A discrete model for the segmentation of chains and strings

A statistical model is presented that can be used to represent a discrete breakage process. It considers a fixed length chain or string made up of n +1 pieces joined together. The chain is stressed at each connection or link andrupture occurs at some of the links. Models are developed to answer the question, “what is the expected proportion of chain segments of a given size?” The model is modified to handle those experiments where only thetotal weight of a given size segment is known. Expressions are obtained for the expected value and variance of the number of segments of a given size. The model is used to predict the expected number of segments which results when a fixed length DNA molecule chain is subjected to carcinogenic agents and is applied to industrial examples.     

A generic randomization device for quantitative response variables

We propose a generic randomization device (RD) for the estimation of mean of quantitative sensitive characteristic that make use of additive and multiplicative scrambled responses with blank card strategy. For this generic RD, we work with 12 choices and derive statistical properties of each model and give many immediate results in corollaries. It is interesting to note that various existing models can now be viewed as the special cases of this RD. Finally, various empirical studies have been done for each of these models to evaluate the efficiency performance.     

R2 Bounds for Predictive Models: What Univariate Properties Tell us About Multivariate Predictability

ABSTRACT

A long-standing puzzle in macroeconomic forecasting has been that a wide variety of multivariate models have struggled to out-predict univariate models consistently. We seek an explanation for this puzzle in terms of population properties. We derive bounds for the predictive R² of the true, but unknown, multivariate model from univariate ARMA parameters alone. These bounds can be quite tight, implying little forecasting gain even if we knew the true multivariate model. We illustrate using CPI inflation data. Supplementary materials for this article are available online.     

The negative contagion reflection of the polya-eggenberger distribution

The Polya-Eggenberger distribution Involves drawing a ball from an urn containing black and white balls and, after each drawing, returning the ball together with s balls of the same color, The model represents positive contagion since the added balls are the same color as the one drawn, See Johnson and Kotz, (1977),

This paper derives and examines the probability distribution which results from the Polya-Eggenberger model with only one change namely, the s additional balls added after each drawing are of the opposite color, producing a negative contagion model.

Formulas in closed form are presented for the probability distribution function, the mean and variance, all binomial moments and, where s is greater than or equal to the number of balls in the urn at start, the mode, A formula for the mode is conjectured where s is less than the number of balls in the urn at start.

Finally, the probability of obtaining k black balls in n drawings is shown in certain instances to be equal to A_nk/n!

where A_nk are the Eulerian numbers.     

Estimation of the scale parameter after a pre-test for homogeneity in a mis-specified regression model

The risk properties of estimators of the scale parameter after a pre-test for homogeneity of the error variances in the two sample linear regression model has received quite an amount of attention in the literature. This literature typically assumes normal disturbances and a properly specified model. In this paper we consider that both equations may be mis-specified by the omission of relevant regressors and that the error distributions may belong to a wider class than the normal distribution. We derive and analyse the exact risk (under quadratic loss) of the pre-test estimator of the scale parameter for the first sub-sample.     

Parameter estimation for a word frequency distribution based on occupancy theory

Compromise Estimators between the generalized Bayes and Bayes estimators with respect to conjugate gamma priors under entropy loss are proposed. The proposed compromise estimators are compared with some suitable generalized Bayes estimators in terms of their frequentist risk performance. Also the RSL approach will be employed to compare the proposed compromise estimators and some admissible generalized Bayes estimators in terms of their Bayes risk performance.     

大学英语演讲与辩论课程模式设置研究

从英语演讲与辩论课程的必要性和可行性入手,着重分析了其开设范围、教学目标、教学内容、教学模式以及考核手段,旨在消除学生固有的只有名人和在比赛时才要演讲的陈旧观念,使之成为真正意义上的＂public speaking＂。     

Optimum designs for estimation of regression parameters in a balanced treatment incomplete block design set-up

The use of covariates in block designs is necessary when the experimental errors cannot be controlled using only the qualitative factors. The choice of values of the covariates for a given set-up attaining minimum variance for estimation of the regression parameters has attracted attention in recent times. In this paper, optimum covariate designs (OCD) have been considered for the set-up of the balanced treatment incomplete block (BTIB) designs, which form an important class of test-control designs. It is seen that the OCDs depend much on the methods of construction of the basic BTIB designs. The series of BTIB designs considered in this paper are mainly those as described by Bechhofer and Tamhane (1981) and Das et al. (2005). Different combinatorial arrangements and tools such as Hadamard matrices and different kinds of products of matrices viz Khatri-Rao product and Kronecker product have been conveniently used to construct OCDs with as many covariates as possible.