Trend smoothness achieved by penalized least squares with the smoothing parameter chosen by optimality criteria

This work presents a study about the smoothness attained by the methods more frequently used to choose the smoothing parameter in the context of splines: Cross Validation, Generalized Cross Validation, and corrected Akaike and Bayesian Information Criteria, implemented with Penalized Least Squares. It is concluded that the amount of smoothness strongly depends on the length of the series and on the type of underlying trend, while the presence of seasonality even though statistically significant is less relevant. The intrinsic variability of the series is not statistically significant and its effect is taken into account only through the smoothing parameter.     

On Pitman's measure of closeness of k-records

Pitman closeness of both the upper and lower k-record statistics to the population quantiles of a location–scale family of distributions is studied. For the population median, the Pitman-closest k-record is also determined. In the case of symmetric distributions, the Pitman closeness probabilities of k-record statistics are shown to be distribution-free, and explicit expressions are also derived for these probabilities. Exact expressions are derived for the required probabilities for uniform and exponential distributions. Numerical results are given for these families and also the Pitman-closest k-record is determined.     

ＧＩＳ技术支持下的北宋初期丝路要道灵州道复原研究

在９世纪后半叶乃至整个１０世纪的丝绸之路东、中段交通网络系统中，灵州道占有一席之地。宋初，大食、回鹘、于阗以及归义军等民族政权多通过灵州道与北宋王朝进行经贸、文化往来。本文主要针对这一时段内灵州道的畅通情况及其道路性质进行探讨，在原有文献考证的基础上，利用考古资料、ＧＩＳ技术，尽可能实现对灵州道古地名数据的精确地理定位，最后使用ＡＲＣＧＩＳ技术，绘制灵州道的道路走向地图，为北宋灵州道区域的政治、经济、文化交流综合研究提供地理学依据。     

Daily Inhalation Rate and Time‐Activity/Location Pattern in Japanese Preschool Children

Lack of data on daily inhalation rate and activity of children has been an issue in health risk assessment of air pollutants. This study aimed to obtain the daily inhalation rate and intensity and frequency of physical activity in relation to the environment in Japanese preschool children. Children aged four–six years (n= 138) in the suburbs of Tokyo participated in this study, which involved three days' continuous monitoring of physical activity using a tri‐axial accelerometer and parent's completion of a time/location diary during daily life. The estimated three‐day mean daily inhalation rate (body temperature, pressure, saturated with water vapor) was 9.9 ± 1.6 m³/day (0.52 ± 0.09 m³/kg/day). The current daily inhalation rate value of 0.580 m³/kg/day proposed for use in health risk assessment in Japan is confirmed to be valid to calculate central value of inhaled dose of air pollutants in five‐ to six‐year‐old children. However, the 95th percentile daily inhalation rate of 0.83 m³/kg/day based on measurement for five‐year‐old children is recommended to be used to provide an upper bound estimate of exposure that ensure the protection of all five‐ to six‐year‐old children from the health risk of air pollutants. Children spent the majority of their time in sedentary and light level of physical activity (LPA) when indoors, while 85% of their time when outdoors was spent in LPA and moderate‐to‐vigorous physical activity. The results suggest the need to consider variability of minute respiratory ventilation rate according to the environment for more refined short‐term health risk assessment.     

Optimal determination of the parameters of some biased estimators using genetic algorithm

In this paper, some new algorithms for estimating the biasing parameters of the ridge, Liu and two-parameter estimators are introduced with the help of genetic algorithm (GA). The proposed algorithms are based on minimizing some statistical measures such as mean square error (MSE), mean absolute error (MAE) and mean absolute prediction error (MAPE). At the same time, the new algorithms allow one to keep the condition number and variance inflation factors to be less than or equal to ten by means of the GA. A numerical example is presented to show the utility of the new algorithms. In addition, an extensive Monte Carlo experiment is conducted. The numerical findings prove that the proposed algorithms enable to eliminate the problem of multicollinearity and minimize the MSE, MAE and MAPE.     

Testing for parameter constancy in the time series direction in panel data models

We propose tests for parameter constancy in the time series direction in panel data models. We construct a locally best invariant test based on Tanaka [Time series analysis: nonstationary and noninvertible distribution theory. New York: Wiley; 1996] and an asymptotically point optimal test based on Elliott and Müller [Efficient tests for general persistent time variation in regression coefficients. Rev Econ Stud. 2006;73:907–940]. We derive the limiting distributions of the test statistics as T→∞ while N is fixed, and calculate the critical values by applying numerical integration and response surface regression. Simulation results show that the proposed tests perform well if we apply them appropriately.     

Estimation of weibull location

A simulation study was carried out to compare the performances of two different simple estimators of the location parameter for a three-parameter Weibull distribution Both Estimators have been suggested by recent paper in the literature. Bras and mean square error are examined for many different sample-size and shape-parameter-value combinations. Strong evidence of the domination of one estimator over the other is found.     

Estimation and diagnostic analysis in skew-generalized-normal regression models

The skew-generalized-normal distribution [Arellano-Valle, RB, Gómez, HW, Quintana, FA. A new class of skew-normal distributions. Comm Statist Theory Methods 2004;33(7):1465–1480] is a class of asymmetric normal distributions, which contains the normal and skew-normal distributions as special cases. The main virtues of this distribution is that it is easy to simulate from and it also supplies a genuine expectation–maximization (EM) algorithm for maximum likelihood estimation. In this paper, we extend the EM algorithm for linear regression models assuming skew-generalized-normal random errors and we develop a diagnostics analyses via local influence and generalized leverage, following Zhu and Lee's approach. This is because Cook's well-known approach would be more complicated to use to obtain measures of local influence. Finally, results obtained for a real data set are reported, illustrating the usefulness of the proposed method.     

Bounded risk estimation of a linear combination of location parameters in negative exponential distributions via three-stage sampling

The paper deals with the problem of bounded risk point estimation for a linear combination of location parameters of two negative exponential distributions. Isogai and Futschik considered the situation when the location and scale parameters are all unknown. They proposed purely sequential procedures and gave second order expansions of the average sample sizes and risks. In this paper we propose three-stage procedures and derive second order expansions of the average sample sizes and risks. Further, we compare the results with those from previous work.     

Sample size re‐estimation incorporating prior information on a nuisance parameter

Prior information is often incorporated informally when planning a clinical trial. Here, we present an approach on how to incorporate prior information, such as data from historical clinical trials, into the nuisance parameter–based sample size re‐estimation in a design with an internal pilot study. We focus on trials with continuous endpoints in which the outcome variance is the nuisance parameter. For planning and analyzing the trial, frequentist methods are considered. Moreover, the external information on the variance is summarized by the Bayesian meta‐analytic‐predictive approach. To incorporate external information into the sample size re‐estimation, we propose to update the meta‐analytic‐predictive prior based on the results of the internal pilot study and to re‐estimate the sample size using an estimator from the posterior. By means of a simulation study, we compare the operating characteristics such as power and sample size distribution of the proposed procedure with the traditional sample size re‐estimation approach that uses the pooled variance estimator. The simulation study shows that, if no prior‐data conflict is present, incorporating external information into the sample size re‐estimation improves the operating characteristics compared to the traditional approach. In the case of a prior‐data conflict, that is, when the variance of the ongoing clinical trial is unequal to the prior location, the performance of the traditional sample size re‐estimation procedure is in general superior, even when the prior information is robustified. When considering to include prior information in sample size re‐estimation, the potential gains should be balanced against the risks.