Ridge estimation of restricted parameters in production techniques

The problem of determining ridge estimates of the regression parameters in a two-input production function model,constrained to be non-negative,has been formulated as an exercise in quadratic programming. Relevant Kuhn-Tucker conditions have been derived and a small simulation studv has been carried out.     

New class of location-parameter discrete probability distributions and their characterizations

A new class of location-parameter discrete probability distributions (LDPD) has been defined where the population mean is the location parameter. It has been shown that some single parameter discrete distributions do not belong to this class and all discrete probability distributions belonging to this class can be characterized by their variances only. Expressions are given for the first four central moments and a recurrence formula for higher central moments has been obtained. Eight theorems are given to characterize the various distributions in the LDPD class.     

Comparison of estimators of the location parameter using pitman's closeness criterion

Necessary and sufficient conditions for a linear estimator to dominate another linear estimator of a location parameter under the Pitman's criterion of comparison are discussed. Consequently it is demonstrated that a linear biased estimator can not dominate a linear unbiased estimator under Pitman's criterion and that the sample mean is the Closest Linear Unbiased Estimator (CLUE). It is also shown that the ridge regression estimator with a known biasing constant can not dominate the ordinary least squares estimator. If an estimator δdominates an estimator δin the average loss sense then sufficient conditions are obtained under which δis also preferred over δunder Pitman's criterion. Further we obtain sufficient conditions under which preference under the Pitman's criterion will lead to preference under the mean squared error sense.     

Chain ratio type estimator for ratio of two population m3ans using auxiliary characters

In this paper we have proposed chain ratio type estimators for ratio of two population means using two auxiliary characters. The expressions for bias and mean square error of these estimators have been derived. A comparison of the proposed estimator with that of double sampling estimator has been made in terms of mean square error. An emperical study has also been made.     

Estimation of mean vector in presence of non-response

Simultaneous estimation of means of several variables is considered for finite population in presence of non-response. Two types of nonresponses (partial and complete) are considered using the technique of sampling and subsampling with equal probabilities without replacement. The optimum sample size and the optimum value of subsampling fraction to be repeated from the nonresponding units of the sample have been obtained for fixed survey budget.     

HAZARD RATE ESTIMATION FOR CENSORED DATA BY WAVELET METHODS

ABSTRACT

We study the estimation of a hazard rate function based on censored data by non-linear wavelet method. We provide an asymptotic formula for the mean integrated squared error (MISE) of nonlinear wavelet-based hazard rate estimators under randomly censored data. We show this MISE formula, when the underlying hazard rate function and censoring distribution function are only piecewise smooth, has the same expansion as analogous kernel estimators, a feature not available for the kernel estimators. In addition, we establish an asymptotic normality of the nonlinear wavelet estimator.     

Inference on the Common Variance of Correlated Normal Random Variables

ABSTRACT

Scale equivariant estimators of the common variance σ², of correlated normal random variables, have mean squared errors (MSE) which depend on the unknown correlations. For this reason, a scale equivariant estimator of σ² which uniformly minimizes the MSE does not exist. For the equi-correlated case, we have developed three equivariant estimators of σ²: a Bayesian estimator for invariant prior as well as two non-Bayesian estimators. We then generalized these three estimators for the case of several variables with multiple unknown correlations. In addition, we developed a system of confidence intervals which produce the desired coverage probability while being efficient in terms of expected length.     

论先秦儒家中庸之异

中庸作为先秦儒家的重要范畴,在"何为中"问题上,大儒们的回答有所不同。孔子将其视为哲学方法论意义上的"道",从全局和全面出发,主张"全为中";子思将中庸上升为宇宙的本体,并认为诚是上达该本体的唯一正确途径,从而提出"诚为中";孟子从性善论出发,必然推演为"仁义为中";荀子为恢复孔子的中庸之道,纠偏思孟的"德性为中",倡导"规范为中"。     

正名的困境及其超越:论《黄金时代》

王小波的《黄金时代》揭示了一个特殊时代的"人"的困境,但困境背后深隐着文化、政治、道德、性别关系等诸多问题,问题聚焦于陈清扬和王二这对男女的"性事",对此的命名、评判和惩罚使"性"成为诸般观念和力量博弈的战场。作者以"黑色幽默"的叙事风格描述了处于劣势的当事人如何以理性清明的坚定信念和狂欢化的游戏策略,逆转了无端受虐的人生颓势,从而最大限度地实现了个人的自我救赎,因之,《黄金时代》在"文学是人学"的层面展现了王小波的雄心和抱负,也在此高度呈现了这部经典的价值。     

《金光大道》三题

浩然的缺陷是时代缺陷的反映,《金光大道》作品主人公高大泉的缺陷既表现为其过分完美,更由于他是被定位在阶级斗争的座标上;关于《金光大道》的争论既显示了历史的进步,