On Symmetrizing Transformation of the Sample Coefficient of Variation from a Normal Population

Variance-stabilizing transformation (VST) for the sample coefficient of variation is often used as a normalizing transformation and may be used for inference on the population coefficient of variation. However, for small samples, the VST may not be symmetric and hence there is a scope of improvement in its performance by seeking a symmetrizing transformation. This article investigates such a transformation that has been obtained by solving a differential equation. The solution may be complex; hence, a numerical strategy is employed in order to make the approximation practically useful. This transformation has been compared with explicitly available VST. The approach has been illustrated on real data from an agricultural experiment concentrating on inference on single samples; however, the method may be generally applicable to multiple samples when testing the homogeneity of coefficients of variation for many populations by following usual normal-theory-based methods applied on transformed statistics.     

Comparing least-squares lines for testing level changes in interrupted time-series analysis

A likelihood ratio test of equality of coefficients of variation or relative errors for two samples of unequal size is presented. The asymptotic distribution is found and the distribution is tabled for small sizes via computer simulation. Kolmogrov-Smirnov confidence intervals are constructed on the percentiles included in the table. Power studies are also simulated and the results indicate that the test has good power for small coefficients of variation     

Omnitab-a simple language for statistical computations

The OMNITAB system of computer programming provides a simple, yet extremely versatile means of communicating with the computer using simple English words and phrases, It is written in FORTRAN and is available for implementation on UNIVAC 1108, IBM 360, Burroughs 5500 and CDC 6600 equipment. It is based on a worksheet, stored in the computer, which is a two dimensional array easy to visualize even by beginners. The system has particular use for students of statistics, of all ages, in that it allows them to interact with the data without requiring that they master any diffiicult and esoteric (for statisticians) computer skills. The programming system is described together with several applications to statistical problems. Full program documentation is available from the authors.     

Estimation of the coefficient of variation for non-normal model using progressive first-failure-censoring data

The coefficient of variation (CV) is extensively used in many areas of applied statistics including quality control and sampling. It is regarded as a measure of stability or uncertainty, and can indicate the relative dispersion of data in the population to the population mean. In this article, based on progressive first-failure-censored data, we study the behavior of the CV of a random variable that follows a Burr-XII distribution. Specifically, we compute the maximum likelihood estimations and the confidence intervals of CV based on the observed Fisher information matrix using asymptotic distribution of the maximum likelihood estimator and also by using the bootstrapping technique. In addition, we propose to apply Markov Chain Monte Carlo techniques to tackle this problem, which allows us to construct the credible intervals. A numerical example based on real data is presented to illustrate the implementation of the proposed procedure. Finally, Monte Carlo simulations are performed to observe the behavior of the proposed methods.     

Therapeutic Hypothermia: Quantification of the Transition of Core Body Temperature Using the Flexible Mixture Bent‐Cable Model for Longitudinal Data

Hypothermia which is induced by reducing core body temperature is a therapeutic tool used to prevent brain damage resulting from physical trauma. However, all physiological systems begin to slow down due to hypothermia and this can result in increased risk of mortality. Therefore quantification of the transition of core body temperature to early hypothermia is of great clinical interest. Conceptually core body temperature may exhibit an either gradual or abrupt transition. Bent‐cable regression is an appealing statistical tool to model such data due to the model's flexibility and readily interpretable regression coefficients. It handles more flexibly models that traditionally have been handled by low‐order polynomial models (for gradual transition) or piecewise linear changepoint models (for abrupt change). We consider a rat model to quantify the temporal trend of core body temperature primarily to address the question: What is the critical time point associated with a breakdown in the compensatory mechanisms following the start of hypothermia therapy? To this end, we develop a Bayesian modelling framework for bent‐cable regression of longitudinal data to simultaneously account for gradual and abrupt transitions. Our analysis reveals that: (i) about 39% of rats exhibit a gradual transition in core body temperature; (ii) the critical time point is approximately the same regardless of transition type; and (iii) both transition types show a significant increase of core body temperature followed by a significant decrease.     

General saddlepoint approximations to distributions under an elliptical population

General saddlepoint approximations are derived for the distributions of statistics under an elliptical population. The technique is applied to obtain the tail probabilities of latent roots of a sample covariance matrix. It is shown that the method based on normalizing transformations by Tsuchiya and Konishi (1997) is efficient for the sample correlation coefficient in an elliptical sample.     

Realized Volatility: A Review

This article reviews the exciting and rapidly expanding literature on realized volatility. After presenting a general univariate framework for estimating realized volatilities, a simple discrete time model is presented in order to motivate the main results. A continuous time specification provides the theoretical foundation for the main results in this literature. Cases with and without microstructure noise are considered, and it is shown how microstructure noise can cause severe problems in terms of consistent estimation of the daily realized volatility. Independent and dependent noise processes are examined. The most important methods for providing consistent estimators are presented, and a critical exposition of different techniques is given. The finite sample properties are discussed in comparison with their asymptotic properties. A multivariate model is presented to discuss estimation of the realized covariances. Various issues relating to modelling and forecasting realized volatilities are considered. The main empirical findings using univariate and multivariate methods are summarized.     

量词变异搭配之正名

语用者常借助表量结构来取得言简义丰这一言语现象已引起学界的广泛关注。对于该言语现象的界定问题虽有学者涉及，但仍值得商榷。文章在对该现象既有定义展开辨析的基础上将其界定为“量词变异搭配”，即语用者借助特定的语境，采用表量结构并通过量词（临时量词）与名词（名词性成分）或语素与名词（名词性成分）之间的超常组合来表情达意，以取得特殊的修辞效果的一种言语现象。一般分为两种情况：常规量词之间的相互借用和常规量词以外的其他词类或语素的活用。期望通过对该类言语现象的正名来促进对其的进一步认识及研究。     

A suggestion for measuring heteroskedasticity

The lack of a generally-accepted measure of the degree of severity of heteroskedasticity is shown to have caused some Monte Carlo studies to draw misleading conclusions. An attractive measure of heteroskedasticity is suggested.     

Modified product estimators of finite population mean in finite sampling

With respect to random sampling from finite population, when the correlation between the auxiliary and the main characteristics is negative, the product estimator is often used to estimate the population mean. The product estimator, however, would have a large mean-squared-error (MSE) if the coefficients of variations for these two characteristics were large and the absolute value of the correlation between them was small. In this paper, we propose a general family of modified product estimators, that include the product estimator as a special case. We provide a discussion on the reduction of the MSE by using the optimal modified product estimator that has the minimal MSE in the proposed family. In certain situations, these reductions of the MSE can be significant.