moving Average Approach for Spatial Statistical Models on Stream Networks” by Jay M. Ver Hoef and Erin E. Peterson. Ver Hoef and Peterson (hereafter VHP) have extended the idea of flow-related statistical dependence in streams to one where dependence may not respect flow, such as might happen when modeling data on fish in connected streams. We congratulate VHP for their innovative paper on using moving average models in stream networks. [ABSTRACT FROM AUTHOR]

Lévy processes have been receiving increasing attention in financial modeling. One distinctive feature of such models is that their characteristic functions are readily available. Inference based on characteristic functions is very useful for studying Levy processes. By incorporating the recent advances in nonparametric approaches, empirical likelihood methods based on characteristic functions are developed in this paper for parameter estimation, testing a particular parametric class including the presence of a jump component in the Levy process and testing for symmetry of a distribution. Simulation and case studies confirm the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

This paper proposes several extensions of the concept of runs to the multivariate setup, and studies the resulting tests of multivariate randomness against serial dependence. Two types of multivariate runs are defined: (i) an elliptical extension of the spherical runs proposed by Marden (1999), and (ii) an original concept of matrix-valued runs. The resulting runs tests themselves exist in various versions, one of which is a function of the number of data-based hyperplanes separating pairs of observations only. All proposed multivariate runs tests are affine-invariant and highly robust: in particular, they allow for heteroscedasticity and do not require any moment assumption. Their limiting distributions are derived under the null hypothesis and under sequences of local vector ARMA alternatives. Asymptotic relative efficiencies with respect to Gaussian Portmanteau tests are computed, and show that, while Marden-type runs tests suffer severe consistency problems, tests based on matrix-valued runs perform uniformly well for moderate-to-large dimensions. A Monte Carlo study confirms the theoretical results and investigates the robustness properties of the proposed procedures. A real-data example is also treated, and shows that combining both types of runs tests may provide some insight on the reason why rejection occurs, hence that Marden-type runs tests, despite their lack of consistency, also are of interest for practical purposes. [ABSTRACT FROM AUTHOR]

This paper introduces an open-ended sequential algorithm for computing the p-value of a test using Monte Carlo simulation. It guarantees that the resampling risk, the probability of a different decision than the one based on the theoretical p-value, is uniformly bounded by an arbitrarily small constant. Previously suggested sequential or nonsequential algorithms, using a bounded sample size, do not have this property. Although the algorithm is open-ended, the expected number of steps is finite, except when the p-value is on the threshold between rejecting and not rejecting. The algorithm is suitable as standard for implementing tests that require (re)sampling. It can also be used in other situations: to check whether a test is conservative, iteratively to implement double bootstrap tests, and to determine the sample size required for a certain power. An R-package implementing the sequential algorithm is available online. [ABSTRACT FROM AUTHOR]

Quantile regression has emerged as a significant extension of traditional linear models and its potential in survival applications has recently been recognized. In this paper we study quantile regression with competing risks data, formulating the model based on conditional quantiles defined using the cumulative incidence function, which includes as a special case an analog to the usual accelerated failure time model. The proposed competing risks quantile regression model provides meaningful physical interpretations of covariate effects and, moreover, relaxes the constancy constraint on regression coefficients, thereby providing a useful, perhaps more flexible, alternative to the popular subdistribution proportional hazards model. We derive an unbiased monotone estimating equation for regression parameters in the quantile model. The uniform consistency and weak convergence of the resulting estimators are established across a quantile continuum. We develop inferences, including covariance estimation, second-stage exploration, and model diagnostics, which can be stably implemented using standard statistical software without involving smoothing or resampling. Our proposals are illustrated via simulation studies and an application to a breast cancer clinical trial. [ABSTRACT FROM AUTHOR]

Empirical likelihood has been found very useful in many different occasions. However, when applied directly to some more complicated statistics such as U-statistics, it runs into serious computational difficulties. In this paper, we introduce a so-called jackknife empirical likelihood (JEL) method. The new method is extremely simple to use in practice. In particular, the JEL is shown to be very effective in handling one and two-sample U-statistics. The JEL can be potentially useful for other nonlinear statistics. [ABSTRACT FROM AUTHOR]

The aim of this paper is to develop an intrinsic regression model for the analysis of positive-definite matrices as responses in a Riemannian manifold and their association with a set of covariates, such as age and gender, in a Euclidean space. The primary motivation and application of the proposed methodology is in medical imaging. Because the set of positive-definite matrices do not form a vector space, directly applying classical multivariate regression may be inadequate in establishing the relationship between positive-definite matrices and covariates of interest, such as age and gender, in real applications. Our intrinsic regression model, which is a semiparametric model, uses a link function to map from the Euclidean space of covariates to the Riemannian manifold of positive-definite matrices. We develop an estimation procedure to calculate parameter estimates and establish their limiting distributions. We develop score statistics to test linear hypotheses on unknown parameters and develop a test procedure based on a resampling method to simultaneously assess the statistical significance of linear hypotheses across a large region of interest. Simulation studies are used to demonstrate the methodology and examine the finite sample performance of the test procedure for controlling the family-wise error rate. We apply our methods to the detection of statistical significance of diagnostic effects on the integrity of white matter in a diffusion tensor study of human immunodeficiency virus. Supplemental materials for this article are available online. [ABSTRACT FROM AUTHOR]