Randomly weighted sums of linearly wide quadrant-dependent random variables with heavy tails

This paper investigates tail behavior of the randomly weighted sum ∑ⁿ_{k = 1}θ_kX_k and reaches an asymptotic formula, where X_k, 1 ? k ? n, are real-valued linearly wide quadrant-dependent (LWQD) random variables with a common heavy-tailed distribution, and θ_k, 1 ? k ? n, independent of X_k, 1 ? k ? n, are n non-negative random variables without any dependence assumptions. The LWQD structure includes the linearly negative quadrant-dependent structure, the negatively associated structure, and hence the independence structure. On the other hand, it also includes some positively dependent random variables and some other random variables. The obtained result coincides with the existing ones.     

Trend estimation of multivariate time series with controlled smoothness

This paper extends the univariate time series smoothing approach provided by penalized least squares to a multivariate setting, thus allowing for joint estimation of several time series trends. The theoretical results are valid for the general multivariate case, but particular emphasis is placed on the bivariate situation from an applied point of view. The proposal is based on a vector signal-plus-noise representation of the observed data that requires the first two sample moments and specifying only one smoothing constant. A measure of the amount of smoothness of an estimated trend is introduced so that an analyst can set in advance a desired percentage of smoothness to be achieved by the trend estimate. The required smoothing constant is determined by the chosen percentage of smoothness. Closed form expressions for the smoothed estimated vector and its variance-covariance matrix are derived from a straightforward application of generalized least squares, thus providing best linear unbiased estimates for the trends. A detailed algorithm applicable for estimating bivariate time series trends is also presented and justified. The theoretical results are supported by a simulation study and two real applications. One corresponds to Mexican and US macroeconomic data within the context of business cycle analysis, and the other one to environmental data pertaining to a monitored site in Scotland.     

Construction of bivariate and multivariate weighted distributions via conditioning

Weighted distributions (univariate and bivariate) have received widespread attention over the last two decades because of their flexibility for analyzing skewed data. In this article, we propose an alternative method to construct a new family of bivariate and multivariate weighted distributions. For illustrative purposes, some examples of the proposed method are presented. Several structural properties of the bivariate weighted distributions including marginal distributions together with distributions of the minimum and maximum, evaluation of the reliability parameter, and verification of total positivity of order two are also presented. In addition, we provide some multivariate extensions of the proposed models. A real-life data set is used to show the applicability of these bivariate weighted distributions.     

Improved estimation methods for unrelated question randomized response techniques

The randomized response technique (RRT) is an important tool, commonly used to avoid biased answers in survey on sensitive issues by preserving the respondents’ privacy. In this paper, we introduce a data collection method for survey on sensitive issues combining both the unrelated-question RRT and the direct question design. The direct questioning method is utilized to obtain responses to a non sensitive question that is related to the innocuous question from the unrelated-question RRT. These responses serve as additional information that can be used to improve the estimation of the prevalence of the sensitive behavior. Furthermore, we propose two new methods for the estimation of the proportion of respondents possessing the sensitive attribute under a missing data setup. More specifically, we develop the weighted estimator and the weighted conditional likelihood estimator. The performances of our estimators are studied numerically and compared with that of an existing one. Both proposed estimators are more efficient than the Greenberg's estimator. We illustrate our methods using real data from a survey study on illegal use of cable TV service in Taiwan.     

Efficiency of the generalized-difference-based weighted mixed almost unbiased two-parameter estimator in partially linear model

In this paper, a generalized difference-based estimator is introduced for the vector parameter β in partially linear model when the errors are correlated. A generalized-difference-based almost unbiased two-parameter estimator is defined for the vector parameter β. Under the linear stochastic constraint r = Rβ + e, we introduce a new generalized-difference-based weighted mixed almost unbiased two-parameter estimator. The performance of this new estimator over the generalized-difference-based estimator and generalized- difference-based almost unbiased two-parameter estimator in terms of the MSEM criterion is investigated. The efficiency properties of the new estimator is illustrated by a simulation study. Finally, the performance of the new estimator is evaluated for a real dataset.     

论美国保护预备被监护人权益的基本原则

预备被监护人是指即将被安排监护的当事人.经过十余年改革,美国成年监护制度形成了保护预备被监护人权益的一系列基本原则.这些原则包括:"实质性损害"标准、最小限制性替代措施、"功能性行为能力"标准、正当程序原则.我国成年监护制度立法理念相对落后,借鉴美国的成功经验来重构和完善我国的成年监护制度具有重要意义.