临界角聚焦误差检测的改进

介绍了光盘系统中临界角聚焦误差检测的改进方法及理论分析，改善了误差检测信号和增益特性，提高了自动聚焦误差控制系统的聚焦精度及稳定性。     

α—较多最优解的梯度特性

对于多目标规划的α—较多最优解,本文给出目标函数的梯度特性.     

关于平面对称紧凸集不等式

本文简论平面对称紧凸集不等式问题,引伸Favard不等式,对不等式中的相关常数给出两种证法。     

Upper Bound for p-Value of the Test of Multivariate Normal Ordered Mean Vectors Against all Alternatives

Consider the problem of testing the isotonic of several p-variate normal mean vectors against all alternatives. It is difficult to compute the exact p-value for this problem of testing with the classical method when the covariance matrices are completely unknown. In the present paper, a test statistic is proposed for this problem of testing. A reformulation of the test statistic is given based on the orthogonal projections on the closed convex cones and then the upper bound for p-value of the test statistic is computed.     

Zenga Distribution and Inequality Ordering

The aim of this article is to establish an ordering related to the inequality for the recently introduced Zenga distribution. In addition to the well-known order based on the Lorenz curve, the order based on I(p) curve is considered. Since the Zenga distribution seems to be suitable to model wealth, financial, actuarial, and, especially, income distributions, these findings are fundamental in the understanding of how parameter values are related to inequality. This investigation shows that for the Zenga distribution, two of the three parameters are inequality indicators.     

LIMIT THEOREMS FOR ASYMPTOTICALLY MINIMAX ESTIMATION OF A DISTRIBUTION WITH INCREASING FAILURE RATE UNDER A RANDOM MIXED CENSORSHIP/TRUNCATION MODEL

ABSTRACT

The search for optimal non-parametric estimates of the cumulative distribution and hazard functions under order constraints inspired at least two earlier classic papers in mathematical statistics: those of Kiefer and Wolfowitz[1] Kiefer, J. and Wolfowitz, J. 1976. Asymptotically Minimax Estimation of Concave and Convex Distribution Functions. Z. Wahrsch. Verw. Gebiete, 34: 73–85. [Crossref], [Web of Science ®] , [Google Scholar] and Grenander[2] Grenander, U. 1956. On the Theory of Mortality Measurement. Part II. Scand. Aktuarietidskrift J., 39: 125–153.  [Google Scholar] respectively. In both cases, either the greatest convex minorant or the least concave majorant played a fundamental role. Based on Kiefer and Wolfowitz's work, Wang3-4 Wang, J.L. 1986. Asymptotically Minimax Estimators for Distributions with Increasing Failure Rate. Ann. Statist., 14: 1113–1131. Wang, J.L. 1987. Estimators of a Distribution Function with Increasing Failure Rate Average. J. Statist. Plann. Inference, 16: 415–427.   found asymptotically minimax estimates of the distribution function F and its cumulative hazard function Λ in the class of all increasing failure rate (IFR) and all increasing failure rate average (IFRA) distributions. In this paper, we will prove limit theorems which extend Wang's asymptotic results to the mixed censorship/truncation model as well as provide some other relevant results. The methods are illustrated on the Channing House data, originally analysed by Hyde.5-6 Hyde, J. 1977. Testing Survival Under Right Censoring and Left Truncation. Biometrika, 64: 225–230. Hyde, J. 1980. “Survival Analysis with Incomplete Observations”. In Biostatistics Casebook 31–46. New York: Wiley Series in Probability and Mathematical Statistics: Applied Probability and Statistics.       

Inequalities for Expected Current Record Statistics

In this article, we obtain sharp distribution-free bounds for the expected value of the gap between the current records and record values as well as upper sharp bounds for the spacings between any two upper current records. We also present two-sided bounds on the errors in approximating the means of current records by inverse hazard functions.     

Model selection in high-dimensional noisy data: a simulation study

In many practical applications, high-dimensional regression analyses have to take into account measurement error in the covariates. It is thus necessary to extend regularization methods, that can handle the situation where the number of covariates p largely exceed the sample size n, to the case in which covariates are also mismeasured. A variety of methods are available in this context, but many of them rely on knowledge about the measurement error and the structure of its covariance matrix. In this paper, we set the goal to compare some of these methods, focusing on situations relevant for practical applications. In particular, we will evaluate these methods in setups in which the measurement error distribution and dependence structure are not known and have to be estimated from data. Our focus is on variable selection, and the evaluation is based on extensive simulations.     

Ordering properties of largest order statistics from independent and heterogeneous Dagum populations

Abstract

The Dagum distribution has been extensively used to model income data, and its features have been appreciated in economics and financial studies. In this article, we discuss ordering properties of largest order statistics from independent and heterogeneous Dagum populations. We present some sufficient conditions for stochastic comparisons between largest order statistics in terms of the reversed hazard rate order, the usual stochastic order, the convex order, the likelihood ratio order and the dispersive order. Several numerical examples are presented to illustrate the results established here.