A NOTE ON EVANESCENT PROCESSES

This note examines the connection between μ-invariant measures for the transition function of a continuous-time Markov chain and those of its q-matrix, Q. The major result establishes a necessary and aufficient condition for a convergent μ-invariant measure for Q to be μ-inhant for the minimal transition function, P, under the assumption that P is honest. This corrects Theorem 6 of Vere-Jones (1969) and the first part of Corollary 1 of Pollett (1986), both of which assert that the above conclusion holds in the absence of this condition. The error was pointed out by E.A. van Doom (1991) and the counterexample which be presented provides the basis for the present arguments. In determining where the error occurred in the original proof, we are able to identify a simple sufficient condition for μ-invariance.     

Holistic trajectories: a study of combined employment, housing and family careers by using multiple-sequence analysis

Summary.  Social science applications of sequence analysis have thus far involved the development of a typology on the basis of an analysis of one or two variables which have had a relatively low number of different states. There is a yet unexplored potential for sequence analysis to be applied to a greater number of variables and thereby a much larger state space. The development of a typology of employment experiences, for example, without reference to data on changes in housing, marital and family status is arguably inadequate. The paper demonstrates the use of sequence analysis in the examination of multivariable combinations of status as they change over time and shows that this method can provide insights that are difficult to achieve through other analytic methods. The data that are examined here provide support to intuitive understandings of clusters of common experiences which are both life course specific and related to socio-economic factors. Housing tenure is found to be of key importance in understanding the holistic trajectories that are examined. This suggests that life course trajectories are sharply differentiated by experience of social housing.     

A general inverse sampling scheme and its application to adaptive cluster sampling

Not having a variance estimator is a seriously weak point of a sampling design from a practical perspective. This paper provides unbiased variance estimators for several sampling designs based on inverse sampling, both with and without an adaptive component. It proposes a new design, which is called the general inverse sampling design, that avoids sampling an infeasibly large number of units. The paper provide estimators for this design as well as its adaptive modification. A simple artificial example is used to demonstrate the computations. The adaptive and non‐adaptive designs are compared using simulations based on real data sets. The results indicate that, for appropriate populations, the adaptive version can have a substantial variance reduction compared with the non‐adaptive version. Also, adaptive general inverse sampling with a limitation on the initial sample size has a greater variance reduction than without the limitation.     

On calculating the fisher information in order statistics

This article gives a simple result for the expression of the Fisher information in order statistics. This result enables us to calculate easily the Fisher information in any set of order statistics whose details have been known to be messy and complicated. We consider here its application in the optimal spacing problem where the exact Fisher information in order statistics has been approximated with the asymptotic information or the reciprocal of the variance of a suitable estimator. This work was supported by Korea Research Foundation Grant(KRF-2000-015-DP0056)     

ON THE INDEPENDENCE OF THE SAMPLE MEAN AND TRANSLATION-INVARIANT STATISTICS FOR MATRIX NORMAL DISTRIBUTIONS

We present an explicit characterization of the joint dependency structure of an n×p matrix normal random matrix such that the p-dimensional sample mean vector is independent of all translation invariant statistics.     

Sampling Returns for Realized Variance Calculations: Tick Time or Transaction Time?

This article introduces a new model for transaction prices in the presence of market microstructure noise in order to study the properties of the price process on two different time scales, namely, transaction time where prices are sampled with every transaction and tick time where prices are sampled with every price change. Both sampling schemes have been used in the literature on realized variance, but a formal investigation into their properties has been lacking. Our empirical and theoretical results indicate that the return dynamics in transaction time are very different from those in tick time and the choice of sampling scheme can therefore have an important impact on the properties of realized variance. For RV we find that tick time sampling is superior to transaction time sampling in terms of mean-squared-error, especially when the level of noise, number of ticks, or the arrival frequency of efficient price moves is low. Importantly, we show that while the microstructure noise may appear close to IID in transaction time, in tick time it is highly dependent. As a result, bias correction procedures that rely on the noise being independent, can fail in tick time and are better implemented in transaction time.     

A regression-based smoothing spline Monte Carlo algorithm for pricing American options in discrete time

American options in discrete time can be priced by solving optimal stopping problems. This can be done by computing so-called continuation values, which we represent as regression functions defined recursively by using the continuation values of the next time step. We use Monte Carlo to generate data, and then we apply smoothing spline regression estimates to estimate the continuation values from these data. All parameters of the estimate are chosen data dependent. We present results concerning consistency and the estimates’ rate of convergence.     

学校早期读写训练对儿童读写成绩的影响

利用儿童家庭一学校早期语言与识字能力系列测验对每个目标儿童语言与识字能力发展进行了评定，并解释了这些测量结果与儿童学校早期语言与识字测量指标之间的关系。结果表明：(1)儿童丰富的同伴关系与词汇量、应变识字能力、下定义能力和理解力有关；(2)教师语言的丰富性有助于儿童语言与识字能力发展；(3)识字课程变量与三岁儿童的应变识字成绩和四岁儿童词汇量和故事理解有关；(4)影响儿童语言与识字能力的因素不是单一的，而是一个因素群。     

具有Virasoro型的无穷维对称代数的群不变模型

本文利用Virasoro型的对称代数的两种具体的实现获得了各种2 1维具有无穷维Kac-Moody-Virasoro型李代数的不变方程。一些熟知的高维可积模型例如KP方程也被给出。     

Sample selection in radiocarbon dating

Archaeologists working on the island of O'ahu, Hawai'i, use radiocarbon dating of samples of organic matter found trapped in fish-pond sediments to help them to learn about the chronology of the construction and use of the aquicultural systems created by the Polynesians. At one particular site, Loko Kuwili, 25 organic samples were obtained and funds were available to date an initial nine. However, on calibration to the calendar scale, the radiocarbon determinations provided date estimates that had very large variances. As a result, major issues of chronology remained unresolved and the archaeologists were faced with the prospect of another expensive programme of radiocarbon dating. This paper presents results of research that tackles the problems associated with selecting samples from those which are still available. Building on considerable recent research that utilizes Markov chain Monte Carlo methods to aid archaeologists in their radiocarbon calibration and interpretation, we adopt the standard Bayesian framework of risk functions, which allows us to assess the optimal samples to be sent for dating. Although rather computer intensive, our algorithms are simple to implement within the Bayesian radiocarbon framework that is already in place and produce results that are capable of direct interpretation by the archaeologists. By dating just three more samples from Loko Kuwili the expected variance on the date of greatest interest could be substantially reduced.