Non‐parametric Copula Estimation Under Bivariate Censoring

In this paper, we consider non‐parametric copula inference under bivariate censoring. Based on an estimator of the joint cumulative distribution function, we define a discrete and two smooth estimators of the copula. The construction that we propose is valid for a large range of estimators of the distribution function and therefore for a large range of bivariate censoring frameworks. Under some conditions on the tails of the distributions, the weak convergence of the corresponding copula processes is obtained in l^∞([0,1]²). We derive the uniform convergence rates of the copula density estimators deduced from our smooth copula estimators. Investigation of the practical behaviour of these estimators is performed through a simulation study and two real data applications, corresponding to different censoring settings. We use our non‐parametric estimators to define a goodness‐of‐fit procedure for parametric copula models. A new bootstrap scheme is proposed to compute the critical values.     

Improved inference for MCP-Mod approach using time-to-event endpoints with small sample sizes

The Multiple Comparison Procedures with Modeling Techniques (MCP-Mod) framework has been recently approved by the U.S. Food, Administration, and European Medicines Agency as fit-for-purpose for phase II studies. Nonetheless, this approach relies on the asymptotic properties of Maximum Likelihood (ML) estimators, which might not be reasonable for small sample sizes. In this paper, we derived improved ML estimators and correction for their covariance matrices in the censored Weibull regression model based on the corrective and preventive approaches. We performed two simulation studies to evaluate ML and improved ML estimators with their covariance matrices in (i) a regression framework (ii) the Multiple Comparison Procedures with Modeling Techniques framework. We have shown that improved ML estimators are less biased than ML estimators yielding Wald-type statistics that controls type I error without loss of power in both frameworks. Therefore, we recommend the use of improved ML estimators in the MCP-Mod approach to control type I error at nominal value for sample sizes ranging from 5 to 25 subjects per dose.     

Bayesian population estimation for small sample capture-recapture data using noninformative priors

One critical issue in the Bayesian approach is choosing the priors when there is not enough prior information to specify hyperparameters. Several improper noninformative priors for capture-recapture models were proposed in the literature. It is known that the Bayesian estimate can be sensitive to the choice of priors, especially when sample size is small to moderate. Yet, how to choose a noninformative prior for a given model remains a question. In this paper, as the first step, we consider the problem of estimating the population size for _Mt$M_{\mathrm{t}}$ model using noninformative priors. The _Mt$M_{\mathrm{t}}$ model has prodigious application in wildlife management, ecology, software liability, epidemiological study, census under-count, and other research areas. Four commonly used noninformative priors are considered. We find that the choice of noninformative priors depends on the number of sampling occasions only. The guidelines on the choice of noninformative priors are provided based on the simulation results. Propriety of applying improper noninformative prior is discussed. Simulation studies are developed to inspect the frequentist performance of Bayesian point and interval estimates with different noninformative priors under various population sizes, capture probabilities, and the number of sampling occasions. The simulation results show that the Bayesian approach can provide more accurate estimates of the population size than the MLE for small samples. Two real-data examples are given to illustrate the method.     

Implementation of an adaptive group sequential design in a bioequivalence study

The study design was a multi-center, multiple-dose, randomized, open-label, 2 x 2 crossover study in patients with advanced solid tumors. Each patient was randomized to receive the test formulation or the reference formulation of the drug. The primary objective of the study was to demonstrate the bioequivalence of the test formulation T relative to the reference formulation R. The primary pharmacokinetic endpoints were AUC and Cmax. Since there were different bioequivalence criteria, different endpoints, with different and highly variable coefficients of variation, an adaptive design with a stopping rule for early establishing the bioequivalence as well as early stopping for futility with a flexible information-based monitoring based on error spending approach was implemented to manage uncertainty in assumptions of variability and expected slow enrollment rates.     

退势单位根检验的小样本性质

在经验研究中,尽管Dickey-Fuller提出的 统计量是应用最广泛的单位根检验,但是,它的检验功效偏低是众所周知的。为了改善Dickey-Fuller检验的功效,本文将时间序列的四种退势方法和 检验、 检验、MAX检验和 检验相结合,通过蒙特卡洛模拟试验研究了16种退势单位根检验的小样本性质。研究发现,退势单位根检验均不同程度地改善了 型检验的功效,特别是退势单位根检验 -KGLS、MAX-KGLS、 -RLS和MAX-RLS具有更理想的小样本性质。     

Bootstrap inference in local polynomial regression of time series

In this paper we consider the inferential aspect of the nonparametric estimation of a conditional function , where X _t,m represents the vector containing the m conditioning lagged values of the series. Here is an arbitrary measurable function. The local polynomial estimator of order p is used for the estimation of the function g, and of its partial derivatives up to a total order p. We consider α-mixing processes, and we propose the use of a particular resampling method, the local polynomial bootstrap, for the approximation of the sampling distribution of the estimator. After analyzing the consistency of the proposed method, we present a simulation study which gives evidence of its finite sample behaviour.     

An outlier detection scheme for dynamical sequential datasets

Outlier detection plays an important role in the pre-treatment of sequential datasets to obtain pure valuable data. This paper proposes an outlier detection scheme for dynamical sequential datasets. First, the conception of forward outlier factor(FOF) and backward outlier factor(BOF) are employed to measure an object’s similarity shared with its sequentially adjacent objects. The object that shows no similarity with its sequential neighbors is labeled as suspicious outliers, which will be treated subsequently to judge whether it is really an outlier in the dataset. Second, the sequentially adjacent suspicious outliers are defined as suspicious outlier series(SOS), then the expected path representing the ideal transition path through the suspicious outliers in the SOS and the measured path representing the real path through all the objects in the SOS are employed, and the ratio of the length of the expected path to that of the measured path indicates whether there exist outliers in the SOS. Third, in the case that there exist outliers in the SOS, if there are N suspicious outliers in the SOS, then 2^N ? 2 remaining path will be generated by removing k(0 < k < N) suspicious outliers and sequentially connecting the remaining ones. The dynamical sequential outlier factor(DSOF) is employed to represent the ratio of the length of measured path of the considered remaining path to the that of the the expected path of the corresponding SOS, and the degree of the objects removed in a remaining path being outliers is indicated by the DSOF. The proposed outlier detection scheme is conducted from a dynamical perspective, and breaks the tight relation between being an outlier and being not similar with adjacent objects. Experiments are conducted to evaluate the effectiveness of the proposed scheme, and the experimental results verify that the proposed scheme has higher detection quality for sequential dataset. In addition, the proposed outlier detection scheme is not dependent on the size of dataset and needs no prior information about the distribution of the data.     

A new two sample type-II progressive censoring scheme

In this paper we introduce a new type-II progressive censoring scheme for two samples. It is observed that the proposed censoring scheme is analytically more tractable than the existing joint progressive type-II censoring scheme proposed by Rasouli and Balakrishnan. The maximum likelihood estimators of the unknown parameters are obtained and their exact distributions are derived. Based on the exact distributions of the maximum likelihood estimators exact confidence intervals are also constructed. For comparison purposes we have used bootstrap confidence intervals also. One data analysis has been performed for illustrative purposes. Finally we propose some open problems.     

Conditionally unbiased estimation in the normal setting with unknown variances

To efficiently and completely correct for selection bias in adaptive two-stage trials, uniformly minimum variance conditionally unbiased estimators (UMVCUEs) have been derived for trial designs with normally distributed data. However, a common assumption is that the variances are known exactly, which is unlikely to be the case in practice. We extend the work of Cohen and Sackrowitz (Statistics & Probability Letters, 8(3):273-278, 1989), who proposed an UMVCUE for the best performing candidate in the normal setting with a common unknown variance. Our extension allows for multiple selected candidates, as well as unequal stage one and two sample sizes.     

Bias-corrected realized variance

We propose a novel “bias-corrected realized variance” (BCRV) estimator based upon the appropriate re-weighting of two realized variances calculated at different sampling frequencies. Our bias-correction methodology is found to be extremely accurate, with the finite sample variance being significantly minimized. In our Monte Carlo experiments and a finite sample MSE comparison of alternative estimators, the performance of our straightforward BCRV estimator is shown to be comparable to other widely-used integrated variance estimators. Given its simplicity, our BCRV estimator is likely to appeal to researchers and practitioners alike for the estimation of integrated variance.