A Bernstein inequality for exponentially growing graphs

In this article, we present a Bernstein inequality for sums of random variables which are defined on a graphical network whose nodes grow at an exponential rate. The inequality can be used to derive concentration inequalities in highly connected networks. It can be useful to obtain consistency properties for non parametric estimators of conditional expectation functions which are derived from such networks.     

An effective estimation strategy for population mean under random non-response situations in two-phase successive sampling

This paper presents a modified exponential type estimation strategy for the current population mean in the presence of random non-response situations in two-occasion successive sampling under two-phase set-up. The properties of the proposed estimators have been examined with the assumption that numbers of sampling units follow a distribution due to random non-response. The performances of the proposed estimators are compared with the estimators designated for the complete response situations. Empirical studies are carried out to show the dominance nature of the proposed estimators over the estimator defined for complete response situations. Appropriate recommendations have been made to the survey practitioners/researchers for their real-life practical applications.     

Tobit regression for modeling mean survival time using data subject to multiple sources of censoring

Mean survival time is often of inherent interest in medical and epidemiologic studies. In the presence of censoring and when covariate effects are of interest, Cox regression is the strong default, but mostly due to convenience and familiarity. When survival times are uncensored, covariate effects can be estimated as differences in mean survival through linear regression. Tobit regression can validly be performed through maximum likelihood when the censoring times are fixed (ie, known for each subject, even in cases where the outcome is observed). However, Tobit regression is generally inapplicable when the response is subject to random right censoring. We propose Tobit regression methods based on weighted maximum likelihood which are applicable to survival times subject to both fixed and random censoring times. Under the proposed approach, known right censoring is handled naturally through the Tobit model, with inverse probability of censoring weighting used to overcome random censoring. Essentially, the re‐weighting data are intended to represent those that would have been observed in the absence of random censoring. We develop methods for estimating the Tobit regression parameter, then the population mean survival time. A closed form large‐sample variance estimator is proposed for the regression parameter estimator, with a semiparametric bootstrap standard error estimator derived for the population mean. The proposed methods are easily implementable using standard software. Finite‐sample properties are assessed through simulation. The methods are applied to a large cohort of patients wait‐listed for kidney transplantation.     

Hybrid pairwise‐likelihood estimation methods for incomplete longitudinal binary data

In longitudinal data, missing observations occur commonly with incomplete responses and covariates. Missing data can have a ‘missing not at random’ mechanism, a non‐monotone missing pattern, and moreover response and covariates can be missing not simultaneously. To avoid complexities in both modelling and computation, a two‐stage estimation method and a pairwise‐likelihood method are proposed. The two‐stage estimation method enjoys simplicities in computation, but incurs more severe efficiency loss. On the other hand, the pairwise approach leads to estimators with better efficiency, but can be cumbersome in computation. In this paper, we develop a compromise method using a hybrid pairwise‐likelihood framework. Our proposed approach has better efficiency than the two‐stage method, but its computational cost is still reasonable compared to the pairwise approach. The performance of the methods is evaluated empirically by means of simulation studies. Our methods are used to analyse longitudinal data obtained from the National Population Health Study.     

心理学的遗忘理论对二语损耗的解释力

语言损耗经过三十年的发展,取得了许多有价值的研究成果。在回顾二语损耗研究的基础上,运用心理学遗忘理论中的提取变慢说（或提取失败说）、干扰说以及遗忘曲线,通过对国内外的二语损耗研究结果进行解释,发现提取速度变慢说（或提取失败说）可以解释二语损耗研究中受损者在产出性技能损耗方面的表现以及产出性技能与接受性技能在损耗方面的差异;干扰说可以解释二语损耗研究中受损者在音素、词汇以及形态-句法等方面的损耗。但是,遗忘曲线却无法解释二语损耗研究中出现的＂最初的稳定状态＂现象与二语损耗的倒置假设。     

On MLEs of the parameters of a modified Weibull distribution for progressively type-2 censored samples

Lifetimes of modern mechanic or electronic units usually exhibit bathtub-shaped failure rates. An appropriate probability distribution to model such data is the modified Weibull distribution proposed by Lai et al. [15]. This distribution has both the two-parameter Weibull and type-1 extreme value distribution as special cases. It is able to model lifetime data with monotonic and bathtub-shaped failure rates, and thus attracts some interest among researchers because of this property. In this paper, the procedure of obtaining the maximum likelihood estimates (MLEs) of the parameters for progressively type-2 censored and complete samples are studied. Existence and uniqueness of the MLEs are proved.     

New Tests of Spatial Segregation Based on Nearest Neighbour Contingency Tables

Abstract.  The spatial clustering of points from two or more classes (or species) has important implications in many fields and may cause segregation or association, which are two major types of spatial patterns between the classes. These patterns can be studied using a nearest neighbour contingency table (NNCT) which is constructed using the frequencies of nearest neighbour types. Three new multivariate clustering tests are proposed based on NNCTs using the appropriate sampling distribution of the cell counts in a NNCT. The null patterns considered are random labelling (RL) and complete spatial randomness (CSR) of points from two or more classes. The finite sample performance of these tests are compared with other tests in terms of empirical size and power. It is demonstrated that the newly proposed NNCT tests perform relatively well compared with their competitors and the tests are illustrated using two example data sets.     

A Model Validation Procedure when Covariate Data are Missing at Random

Abstract. In the presence of missing covariates, standard model validation procedures may result in misleading conclusions. By building generalized score statistics on augmented inverse probability weighted complete‐case estimating equations, we develop a new model validation procedure to assess the adequacy of a prescribed analysis model when covariate data are missing at random. The asymptotic distribution and local alternative efficiency for the test are investigated. Under certain conditions, our approach provides not only valid but also asymptotically optimal results. A simulation study for both linear and logistic regression illustrates the applicability and finite sample performance of the methodology. Our method is also employed to analyse a coronary artery disease diagnostic dataset.     

Asymptotic expansions and the reliability of tests in accelerated failure time models

This paper gives matrix formilae for the O(n^-1 ) cerrecti0n applicable to asymptotically efficient conditional moment tests. These formulae only require expectations of functions involving, at most, second order derivatives of the log-likelihood; unlike those previously providcd by Ferrari and Corddro(1994). The correction is used to assess the reliability of first order asymptotic theory for arbitrary residual-based diagnostics in a class of accelerated failure time models: this correction is always parameter free, depending only on the number of included covariates in the regression design. For all but one of the tests considered, first order theory is found to be extremely unreliable, even in quite large samples, although this may not be widely appreciated by applied workers.     

An empirical bias–variance analysis of DECORATE ensemble method at different training sample sizes

DECORATE (Diverse Ensemble Creation by Oppositional Relabeling of Artificial Training Examples) is a classifier combination technique to construct a set of diverse base classifiers using additional artificially generated training instances. The predictions from the base classifiers are then integrated into one by the mean combination rule. In order to gain more insight about its effectiveness and advantages, this paper utilizes a large experiment to study the bias–variance analysis of DECORATE as well as some other widely used ensemble methods (such as bagging, AdaBoost, random forest) at different training sample sizes. The experimental results yield the following conclusions. For small training sets, DECORATE has a dominant advantage over its rivals and its success is attributed to the larger bias reduction achieved by it than the other algorithms. With increase in training data, AdaBoost benefits most and the bias reduced by it gradually turns to be significant while its variance reduction is also medium. Thus, AdaBoost performs best with large training samples. Moreover, random forest behaves always second best regardless of small or large training sets and it is seen to mainly decrease variance while maintaining low bias. Bagging seems to be an intermediate one since it reduces variance primarily.