The two-sample -test with a known ratio of variances

We consider the two-sample t-test where error variances are unknown but with known relationships between them. This situation arises, for example, when two measuring instruments average different number of replicates to report the response. In particular we compare our procedure with the usual Satterthwaite approximation in the two sample t-test with variances unequal. Our procedure uses the knowledge of a known ratio of variances while the Satterthwaite approximation assumes only that the two variances are unequal. Simulations show that our procedure has both better size and better power than the Satterthwaite approximation. Finally, we consider an extension of our results to the General Linear Model.     

Estimating the Lyapunov exponent from chaotic time series with dynamic noise

In this paper, we propose an estimator of the Lyapunov exponent of the skeleton for chaotic time series with dynamic noise and prove the consistency of the estimator under some assumptions.     

Gender differences in financial risk tolerance

The purpose of this research is to explore gender differences in financial risk tolerance using a large, nationally representative dataset, the Survey of Consumer Finances. The impact of the explanatory variables in the model is allowed to differ between men and women to decompose gender differences in financial risk tolerance. The results indicate that gender differences in financial risk tolerance are explained by gender differences in the individual determinants of financial risk tolerance, and that the disparity does not result from gender in and of itself. The individual variables that moderate the relationship between gender and high risk tolerance are income uncertainty and net worth, with income uncertainty moderating the relationship between gender and some risk tolerance. Financial fiduciaries should understand the differences in income uncertainty and net worth between men and women and how those differences relate to risk tolerance.     

10-13世纪中朝日文化交流与东亚文化圈

10-13世纪,中国文化仍以其独特魅力吸引着朝鲜和日本。同时,随着各国民族文化的发展,文化中异质成分、创新成分的不断增多,日本、朝鲜对中国大陆的文化输出日益明显起来。这对东亚文化圈的巩固和发展起了至关重要的作用。     

United statistics,confidence quantiles,Bayesian statistics

A survey of research by Emanuel Parzen on how quantile functions provide elegant and applicable formulas that unify many statistical methods, especially frequentist and Bayesian confidence intervals and prediction distributions. Section 0: In honor of Ted Anderson's 90th birthday; Section 1: Quantile functions, endpoints of prediction intervals; Section 2: Extreme value limit distributions; Sections 3, 4: Confidence and prediction endpoint function: Uniform(0,θ)$(0,\theta )$, exponential; Sections: 5, 6: Confidence quantile and Bayesian inference normal parameters μ$\mu$, σ$\sigma$; Section 7: Two independent samples confidence quantiles; Section 8: Confidence quantiles for proportions, Wilson's formula. We propose ways that Bayesians and frequentists can be friends!     

Waiting time distributions for a run with additional constraints

This paper proposes a method for obtaining the exact probability of occurrence of the first success run of specified length with the additional constraint that at every trial until the occurrence of the first success run the number of successes up to the trial exceeds that of failures. For the sake of the additional constraint, the problem cannot be solved by the usual method of conditional probability generating functions. An idea of a kind of truncation is introduced and studied in order to solve the problem. Concrete methods for obtaining the probability in the cases of Bernoulli trials and time-homogeneous {0,1}$\{0,1\}$-valued Markov dependent trials are given. As an application of the results, a modification of the start-up demonstration test is studied. Numerical examples which illustrate the feasibility of the results are also given.     

Lower bounds of the wrap-around -discrepancy and relationships between MLHD and uniform design with a large size

The wrap-around (WD) L₂-discrepancy has been commonly used in experimental designs. In this paper, some lower bounds of the WD L₂-discrepancy for asymmetrical U-type designs are given and the expectation and variance of midpoint Latin hypercube designs (LHD) are also obtained. Relationships between midpoint LHD and uniform designs for symmetrical and asymmetrical cases are discussed in the sense of comparing the lower bound and the expectation of squared wrap-around L₂-discrepancy of U-type designs. Some comparisons between simple random sampling and the lower bounds of U-type designs are given.     

On the comparison of the pre-test and shrinkage estimators for the univariate normal mean

The estimation of the mean of an univariate normal population with unknown variance is considered when uncertain non-sample prior information is available. Alternative estimators are defined to incorporate both the sample as well as the non-sample information in the estimation process. Some of the important statistical properties of the restricted, preliminary test, and shrinkage estimators are investigated. The performances of the estimators are compared based on the criteria of unbiasedness and mean square error in order to search for a ‘best’ estimator. Both analytical and graphical methods are explored. There is no superior estimator that uniformly dominates the others. However, if the non-sample information regarding the value of the mean is close to its true value, the shrinkage estimator over performs the rest of the estimators. Received: June 19, 1999; revised version: March 23, 2000     

Semiparametric inference for survival models with step process covariates

The authors consider Bayesian methods for fitting three semiparametric survival models, incorporating time‐dependent covariates that are step functions. In particular, these are models due to Cox [Cox ( 1972 ) Journal of the Royal Statistical Society, Series B, 34, 187–208], Prentice & Kalbfleisch and Cox & Oakes [Cox & Oakes ( 1984 ) Analysis of Survival Data, Chapman and Hall, London]. The model due to Prentice & Kalbfleisch [Prentice & Kalbfleisch ( 1979 ) Biometrics, 35, 25–39], which has seen very limited use, is given particular consideration. The prior for the baseline distribution in each model is taken to be a mixture of Polya trees and posterior inference is obtained through standard Markov chain Monte Carlo methods. They demonstrate the implementation and comparison of these three models on the celebrated Stanford heart transplant data and the study of the timing of cerebral edema diagnosis during emergency room treatment of diabetic ketoacidosis in children. An important feature of their overall discussion is the comparison of semi‐parametric families, and ultimate criterion based selection of a family within the context of a given data set. The Canadian Journal of Statistics 37: 60–79; © 2009 Statistical Society of Canada     

Likelihood analysis of joint marginal and conditional models for longitudinal categorical data

The authors develop a Markov model for the analysis of longitudinal categorical data which facilitates modelling both marginal and conditional structures. A likelihood formulation is employed for inference, so the resulting estimators enjoy the optimal properties such as efficiency and consistency, and remain consistent when data are missing at random. Simulation studies demonstrate that the proposed method performs well under a variety of situations. Application to data from a smoking prevention study illustrates the utility of the model and interpretation of covariate effects. The Canadian Journal of Statistics © 2009 Statistical Society of Canada