Statistical inference on censored data for targeted clinical trials under enrichment design

For the traditional clinical trials, inclusion and exclusion criteria are usually based on some clinical endpoints; the genetic or genomic variability of the trial participants are not totally utilized in the criteria. After completion of the human genome project, the disease targets at the molecular level can be identified and can be utilized for the treatment of diseases. However, the accuracy of diagnostic devices for identification of such molecular targets is usually not perfect. Some of the patients enrolled in targeted clinical trials with a positive result for the molecular target might not have the specific molecular targets. As a result, the treatment effect may be underestimated in the patient population truly with the molecular target. To resolve this issue, under the exponential distribution, we develop inferential procedures for the treatment effects of the targeted drug based on the censored endpoints in the patients truly with the molecular targets. Under an enrichment design, we propose using the expectation–maximization algorithm in conjunction with the bootstrap technique to incorporate the inaccuracy of the diagnostic device for detection of the molecular targets on the inference of the treatment effects. A simulation study was conducted to empirically investigate the performance of the proposed methods. Simulation results demonstrate that under the exponential distribution, the proposed estimator is nearly unbiased with adequate precision, and the confidence interval can provide adequate coverage probability. In addition, the proposed testing procedure can adequately control the size with sufficient power. On the other hand, when the proportional hazard assumption is violated, additional simulation studies show that the type I error rate is not controlled at the nominal level and is an increasing function of the positive predictive value. A numerical example illustrates the proposed procedures. Copyright © 2013 John Wiley & Sons, Ltd.     

A bootstrap procedure in linear regression with nonstationary errors

In the context of linear regression with dependent and nonstationary errors, the classical moving-block bootstrap (MBB) fails to capture the nonstationarity of the errors. A new bootstrap procedure called the blocking external bootstrap (BEB) is proposed to overcome the problem. The consistency of the BEB in estimating the variance of the least-squares estimator is studied in the case of α-mixing and nonstationary sequence of errors. It is shown that the BEB only achieves partial correction if the block size is fixed. Complete consistency is achieved by the BEB when the block size is allowed to go to infinity. We also study the first-order consistency of the least squares estimator based on the BEB. A simulation study is carried out to assess the performance of the BEB versus the MBB in estimating the variance of the least-squares estimator. Finally, some open problems are discussed.     

Estimation of the Moment Generating Function

A number of statistical problems use the moment generating function (mgf) for purposes other than determining the moments of a distribution. If the distribution is not completely specified, then the mgf must be estimated from available data. The empirical mgf makes no assumptions concerning the underlying distribution except for the existence of the mgf. In contrast to the nonparametric approach provided by the empirical mgf, alternative estimators can be formed based on an assumed parametric model. Comparison of these approaches is considered for two parametric models; the normal and a one parameter gamma. Comparison criteria are efficiency and empirical confidence interval coverage. In general the parametric estimators outperform the empirical mgf when the model is correct. The comparisons are extended to underlying models which are two component mixtures from the distributional family assumed by the parametric estimators. Under the mixture models the superiority of the parametric estimator depends upon the model, value of the argument of the mgf, and the comparison criterion. The empirical mgf is the better estimator in some cases.     

Single-Variable Threshold Effects in Ordered Response Models With an Application to Estimating the Income-Happiness Gradient

This short article extends well-known threshold models to the ordered response setting. We consider the case where the sample is endogenously split to estimate regime-dependent coefficients for one variable of interest, while keeping the other coefficients and auxiliary parameters constant across the threshold. We use Monte Carlo methods to examine the behavior of the model. In addition, we derive the formulae for the partial effects associated with the model. We apply our threshold model to the relationship between income and self-reported happiness using data drawn from the U.S. General Social Survey. While the findings suggest the presence of a threshold in the income-happiness gradient at approximately U.S. $76,000, no evidence is found in support of a satiation point. Supplementary materials for this article are available online.     

Reliability analysis for gap null gate based on model comparison criterion

The length of the gap is the key factor affecting its reliability. Based on the mechanism of the gap null gate, this paper regards the two endpoint thresholds of the gap length as bivariate random variables and establishes successful response models. Score test statistic is presented to test the correlation coefficient. The DIC criterion is also provided to compare the models. With the experimental data of the gap null gate, we build Probit model and Logit model as the successful response models, and prove that the correlation coefficients in the both models can be regarded as 0. By comparing the DIC value, we find that the Probit model is more suitable to describe the distribution of the endpoint thresholds of the reliability window. Finally, both the point estimation and interval estimation results of the reliability window are given to illustrate the feasibility of the method shown in the paper.     

The survival of newly founded firms: a case-study into varying-coefficient models

Summary.  The success of a newly founded firm depends on various initial risk factors or start-up conditions such as the market that the business is aiming for, the experience and the age of the founder, the preparation before the launch, the financial frame and the legal form of the firm. These risk factors determine the chance of survival for the venture. However, the effects of these risk factors may change with time. Some effects may vanish whereas others remain constant. We analyse the survival of 1123 newly founded firms in the state of Bavaria, Germany. Our focus is on the investigation of time variation in the effects of risk factors. Time variation is tackled within the framework of varying-coefficient models, where time smoothly modifies the effects of risk factors. An important issue in our analysis is the separation of risk factors which have time-varying effects from those which have time constant effects. We make use of the Akaike criterion to separate these two types of risk factor.     

Bridge Estimators in the Partially Linear Model with High Dimensionality

This article studies variable selection and parameter estimation in the partially linear model when the number of covariates in the linear part increases to infinity. Using the bridge penalty method, we succeed in selecting the important covariates of the linear part. Under regularity conditions, we have shown that the bridge penalized estimator of the parametric part enjoys the oracle property. We also obtain the convergence rate of the estimator of the nonparametric part. Simulation studies show that the bridge estimator performs as well as the oracle estimator for the partially linear model. An application is analyzed to illustrate the bridge procedure.     

A bivariate fractionally cointegrated relationship in the context of cyclical structures

This paper deals with the analysis of cointegration in a bivariate system. However, we depart from the classic concept of cointegration in two aspects. First, we permit fractional degrees of integration in both the parent series and in their linear combination. Second, instead of assuming that the pole or singularity in the spectrum takes places at the zero frequency, we consider the case where the singularity occurs at a frequency λ in the interval (0, π]. We use a procedure that follows the same lines as the two-step testing strategy of R.F. Engle, and C.W.J. Granger, [Cointegration and error correction model. Representation, estimation and testing, Econometrica 55 (1987), pp. 251–276]. Thus, we test first the order of integration in the individual series, which are specified in terms of the Gegenbauer polynomials. Then, if the two series share the same degree of integration at a given frequency, we test the null hypothesis of no cointegration against the alternative of fractional cyclical cointegration, by testing the order of integration on the estimated residuals from the cointegrating regression. Finite sample critical values are obtained, and the power properties of the test are examined. An empirical application is also carried out at the end of the article.     

Fuzzy parametric sample selection model: Monte Carlo simulation approach

Over a few decades, regression model has received considerable attention and has been shown to be successful when applied together with other models. One of the most successful models is the sample selection model or the selectivity model. However, uncertainties and ambiguities do exist in the models, particularly the relationship between the endogenous and exogenous variables. Therefore, it will disrupt the ability and effectiveness of the model proceeded to give the estimated value that can explain the actual situation of a phenomenon. These are the questions and problems that are yet to be explored and the main aim of this study. A new framework for estimation of the sample selection model using the concept of fuzzy modelling is introduced. In this approach, a flexible fuzzy concept hybrid with the parametric sample selection model is known as fuzzy parametric sample selection model (FPSSM). The elements of vagueness and uncertainty in the models are represented in the model construction, as a way of increasing the available information to produce a more accurate model. This led to the development of the convergence theorem presented in the form of triangular fuzzy numbers to be used in the model. Consistency is an indicator of effectiveness of the developed models and justified using Monte Carlo simulation. Consistency and efficiency of the proposed model are considered in this study. In order to achieve that condition, a Monte Carlo simulation is used. Hence, the error terms of FPSSM are assumed to follow the normal and the chi-square distributions. Simulation results show that FPSSM is consistent and efficient when its distributions are normal. Instead, the FPSSM by chi-square distribution is found to be inconsistent.     

流动人口女性个体的生育间隔影响因素研究——基于2016年全国流动人口动态监测调查数据

本文采用2016年全国流动人口动态监测调查数据,运用半参数Cox回归对我国流动人口的生育间隔进行分析。结果发现：第一,不仅人口流动会延迟女性的生育时间,而且受教育水平的提高对女性的婚育间隔、第一次生育间隔均有显著的延迟效应。第二,结婚年龄越大,婚后越有可能选择尽早生育,且不同初婚时间对生育间隔的影响差异明显。同时,参加医疗保险对婚育间隔存在显著的缩短效应,而参加生育保险对生育间隔存在显著的延迟效应。越有经济实力以及在工作中担任重要职位的女性越有可能扩大生育间隔;而随着婚育间隔的扩大,第一次生育间隔反而会缩短。第三,初育子女的性别对第一次生育间隔的影响存在显著差异,即若初次生育为女性,则第一次生育间隔会缩短。第四,根据生育政策效果分析发现,放开生育政策虽无法促使女性缩短婚育间隔,但会明显缩短第一次生育间隔。     

Estimation of bivariate and marginal distributions with censored data

Summary. Consider a pair of random variables, both subject to random right censoring. New estimators for the bivariate and marginal distributions of these variables are proposed. The estimators of the marginal distributions are not the marginals of the corresponding estimator of the bivariate distribution. Both estimators require estimation of the conditional distribution when the conditioning variable is subject to censoring. Such a method of estimation is proposed. The weak convergence of the estimators proposed is obtained. A small simulation study suggests that the estimators of the marginal and bivariate distributions perform well relatively to respectively the Kaplan–Meier estimator for the marginal distribution and the estimators of Pruitt and van der Laan for the bivariate distribution. The use of the estimators in practice is illustrated by the analysis of a data set.     

Analysis of a Feedback Fluid Model for Heterogeneous TCP Sources

In this paper we consider a bottleneck link and buffer used by one or two fluid sources that are subject to feedback. The feedback is such that the model captures essential aspects of the behavior of the Transmission Control Protocol as used in the Internet. During overflow, the buffer sends negative feedback signals to the sources to indicate that the sending rate should be reduced. Otherwise the buffer sends positive signals so as to increase the rate. In this context we find closed form expressions for the solution of the one-source case. The two-source case extends the single-source model considerably: we can control the behavior and parameters of each source individually. This enables us to study the impact of these parameters on the sharing of links and buffers. For the two-source case we solve the related two-point boundary value problem in the stationary case. We also establish a numerically efficient procedure to compute the coefficients of the solution of the differential equations. The numerical results of this model are presented in an accompanying paper.     

Tests for structural break in quantile regressions

The paper compares the existing tests for parameter instability in quantile regression. One is based on the estimated objective function and the other on the gradient. Their definition determines their characteristics and helpfulness. The former allows to check if the impact of a break on the entire equation changes across quantiles while a modified version of the latter verifies if the break affects only some coefficients or all of them and helps locating the break point. In addition the paper presents a Lagrange multiplier test for structural break. The advantage of the LM test is in the ease of implementation, since it simply requires the estimation of an auxiliary regression. An example shows the characteristics of each test. A Monte Carlo study concludes the analysis.     

Modelling and analysis of recall-based competing risks data

In this paper we consider the analysis of recall-based competing risks data. The chance of an individual recalling the exact time to event depends on the time of occurrence of the event and time of observation of the individual. In particular, it is assumed that the probability of recall depends on the time elapsed since the occurrence of an event. In this study we consider the likelihood-based inference for the analysis of recall-based competing risks data. The likelihood function is constructed by incorporating the information about the probability of recall. We consider the maximum likelihood estimation of parameters. Simulation studies are carried out to examine the performance of the estimators. The proposed estimation procedure is applied to a real life data set.     

带线性约束的多元线性回归模型参数估计

本文首先构造线性约束条件下的多元线性回归模型的样本似然函数,利用Lagrange法证明其合理性。其次,从似然函数的角度讨论线性约束条件对模型参数的影响,对由传统理论得出的参数估计作出贝叶斯与经验贝叶斯的改进。做贝叶斯改进时,将矩阵正态-Wishart分布作为模型参数和精度阵的联合共轭先验分布,结合构造的似然函数得出参数的后验分布,计算出参数的贝叶斯估计;做经验贝叶斯改进时,将样本分组,从方差的角度讨论由子样得出的参数估计对总样本的参数估计的影响,计算出经验贝叶斯估计。最后,利用Matlab软件生成的随机矩阵做模拟。结果表明,这两种改进后的参数估计均较由传统理论得出的参数估计更精确,拟合结果的误差比更小,可信度更高,在大数据的情况下,这种计算方法的速度更快。     

Asymptotic Unbiased Kernel Estimator for Line Transect Sampling

In this article, we propose a new estimator for the density of objects using line transect data. The proposed estimator combines the nonparametric kernel estimator with parametric detection function: the exponential or the half normal detection function to estimate the density of objects. The selection of the detection function depends on the testing of the shoulder condition assumption. If the shoulder condition is true then the half-normal detection function is introduced together with the kernel estimator. Otherwise, the negative exponential is combined with the kernel estimator. Under these assumptions, the proposed estimator is asymptotically unbiased and it is strongly consistent estimator for the density of objects using line transect data. The simulation results indicate that the proposed estimator is very successful in taking the advantage of the parametric detection function available.     

Performance of the shrinkage preliminary test ridge regression estimators based on the conflicting of W,LR and LM tests

The shrinkage preliminary test ridge regression estimators (SPTRRE) based on the Wald (W), the likelihood ratio (LR) and the Lagrangian multiplier (LM) tests are considered in this paper. The bias and the risk functions of the proposed estimators are derived. The regions of optimality of the estimators are determined under the quadratic risk function. Under the null hypothesis, the SPTRRE based on LM test has the smallest risk, followed by the estimators based on LR and W tests. However, the SPTRRE based on W test performs the best followed by the LR and LM based estimators when the parameter moves away from the subspace of the restrictions. The conditions of superiority of the proposed estimator for both ridge and departure parameters are discussed. The optimum choice of the level of significance becomes the traditional choice by using the W test for all non-negative ridge parameters.     

Markowitz模型与Black—Litterman投资人情绪对资产组合的影响模型比较研究

由于马尔科维茨资产组合模型存在放大方差和对输入变量异常敏感以及无卖空约束下的无意义的权重问题,使均值方差模型很难在实际中应用。针对该模型的缺陷,利用BMA模型优化Black-Litterman模型观点加入方式,详细设定了模型观点矩阵,利用非贝叶斯法则构建了投资人对观念的置信度,明确计算了隐含均衡收益和上证指数数据,再次证实了投资人情绪对传统资产组合模型结果的影响,并从数理模型上阐释了两个模型所依据的理论基础。     

Degradation modeling based on gamma process models with random effects

The random effects in a gamma process are introduced in terms of its scale parameter. However, the scale parameter affects both its mean and variance. Hence, the variation of the degradation rates and the within degradation increments are expected to be large. For some products, the random effects affect just the rate or just the volatility of the process. Thus, two modifications of the parameters' structure of the gamma process are proposed. One implies that the random effects affect just the volatility and the second just the rate. A Bayesian estimation approach is provided and implemented in two case studies.     

Testing for Nonlinear Autoregression

This article considers consistent testing the null hypothesis that the conditional mean of an economic time series is linear in past values. Two specific tests are discussed, the Cramér–von Mises and the Kolmogorov–Smirnov tests. The particular feature of the proposed tests is that the bootstrap is used to estimate the nonstandard asymptotic distributions of the test statistics considered. The tests are justified theoretically by asymptotics, and their finite-sample behaviors are studied by means of Monte Carlo experiments. The tests are applied to five U.S. monthly series, and evidence of nonlinearity is found for the first difference of the logarithm of the personal income and for the first difference of the unemployment rate. No evidence of nonlinearity is found for the first difference of the logarithm of the U.S. dollar/Japanese Yen exchange rate, for the first difference of the 3-month T-bill interest rate and for the first difference of the logarithm of the M2 money stock. Contrary to typically used tests, the proposed testing procedures are robust to the presence of conditional heteroscedasticity. This may explain the results for the exchange rate and the interest rate.