光学分辨率判据和可见度

本文研究了两个非相干点光源靠近时，在圆孔的夫琅和费衍射下两个光斑之间可见度的变化情况。对于不同判据，可见度有明显差异，表现出各种判据的不一致性。同时还研究了光栅的夫琅和费衍射，当两明条纹很靠近时，可见度的变化情况。同样可以得到各判据相应的数值。     

Selecting the optimum k in ridge regression

Two ridge rules are proposed for selecting the optimal k in ridge regression . Since the sampling distribution of the proposed rules are mathematically in tractable , a Monte Carlo study is conducted to examine their statisticl properties . Numerical results of the simulations in dicate that the performance of ridge rules depends upon the risk function used. Nevertheless, one of the ridge rules does produce a smaller mean squared error than the least squares estimator with the probability greater than 0.57 for all situations.     

Estimations of a threshold parameter in cox regression

Therneau et al (1990) used martingale residual plots to study the threshold effect of some covariates in a proportional hazard regression model for survival data subject to right censoring. We show that the maximum partial likelihood estimate provides an asymptotically consistent estimator for the unknown threshold. This procedure is illustrated by applying it to a data set from a cohort of patients with B-lineage leukemia treated at St. Jude Children's Research Hospital.     

Computation of probability and non-centrality parameter of a non-central f-distribution

The small sample properties of the score function approximation to the maximum likelihood estimator for the three-parameter lognormal distribution using an alternative parameterization are considered. The new set of parameters is a continuous function of the usual parameters. However, unlike with the usual parameterization, the score function technique for this parameterization is extremely insensitive to starting values. Further, it is shown that whenever the sample third moment is less than zero, a local maximum to the likelihood function exists at a boundary point. For the usual parameterization, this point is unattainable. However, the alternative parameter space can be expanded to include these boundary points. This procedure results in good estimates of the expected value, variance, extreme percentiles and other parameters of the distribution even in samples where, with the typical parameterization, the estimation procedure fails to converge.     

Change Point Detection in The Skew-Normal Model Parameters

Bayesian inference under the skew-normal family of distributions is discussed using an arbitrary proper prior for the skewness parameter. In particular, we review some results when a skew-normal prior distribution is considered. Considering this particular prior, we provide a stochastic representation of the posterior of the skewness parameter. Moreover, we obtain analytical expressions for the posterior mean and variance of the skewness parameter. The ultimate goal is to consider these results to one change point identification in the parameters of the location-scale skew-normal model. Some Latin American emerging market datasets are used to illustrate the methodology developed in this work.     

Refining binomial confidence intervals

A method for refining an equivariant binomial confidence procedure is presented which, when applied to an existing procedure, produces a new set of equivariant intervals that are uniformly superior. The family of procedures generated from this method constitute a complete class within the class of all equivariant procedures. In certain cases it is shown that this class is also minimal complete. Also, an optimally property, monotone minimaxity, is investigated, and monotone minimax procedures are constructed.     

A NEW APPROACH TO MAXIMUM LIKELIHOOD ESTIMATION OF THE THREE-PARAMETER GAMMA AND WEIBULL DISTRIBUTIONS

A new approach, is proposed for maximum likelihood (ML) estimation in continuous univariate distributions. The procedure is used primarily to complement the ML method which can fail in situations such as the gamma and Weibull distributions when the shape parameter is, at most, unity. The new approach provides consistent and efficient estimates for all possible values of the shape parameter. Its performance is examined via simulations. Two other, improved, general methods of ML are reported for comparative purposes. The methods are used to estimate the gamma and Weibull distributions using air pollution data from Melbourne. The new ML method is accurate when the shape parameter is less than unity and is also superior to the maximum product of spacings estimation method for the Weibull distribution.     

AN EXCLUSIVE REGRESSORS BINARY MIXTURE MODEL WITH AN APPLICATION TO LABOUR SUPPLY

This paper suggests a new type of mixture regression model, in which each mixture component is explained by its own regressors. Thus, the dependent variable can be driven by one of several unobservable explanatory mechanisms, each of which has its own distinct variables. An extension of the simulated annealing algorithm is introduced to fit this general mixture model. The paper also suggests a new technique for estimating the covariance matrix of estimators in a mixture model. Finally, empirical studies of a labour supply example show that our proposed model can perform much better than conventional logistic or mixture models.     

COMBINING INFORMATION FROM LINEAR MODELS ON POSSIBLY DIFFERENT SCALES

This paper examines the joint statistical analysis of M independent data sets, the jth of which satisfies the model λ_j Y_j=X_jB +ε_j, where the λ_j are unknown and the ε_i are normally distributed with a known correlation structure. The maximum likelihood equations, their asymptotic covariance matrix, and the likelihood ratio test of the hypothesis that the λ_js are all equal are derived. These results are applied to two examples.     

用XRF基本参数法定量计算多层薄膜的厚度

针对多层薄膜材料，用ＸＲＦ基本参数（ＦＰ）法定量分析计算多层薄膜试样的厚度。除了考虑直接受人射束激发产生初级荧光外，还考虑试样中其它元素初级荧光辐射而引起的层间和层内二次荧光。以计算三层膜荧光强度为例，提出各种不同情况下计算初级和次级荧光强度的表达式。讨论二次荧光相对于，总强度的贡献。计算方法也能很好地用在大于三层膜及块样的Ｘ荧光强度计算。