THE CONVERGENCE RATE OF SEQUENTIAL FIXED-WIDTH CONFIDENCE INTERVALS FOR REGULAR FUNCTIONALS

Let X₁X₂,.be i.i.d. random variables and let U_n= (n r)^-1S?^(n,r) h (X_i1,., X_ir,) be a U-statistic with EU_n= v, v unknown. Assume that g(X₁) =E[h(X₁,.,X_r) - v |X₁]has a strictly positive variance s?². Further, let a be such that φ(a) - φ(-a) =α for fixed α, 0 < α < 1, where φ is the standard normal d.f., and let S²_n be the Jackknife estimator of n Var U_n. Consider the stopping times N(d)= min {n: S²_n: + n^-1≤²a^-2},d > 0, and a confidence interval for v of length 2d,of the form I_n,d= [U_n,-d, Un + d]. We assume that Var U_n is unknown, and hence, no fixed sample size method is available for finding a confidence interval for v of prescribed width 2d and prescribed coverage probability α Turning to a sequential procedure, let I_N(d),d be a sequence of sequential confidence intervals for v. The asymptotic consistency of this procedure, i.e. lim_{d → 0}P(v ∈ I_N(d),d)=α follows from Sproule (1969). In this paper, the rate at which |P(v ∈ I_N(d),d) converges to α is investigated. We obtain that |P(v ∈ I_N(d),d) - α| = 0 (d^{1/2-(1+k)/2(1+m)}), d → 0, where K = max {0,4 - m}, under the condition that E|h(X₁, X_r)|^m < ∞m > 2. This improves and extends recent results of Ghosh & DasGupta (1980) and Mukhopadhyay (1981).     

Sequential procedures based on M-estimators with discontinuous score functions

Bounded-width sequential confidence intervals and sequential tests for regression parameter based on M-estimators are extended to the case where the score-functions generating the M-estimators have jump-discontinuities. In the context of the asymptotic normality of the stopping variable, for the confidence interval problem, it is observed that the jump-discontinuities induce a slower rate of convergence. The proofs of the main theorems rest on the weak convergence of some related processes and this is also studied.     

A New Look at the Psychometric Paradigm of Perception of Hazards

The psychometric paradigm has been the most influential model in the field of risk analysis. The "cognitive maps" of hazards produced by the paradigm seem to explain how laypeople perceive the various risks they face. Because most of the studies used aggregated data, analyzed using principal component analysis, it is not known whether the model neglects individual differences in risk perception. There has been much criticism on the fact that few studies have examined individual differences in the cognitive representation of hazards. In order to detect and describe the internal structure of the three-way data, we conducted a three-way component analysis (3MPCA). Data for the present analysis were derived from a mail survey conducted in Switzerland. Participants were asked to judge 9 attributes for 26 hazards. Individual differences in the cognitive representation of hazards were correlated with external variables (e.g., general trust). The results suggest that methods permitting individual differences should be used more frequently and that utilizing different methods could provide greater insight into the cognitive representation of risks.     

近10年来我国农民工问题研究述评

农民工问题是中国农民在城镇化、现代化进程中伴生的重大人口与经济社会问题。以《中国青年研究》近10年来199篇刊文为样本,分析发现,农民工问题研究主要集中在民生保障、流动融入、家庭生活、政治维权及随迁子女教育等几大方面。研究者问题意识强烈,论述逻辑清晰;研究视角多元纷呈,理论阐释有待提升;注重实证分析但操作方法尚需科学规范,研究论域值得进一步拓展和深化,特别是女性农民工、流动儿童、中老年农民工及其他相关弱势群体需要重点关注。     

我国高校教师教学能力研究的问题域、反思及其走向

我国高校教师教学能力研究的问题域主要体现为:认识论研究,教学能力是什么;价值论研究,教学能力的作用;方法论研究,教学能力如何提升。研究中存在的问题是:研究视角偏窄,研究主题覆盖面小;研究方法单一,研究结论针对性不强;宏观规划研究缺乏,制度体系研究不够。今后的研究中要考虑教师和学生的主体地位和需求,强化量化研究与质性研究的协同,注重高校之间的横向联系,加强规章制度建设。     

Time Series Modeling of Degradation Due to Outdoor Weathering

Environmental variables have an important effect on the reliability of many products such as coatings and polymeric composites. Long-term prediction of the performance or service life of such products must take into account the probabilistic/stochastic nature of the outdoor weather. In this article, we propose a time series modeling procedure to model the time series data of daily accumulated degradation. Daily accumulated degradation is the total amount of degradation accrued within one day and can be obtained by using a degradation rate model for the product and the weather data. The fitted model of the time series can then be used to estimate the future distribution of cumulative degradation over a period of time, and to compute reliability measures such as the probability of failure. The modeling technique and estimation method are illustrated using the degradation of a solar reflector material. We also provide a method to construct approximate confidence intervals for the probability of failure.     

Inference for the Mean Residual Life Function via Empirical Likelihood

In addition to the distribution function, the mean residual life (MRL) function is the other important function which can be used to characterize a lifetime in survival analysis and reliability. For inference on the MRL function, some procedures have been proposed in the literature. However, the coverage accuracy of such procedures may be low when the sample size is small. In this article, an empirical likelihood (EL) inference procedure of MRL function is proposed and the limiting distribution of the EL ratio for MRL function is derived. Based on the result, we obtain confidence interval/band for the MRL function. The proposed method is compared with the normal approximation based method through simulation study in terms of coverage probability.     

Inference for a Linear Functional of Cumulative Hazard Function Via Empirical Likelihood

This article discusses sampling plans, that is, the allocation of sampling units, for computing tolerance limits in a balanced one--way random-effects model. The expected width of the tolerance interval is derived and used as the basis for comparing different sampling plans. A well-known cost function and examples are used to facilitate the discussion.     

Empirical Likelihood Inference for the Parameter in Additive Partially Linear EV Models

In this article, we consider empirical likelihood inference for the parameter in the additive partially linear models when the linear covariate is measured with error. By correcting for attenuation, a corrected-attenuation empirical log-likelihood ratio statistic for the unknown parameter β, which is of primary interest, is suggested. We show that the proposed statistic is asymptotically standard chi-square distribution without requiring the undersmoothing of the nonparametric components, and hence it can be directly used to construct the confidence region for the parameter β. Some simulations indicate that, in terms of comparison between coverage probabilities and average lengths of the confidence intervals, the proposed method performs better than the profile-based least-squares method. We also give the maximum empirical likelihood estimator (MELE) for the unknown parameter β, and prove the MELE is asymptotically normal under some mild conditions.     

Coherent Frequentism: A Decision Theory Based on Confidence Sets

By representing fair betting odds according to one or more pairs of confidence set estimators, dual parameter distributions called confidence posteriors secure the coherence of actions without any prior distribution. This theory reduces to the maximization of expected utility when the pair of posteriors is induced by an exact or approximate confidence set estimator or when a reduction rule is applied to the pair. Unlike the p-value, the confidence posterior probability of an interval hypothesis is suitable as an estimator of the indicator of hypothesis truth since it converges to 1 if the hypothesis is true or to 0 otherwise.