Local Power Analyses of Goodness-of-fit Tests for Copulas

Abstract.  The asymptotic behaviour of several goodness-of-fit statistics for copula families is obtained under contiguous alternatives. Many comparisons between a Cramér–von Mises functional of the empirical copula process and new moment-based goodness-of-fit statistics are made by considering their associated asymptotic local power curves. It is shown that the choice of the estimator for the unknown parameter can have a significant influence on the power of the Cramér–von Mises test and that some of the moment-based statistics can provide simple and efficient goodness-of-fit methods.     

Robust m-estimators

This paper provides a summary of the influence function approach to robust estimation of parametric models. Hampel's optimality results for M-estimators with a bounded influence function is generalized to allow for arbitrary choices of the asymptotic efficiency criterion and the norm of the influence function. Further extensions to other cases of practical interest are also considered.     

Estimation of regression models with equi-correlated responses when some observations on the response variable are missing

The present article deals with the problem of estimation of parameters in a linear regression model when some data on response variable is missing and the responses are equi-correlated. The ordinary least squares and optimal homogeneous predictors are employed to find the imputed values of missing observations. Their efficiency properties are analyzed using the small disturbances asymptotic theory. The estimation of regression coefficients using these imputed values is also considered and a comparison of estimators is presented.     

电子商务合同法律适用原则探析

为保证电子商务的健康发展，需对传统商事合同法律适用原则作必要的调整和改革，以满足合理确定电子商务合同准据法的需要：一是进一步减少对意思自治原则的限制；二是更加重视对最密切联系原则的运用；三是继续强调消费者权益保护法的直接适用；四是更多采用法律适用上的分割方法。     

大学生法治精神培养论

法治精神是人民群众战胜邪恶、维护正义的守护神。高等教育的重任之一就是重点培养大学生懂得依法治国的基本理论,提高法治观念,熟悉法律条款,严格地以法律来规范自己的言行,敢于拿起法律之剑治理国家,维护人民权益的法治精神,使之成为一名自觉的继承者、实践者或捍卫者。     

Provincial Conditional Income Convergence in China, 1953-1997: A Panel Data Approach

This paper examines the tendency towards income convergence among China's main provinces during the two periods: the pre-reform period 1953-1977 and the reform period 1978-1997 using the framework of the Solow growth model. The panel data method accounts for not only province-specific initial technology level but also the heterogeneity of the technological progress rate between the fast-growing coastal and interior provinces. Estimation problems of weak instruments and endogeneity are addressed by the use of a system generalized method of moments (GMM) estimator. The main empirical finding is that there is a system-wide income divergence during the reform period because the coastal provinces do not share a common technology progress rate with the interior provinces.     

Improved estimators for the selected location parameters

_i , i = 1, 2, ..., k be k independent exponential populations with different unknown location parameters θ _i , i = 1, 2, ..., k and common known scale parameter σ. Let Y _i denote the smallest observation based on a random sample of size n from the i-th population. Suppose a subset of the given k population is selected using the subset selection procedure according to which the population π _i is selected iff Y _i ≥Y ₍₁₎−d, where Y ₍₁₎ is the largest of the Y _i 's and d is some suitable constant. The estimation of the location parameters associated with the selected populations is considered for the squared error loss. It is observed that the natural estimator dominates the unbiased estimator. It is also shown that the natural estimator itself is inadmissible and a class of improved estimators that dominate the natural estimator is obtained. The improved estimators are consistent and their risks are shown to be O(kn ⁻²). As a special case, we obtain the coresponding results for the estimation of θ₍₁₎, the parameter associated with Y ₍₁₎. Received: January 6, 1998; revised version: July 11, 2000     

Best monotone M‐estimators

The author shows how to find M‐estimators of location whose generating function is monotone and which are optimal or close to optimal. It is easy to identify a consistent sequence of estimators in this class. In addition, it contains simple and efficient approximations in cases where the likelihood function is difficult to obtain. In some neighbourhoods of the normal distribution, the loss of efficiency due to the approximation is quite small. Optimal monotone M‐estimators can also be determined in cases when the underlying distribution is known only up to a certain neighbourhood. The author considers the e‐contamination model and an extension thereof that allows the distributions to be arbitrary outside compact intervals. His results also have implications for distributions with monotone score functions. The author illustrates his methodology using Student and stable distributions.     

NONPARAMETRIC QUANTILE ESTIMATION FROM RECORD-BREAKING DATA

Sometimes, in industrial quality control experiments and destructive stress testing, only values smaller than all previous ones are observed. Here we consider nonparametric quantile estimation, both the ‘sample quantile function’ and kernel-type estimators, from such record-breaking data. For a single record-breaking sample, consistent estimation is not possible except in the extreme tails of the distribution. Hence replication is required, and for m. such independent record-breaking samples the quantile estimators are shown to be strongly consistent and asymptotically normal as m-→∞. Also, for small m, the mean-squared errors, biases and smoothing parameters (for the smoothed estimators) are investigated through computer simulations.     

Comparing robust generalized variances and comments on efficiency

Numerous papers have considered the problem of comparing univariate measures of dispersion corresponding to two independent groups. This paper considers a multivariate generalization of this problem where the goal is to compare robust generalized variances. For reasons given in the paper, attention is focused on a particular W-estimator where multivariate outliers are downweighted via a projection-type outlier detection method. Included are results on the small-sample efficiency of several estimators plus comments on using the usual generalized variance.