刻画知识与信念的自信逻辑系统

理性认知主体的知识与信念具有可反省性、知识向信念转化等特征。我们可仿造真性模态逻辑的技术方法定义普遍有效式,构造极小正规认知系统ME。该系统具有可靠性和完备性,在此基础上添加一些公理序列可得到许多不同的正规认知逻辑系统。这些系统都从某种意义上刻画了知识与信念,揭示了二者的区别与联系。出于不同的认识论观点,这些系统在公理序列的选择、刻画知识与信念的程度、推理能力等方面存在着一定的差别。     

Asymptotic Normality of the QMLE Estimator of ARCH in the Nonstationary Case

We establish consistency and asymptotic normality of the quasi‐maximum likelihood estimator in the linear ARCH model. Contrary to the existing literature, we allow the parameters to be in the region where no stationary version of the process exists. This implies that the estimator is always asymptotically normal.     

Bootstrap Unit Root Tests

We consider the bootstrap unit root tests based on finite order autoregressive integrated models driven by iid innovations, with or without deterministic time trends. A general methodology is developed to approximate asymptotic distributions for the models driven by integrated time series, and used to obtain asymptotic expansions for the Dickey–Fuller unit root tests. The second‐order terms in their expansions are of stochastic orders O_p(n^−1/4) and O_p(n^−1/2), and involve functionals of Brownian motions and normal random variates. The asymptotic expansions for the bootstrap tests are also derived and compared with those of the Dickey–Fuller tests. We show in particular that the bootstrap offers asymptotic refinements for the Dickey–Fuller tests, i.e., it corrects their second‐order errors. More precisely, it is shown that the critical values obtained by the bootstrap resampling are correct up to the second‐order terms, and the errors in rejection probabilities are of order o(n^−1/2) if the tests are based upon the bootstrap critical values. Through simulations, we investigate how effective is the bootstrap correction in small samples.     

On Efficient Estimators of the Proportion of True Null Hypotheses in a Multiple Testing Setup

We consider the problem of estimating the proportion θ of true null hypotheses in a multiple testing context. The setup is classically modelled through a semiparametric mixture with two components: a uniform distribution on interval [0,1] with prior probability θ and a non‐parametric density f . We discuss asymptotic efficiency results and establish that two different cases occur whether f vanishes on a non‐empty interval or not. In the first case, we exhibit estimators converging at a parametric rate, compute the optimal asymptotic variance and conjecture that no estimator is asymptotically efficient (i.e. attains the optimal asymptotic variance). In the second case, we prove that the quadratic risk of any estimator does not converge at a parametric rate. We illustrate those results on simulated data.     

Non‐Parametric Estimation of the Conditional Distribution of the Interjumping Times for Piecewise‐Deterministic Markov Processes

This paper presents a non‐parametric method for estimating the conditional density associated to the jump rate of a piecewise‐deterministic Markov process. In our framework, the estimation needs only one observation of the process within a long time interval. Our method relies on a generalization of Aalen's multiplicative intensity model. We prove the uniform consistency of our estimator, under some reasonable assumptions related to the primitive characteristics of the process. A simulation study illustrates the behaviour of our estimator.     

M-estimation of the accelerated failure time model under a convex discrepancy function

Based on the Kaplan–Meier weight functions, we introduce a class of M-estimators of regression parameters for the accelerated failure time (AFT) model with right censored data. The proposed M-estimator is root-n consistent and asymptotically normal under appropriate assumptions. For robustness analysis, we also derive the corresponding influence functions. Appropriate criteria are developed for tests of hypotheses concerning regression parameters. The results are applied to several particular cases. We evaluate the finite-sample performance of the proposed methods through extensive simulation studies.     

Labeling Same-Sex Sexuality in a Tolerant Society That Values Normality: The Dutch Case

Studies have pointed to a trend in Western societies toward the normalization of homosexuality and emerging “post-gayness” among young people, who no longer consider their sexual identity meaningful in defining themselves. This article takes a closer look at the Dutch case where tolerance is regarded as a national virtue, while society remains heteronormative. In 38 interviews with Dutch same-sex-attracted young people, we investigated the labels they used to describe their sexual orientation to reveal what they can tell us about normalization, tolerance, and heteronormativity. In their labeling strategies, participants de-emphasized their sexual identity, othered, and reinforced the hetero/homo binary. They preferred labels without connotations to gender expression. While post-gay rhetoric was ideologically appealing, its use was not an outcome of their sexual orientation having become insignificant; it rather enabled them to produce normality. We discuss the findings against the backdrop of “Dutch tolerance,” which rests on an ideology of normality.     

Normal Mixture Quasi-maximum Likelihood Estimator for GARCH Models

Abstract.  The generalized autoregressive conditional heteroscedastic (GARCH) model has been popular in the analysis of financial time series data with high volatility. Conventionally, the parameter estimation in GARCH models has been performed based on the Gaussian quasi-maximum likelihood. However, when the innovation terms have either heavy-tailed or skewed distributions, the quasi-maximum likelihood estimator (QMLE) does not function well. In order to remedy this defect, we propose the normal mixture QMLE (NM-QMLE), which is obtained from the normal mixture quasi-likelihood, and demonstrate that the NM-QMLE is consistent and asymptotically normal. Finally, we present simulation results and a real data analysis in order to illustrate our findings.     

Cressie–Read Power-Divergence Statistics for Non-Gaussian Vector Stationary Processes

Abstract.  For a class of vector-valued non-Gaussian stationary processes, we develop the Cressie–Read power-divergence (CR) statistic approach which has been proposed for the i.i.d. case. The CR statistic includes empirical likelihood as a special case. Therefore, by adopting this CR statistic approach, the theory of estimation and testing based on empirical likelihood is greatly extended. We use an extended Whittle likelihood as score function and derive the asymptotic distribution of the CR statistic. We apply this result to estimation of autocorrelation and the AR coefficient, and get narrower confidence intervals than those obtained by existing methods. We also consider the power properties of the test based on asymptotic theory. Under a sequence of contiguous local alternatives, we derive the asymptotic distribution of the CR statistic. The problem of testing autocorrelation is discussed and we introduce some interesting properties of the local power.