Test for independence between time to failure and cause of failure in competing risks with k causes

In this paper, we develop a simple nonparametric test for testing the independence of time to failure and cause of failure in competing risks set up. We generalise the test to the situation where failure data is right censored. We obtain the asymptotic distribution of the test statistics for complete and censored data. The efficiency loss due to censoring is studied using Pitman efficiency. The performance of the proposed test is evaluated through simulations. Finally we illustrate our test procedure using three real data sets.     

Local Estimation of the Conditional Stable Tail Dependence Function

We consider the local estimation of the stable tail dependence function when a random covariate is observed together with the variables of main interest. Our estimator is a weighted version of the empirical estimator adapted to the covariate framework. We provide the main asymptotic properties of our estimator, when properly normalized, in particular the convergence of the empirical process towards a tight centred Gaussian process. The finite sample performance of our estimator is illustrated on a small simulation study and on a dataset of air pollution measurements.     

Aspects of Dependence in Generalized Farlie-Gumbel-Morgenstern Distributions

In this article, we obtained a dependence measure for generalized Farlie-Gumbel-Morgenstern (FGM) family in view of Kochar and Gupta (1987 Kochar , S. G. , Gupta , R. P. ( 1987 ). Competitors of Kendall-tau test for testing independence against PQD . Biometrika 74 ( 3 ): 664 – 669 .[Crossref], [Web of Science ®] , [Google Scholar]) and then compared this measure with Spearman's rho and Kendall's tau in FGM family. Moreover, we evaluated the empirical power of the class of distribution-free tests proposed by Kochar and Gupta (1987 Kochar , S. G. , Gupta , R. P. ( 1987 ). Competitors of Kendall-tau test for testing independence against PQD . Biometrika 74 ( 3 ): 664 – 669 .[Crossref], [Web of Science ®] , [Google Scholar], 1990 Kochar , S. G. , Gupta , R. P. ( 1990 ). Distribution-free tests based on sub-sample extrema for testing against positive dependence . Australian Journal of Statistics 32 : 45 – 51 .[Crossref] , [Google Scholar]) based on exact distribution of a U-statistics. This is derived via a simulation study for sample of sizes n = 6, 8, 10, 12, 16, and 20. Also, we compared our simulation results with those achieved by Amini et al. (2010 Amini , M. , Jabbari , H. , Mohtashami Borzadaran , G. R. , Azadbakhsh , M. ( 2010 ). Power comparison of independence test for the Farlie-Gumbel-Moregenstern family . Communications of the Korean Statistical Society 17 ( 4 ): 493 – 505 .[Crossref] , [Google Scholar]) and Güven and Kotz (2008 Güven , B. , Kotz , S. ( 2008 ). Test of independence for generalized Farlie-Gumbel-Morgenstern distributions . Journal of Computational and Applied Mathematics 212 : 102 – 111 .[Crossref], [Web of Science ®] , [Google Scholar]).     

多维时间序列的条件独立性检验及其在股市相依关系中的应用

提出多维时间序列中各分量之间直接联系存在性的信息论检验方法,构造了条件互信息统计量检验分量间的条件独立性,统计量的显著性用置换检验决定.将提出的方法应用到国际股票市场,研究收益率序列相依关系,结果表明,此方法能有效检验各分量之间的直接联系和间接联系.     

Non-Parametric Testing of Conditional Variance Functions in Time Series

This paper proposes a non‐parametric test for examining hypotheses about variance functions under stationarity and ergodicity conditions. Special cases of nonlinear time series models are studied, and it is found that under mild conditions the test is consistent. Its power is examined in a simulation study.     

On Detecting the Dependence of Time Series

The author suggests a heuristic method for detecting the dependence of random time series that can be used in the case when this dependence is relatively weak, such that the traditional methods are not effective. The method requires comparison of some special functionals on the sample characteristic functions with the same functionals computed for the benchmark time series with a known degree of correlation. Some experiments for financial time series are presented.     

Estimating and Testing Nonlinear Local Dependence Between Two Time Series

ABSTRACT

The most common measure of dependence between two time series is the cross-correlation function. This measure gives a complete characterization of dependence for two linear and jointly Gaussian time series, but it often fails for nonlinear and non-Gaussian time series models, such as the ARCH-type models used in finance. The cross-correlation function is a global measure of dependence. In this article, we apply to bivariate time series the nonlinear local measure of dependence called local Gaussian correlation. It generally works well also for nonlinear models, and it can distinguish between positive and negative local dependence. We construct confidence intervals for the local Gaussian correlation and develop a test based on this measure of dependence. Asymptotic properties are derived for the parameter estimates, for the test functional and for a block bootstrap procedure. For both simulated and financial index data, we construct confidence intervals and we compare the proposed test with one based on the ordinary correlation and with one based on the Brownian distance correlation. Financial indexes are examined over a long time period and their local joint behavior, including tail behavior, is analyzed prior to, during and after the financial crisis. Supplementary material for this article is available online.     

Conditional specifications of multivariate pareto and student distributions

A random vector has a multivariate Pareto distribution if one of its univariate conditional distribution is Pareto and some of its marginals are identically distributed.A general method developed in the course of the proof of this result is applied also to characterize the multivariate Student (Cauchy) measure by one univariate Student conditional distribution.     

A Conditional Density Approach to the Order Determination of Time Series

The study focuses on the selection of the order of a general time series process via the conditional density of the latter, a characteristic of which is that it remains constant for every order beyond the true one. Using simulated time series from various nonlinear models we illustrate how this feature can be traced from conditional density estimation. We study whether two statistics derived from the likelihood function can serve as univariate statistics to determine the order of the process. It is found that a weighted version of the log likelihood function has desirable robust properties in detecting the order of the process.     

Unified Conditional Frequentist and Bayesian Testing of Composite Hypotheses

Testing of a composite null hypothesis versus a composite alternative is considered when both have a related invariance structure. The goal is to develop conditional frequentist tests that allow the reporting of data-dependent error probabilities, error probabilities that have a strict frequentist interpretation and that reflect the actual amount of evidence in the data. The resulting tests are also seen to be Bayesian tests, in the strong sense that the reported frequentist error probabilities are also the posterior probabilities of the hypotheses under default choices of the prior distribution. The new procedures are illustrated in a variety of applications to model selection and multivariate hypothesis testing.     

Testing equality of cause-specific hazard rates corresponding to m competing risks among K groups

In this paper, a class of tests is developed for comparing the cause-specific hazard rates of m competing risks simultaneously in K ( 2) groups. The data available for a unit are the failure time of the unit along with the identifier of the risk claiming the failure. In practice, the failure time data are generally right censored. The tests are based on the difference between the weighted averages of the cause-specific hazard rates corresponding to each risk. No assumption regarding the dependence of the competing risks is made. It is shown that the proposed test statistic has asymptotically chi-squared distribution. The proposed test is shown to be optimal for a specific type of local alternatives. The choice of weight function is also discussed. A simulation study is carried out using multivariate Gumbel distribution to compare the optimal weight function with a proposed weight function which is to be used in practice. Also, the proposed test is applied to real data on the termination of an intrauterine device.An erratum to this article can be found at     

On an Asymptotic Theory of Conditional and Unconditional Coverage Probabilities of Empirical Bayes Confidence Intervals

Empirical Bayes (EB) methodology is now widely used in statistics. However, construction of EB confidence intervals is still very limited. Following Cox (1975 ), Hill (1990 ) and Carlin & Gelfand (1990 , 1991 ), we consider EB confidence intervals, which are adjusted so that the actual coverage probabilities asymptotically meet the target coverage probabilities up to the second order. We consider both unconditional and conditional coverage, conditioning being done with respect to an ancillary statistic.     

Average Collapsibility of Distribution Dependence and Quantile Regression Coefficients

Abstract. The Yule–Simpson paradox notes that an association between random variables can be reversed when averaged over a background variable. Cox and Wermuth introduced the concept of distribution dependence between two random variables X and Y, and gave two dependence conditions, each of which guarantees that reversal of qualitatively similar conditional dependences cannot occur after marginalizing over the background variable. Ma, Xie and Geng studied the uniform collapsibility of distribution dependence over a background variable W, under stronger homogeneity condition. Collapsibility ensures that associations are the same for conditional and marginal models. In this article, we use the notion of average collapsibility, which requires only the conditional effects average over the background variable to the corresponding marginal effect and investigate its conditions for distribution dependence and for quantile regression coefficients.     

Estimation of conditional cumulative incidence functions under generalized semiparametric regression models with missing covariates,with application to analysis of biomarker correlates in vaccine trials

This article presents generalized semiparametric regression models for conditional cumulative incidence functions with competing risks data when covariates are missing by sampling design or happenstance. A doubly robust augmented inverse probability weighted (AIPW) complete-case approach to estimation and inference is investigated. This approach modifies IPW complete-case estimating equations by exploiting the key features in the relationship between the missing covariates and the phase-one data to improve efficiency. An iterative numerical procedure is derived to solve the nonlinear estimating equations. The asymptotic properties of the proposed estimators are established. A simulation study examining the finite-sample performances of the proposed estimators shows that the AIPW estimators are more efficient than the IPW estimators. The developed method is applied to the RV144 HIV-1 vaccine efficacy trial to investigate vaccine-induced IgG binding antibodies to HIV-1 as correlates of acquisition of HIV-1 infection while taking account of whether the HIV-1 sequences are near or far from the HIV-1 sequences represented in the vaccine construct.     

Asymptotic Behavior of Random Time Ruin Probability Under Heavy-Tailed Claim Sizes and Dependence Structure

This article deals with the renewal risk model, in which there exists some asymptotic dependence relation between claim sizes and the inter-arrival times, and claim sizes are subexponential. Under this setting, we investigate the tail behaviour of random time ruin probability as the initial risk reserve x tends to infinity. We obtain the similar asymptotic formula as the previous results.     

On asymptotic normality of likelihood and conditional analysis

The likelihood function from a large sample is commonly assumed to be approximately a normal density function. The literature supports, under mild conditions, an approximate normal shape about the maximum; but typically a stronger result is needed: that the normalized likelihood itself is approximately a normal density. In a transformation-parameter context, we consider the likelihood normalized relative to right-invariant measure, and in the location case under moderate conditions show that the standardized version converges almost surely to the standard normal. Also in a transformation-parameter context, we show that almost sure convergence of the normalized and standardized likelihood to a standard normal implies that the standardized distribution for conditional inference converges almost surely to a corresponding standard normal. This latter result is of immediate use for a range of estimating, testing, and confidence procedures on a conditional-inference basis.     

Regression Analysis of Length‐biased and Right‐censored Failure Time Data with Missing Covariates

Length‐biased and right‐censored failure time data arise from many fields, and their analysis has recently attracted a great deal of attention. Two examples of the areas that often produce such data are epidemiological studies and cancer screening trials. In this paper, we discuss regression analysis of such data in the presence of missing covariates, for which no established inference procedure seems to exist. For the problem, we consider the data arising from the proportional hazards model and propose two inverse probability weighted estimation procedures. The asymptotic properties of the resulting estimators are established, and the extensive simulation study conducted for the evaluation of the proposed methods suggests that they work well for practical situations.     

Lystematic sampling of two-dimensional surfaces and related problems

The paper is largely concerned with twenty-one possible methods of sampling a plane area, with points as sampling units, for the purpose of estimating a portion of this area having certain defined characteristics. These methods result from a combination, two at a time, of random, stratified and systematic sampling in two perpendicular directions, with or without alignment of the sampled points. Eleven of these methods involve systematic sampling in one or both directions. The estimate of the proportion of the area of interest is simply the proportion of points in the total area, falling within the area having the defined characteristics. For each method the variance function is derived. Fourteen different types of space covariance functions are involved in these variance functions.     

On the Product of Inverse Wishart and Normal Distributions with Applications to Discriminant Analysis and Portfolio Theory

Abstract. In this article we analyse the product of the inverse Wishart matrix and a normal vector. We derive the explicit joint distribution of the components of the product. Furthermore, we suggest several exact tests of general linear hypothesis about the elements of the product. We illustrate the developed techniques on examples from discriminant analysis and from portfolio theory.     

Two-Sample Statistics for Testing the Equality of Survival Functions Against Improper Semi-parametric Accelerated Failure Time Alternatives: An Application to the Analysis of a Breast Cancer Clinical Trial

This paper presents two-sample statistics suited for testing equality of survival functions against improper semi-parametric accelerated failure time alternatives. These tests are designed for comparing either the short- or the long-term effect of a prognostic factor, or both. These statistics are obtained as partial likelihood score statistics from a time-dependent Cox model. As a consequence, the proposed tests can be very easily implemented using widely available software. A breast cancer clinical trial is presented as an example to demonstrate the utility of the proposed tests.