Probability density estimation with data missing at random when covariables are present

This paper addresses the problem of the probability density estimation in the presence of covariates when data are missing at random (MAR). The inverse probability weighted method is used to define a nonparametric and a semiparametric weighted probability density estimators. A regression calibration technique is also used to define an imputed estimator. It is shown that all the estimators are asymptotically normal with the same asymptotic variance as that of the inverse probability weighted estimator with known selection probability function and weights. Also, we establish the mean squared error (MSE) bounds and obtain the MSE convergence rates. A simulation is carried out to assess the proposed estimators in terms of the bias and standard error.     

Minimum control charts

Standard control charts are very sensitive to estimation effects and/or deviations from normality. Hence a program has been carried out to remedy these problems. This is quite adequate in most circumstances, but not in all. In the present paper, the remaining complication is attacked: what to do if a nonparametric approach is indicated, but too few control observations are available for the estimation step? It is shown that grouping the observations during the monitoring phase works well. Surprisingly, rather than using the group averages, it is definitely preferable to compare the minimum for each group to a suitably chosen upper control limit. (And in the two-sided case, also the maximum to an analogous lower control limit.) This ‘minimum control chart’ is demonstrated to be quite attractive: it is easy to explain and to implement. Moreover, while it is truly nonparametric, its power of detection is comparable to that of the customary, normality assuming, charts based on averages.     

Information attainable in some randomly incomplete multivariate response models

In a general parametric setup, a multivariate regression model is considered when responses may be missing at random while the explanatory variables and covariates are completely observed. Asymptotic optimality properties of maximum likelihood estimators for such models are linked to the Fisher information matrix for the parameters. It is shown that the information matrix is well defined for the missing-at-random model and that it plays the same role as in the complete-data linear models. Applications of the methodologic developments in hypothesis-testing problems, without any imputation of missing data, are illustrated. Some simulation results comparing the proposed method with Rubin's multiple imputation method are presented.     

Confidence intervals for the scale parameter of exponential distribution based on Type II doubly censored samples

This paper deals with the problem of interval estimation of the scale parameter in the two-parameter exponential distribution subject to Type II double censoring. Base on a Type II doubly censored sample, we construct a class of interval estimators of the scale parameter which are better than the shortest length affine equivariant interval both in coverage probability and in length. The procedure can be repeated to make further improvement. The extension of the method leads to a smoothly improved confidence interval which improves the interval length with probability one. All improved intervals belong to the class of scale equivariant intervals.     

从洛克的两种性质思想探析客体的客观性问题

主客体问题在哲学认识论中占有重要的地位,吸引着哲学家们不断的探索和研究。该文首先简要概括了洛克的两种性质学说,然后分析了两种性质学说的实质,评价了他对客体学说的进一步发展所作的贡献及其观点中的局限性,最后对客体的实质作出了尝试性探讨并重新评判了符合论真理观。     

Māori experiences of multiple forms of discrimination: findings from Te Kupenga 2013

ABSTRACT

Comprehensive exploration of Māori experiences of discrimination in Aotearoa New Zealand remains limited, particularly in relation to exposure to multiple and interlocking forms of discrimination. This paper presents findings from a secondary analysis of Te Kupenga 2013, the first Māori Social Survey, examining patterning and prevalence of different forms of discrimination for Māori (n?=?5,549). Māori report experiencing multiple forms of discrimination, both over their lifetimes and within the last year. Although racial discrimination was the most commonly reported form, Māori also experience discrimination on the basis of other grounds including age, gender, and income. Māori also report exposure to multiple forms of discrimination. Discrimination occurred in a range of settings, with schools and workplaces common sites. The findings support the lived reality of Māori that racial and other forms of discrimination are pervasive, and experienced in multiple domains across the life course, representing a persistent breach of rights. It is critical that other forms of discrimination are measured alongside racism in order to understand and address the realities of multiple discrimination for Māori in Aotearoa New Zealand.     

Large‐sample tests of extreme‐value dependence for multivariate copulas

Starting from the characterization of extreme‐value copulas based on max‐stability, large‐sample tests of extreme‐value dependence for multivariate copulas are studied. The two key ingredients of the proposed tests are the empirical copula of the data and a multiplier technique for obtaining approximate p‐values for the derived statistics. The asymptotic validity of the multiplier approach is established, and the finite‐sample performance of a large number of candidate test statistics is studied through extensive Monte Carlo experiments for data sets of dimension two to five. In the bivariate case, the rejection rates of the best versions of the tests are compared with those of the test of Ghoudi et al. (1998) recently revisited by Ben Ghorbal et al. (2009). The proposed procedures are illustrated on bivariate financial data and trivariate geological data. The Canadian Journal of Statistics 39: 703–720; 2011. © 2011 Statistical Society of Canada     

乳化炸药装药机螺旋叶片基于UG参数化设计研究

通过构建叶片数学模型,在UG平台上完成乳化炸药装药机螺旋叶片参数化设计,给出构造叶片模板、创建UG参数化设计界面及UG二次开发设计步骤,并基于UG/OPEN API,采用C/C＋＋语言开发出参数化设计系统,编制应用程序,为后续螺旋叶片的三维制造提供了便捷的设计模型。     

Robust Lagrange multiplier test for detecting ARCH/GARCH effect using permutation and bootstrap

The Lagrange Multiplier (LM) test is one of the principal tools to detect ARCH and GARCH effects in financial data analysis. However, when the underlying data are non‐normal, which is often the case in practice, the asymptotic LM test, based on the χ²‐approximation of critical values, is known to perform poorly, particularly for small and moderate sample sizes. In this paper we propose to employ two re‐sampling techniques to find critical values of the LM test, namely permutation and bootstrap. We derive the properties of exactness and asymptotically correctness for the permutation and bootstrap LM tests, respectively. Our numerical studies indicate that the proposed re‐sampled algorithms significantly improve size and power of the LM test in both skewed and heavy‐tailed processes. We also illustrate our new approaches with an application to the analysis of the Euro/USD currency exchange rates and the German stock index. The Canadian Journal of Statistics 40: 405–426; 2012 © 2012 Statistical Society of Canada