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1.

Karl Pearson in Russian Contexts

**总被引：4，自引：4，他引：0** Eugene Seneta 《Revue internationale de statistique》2009,77(1):118-146

The confluence of statistics and probability into mathematical statistics in the Russian Empire through the interaction, 1910–1917, of A.A. Chuprov and A.A. Markov was influenced by the writings of the English Biometric School, especially those of Karl Pearson. The appearance of the Russian-language exposition of Pearsonian ideas by E. E. Slutsky in 1912 was instrumental in this confluence. Slutsky's predecessors in such writings (Lakhtin, Orzhentskii, and Leontovich) were variously of mathematical, political economy, and biological backgrounds. Work emanating from the interpolational nature of Pearson's system of frequency curves was continued subsequently through the work of Markov, Bernstein, Romanovsky, and Kravchuk (Krawtchouk), who laid a solid probabilistic foundation. The correlational nature in the interpolational early work of Chebyshev, and work of the English Biometric School in the guise of linear least-squares fitting exposited as the main component of Slutsky's book, was developed in population as well as sample context by Chuprov. He also championed the expectation operation in providing exact relations between sample and population moments, in direct interaction with Karl Pearson. Romanovsky emerges as the most adaptive and modern mathematical statistician. 相似文献

2.

基于分数布朗运动和跳过程的股本权证定价模型

**总被引：2，自引：0，他引：2**考虑到金融市场中资产价格具有的记忆性和长期相关性,模型假设股本权证标的资产价格服从分数布朗运动过程;并考虑到市场存在不确定因素而引起的价格巨大的波动,在模型中又引入了一个跳过程。首先得出权证定价的一般公式,最后在考虑股本权证行权后产生的稀释效应,得出稀释调整后的股本权证定价公式,并将其延伸到支付红利情况下。 相似文献

3.

Financial returns (log-increments) data, Y

We consider as possible models for the common distribution four instances of the General Normal Variance-Mean Model (GNVM), which is described by Y | V ∼ N ( a ( b + V ), c

_{ t }, t = 1,2,…, are treated as a stationary process, with the common distribution at each time point being not necessarily symmetric.We consider as possible models for the common distribution four instances of the General Normal Variance-Mean Model (GNVM), which is described by Y | V ∼ N ( a ( b + V ), c

^{2}V + d^{2}) where V is a nonnegative random variable and a, b, c and d are constants. When V is Gamma distributed and d = 0, Y has the skewed Variance-Gamma distribution (VG). When V follows a Half Normal distribution and c = 0, Y has the well-known Skew Normal (SN) distribution. We also consider two cases where V is Exponentially distributed. Bounds for skewness and kurtosis in each case are found in terms of the moments of the V . These are useful in determining whether the Method of Moments for a given model is feasible. The problem of overdetermination of parameters via estimating equations is examined. 5 data sets of actual returns data, chosen because of their earlier occurrence in the literature, are analysed using each of the 4 models. 相似文献4.

Eugene Seneta 《Revue internationale de statistique》2003,71(2):319-334

In the 19th century, causes of empirically observed stability of averages in settings relating to human behaviour were a topic of intense discussion in western Europe. This followed an extensive study of empirical stability by the founder of modern statistics (and of the International Statistical Institute) L.A.J. Quetelet, published in 1835, in what he called "Social Physics". The eminent mathematician of strong probabilistic and philosophical inclination and Russian Orthodox religious belief, P.A. Nekrasov, took up and modified Quetelet's Social Physics in 1902, with (social) independence seen as prime cause of statistical regularity. Our paper focuses on the role free will plays in the statistical writings of Quetelet and of Nekrasov. The work of the latter has remained little known in general, mainly for politico-ideological reasons. 相似文献

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6.

垄断市场中双寡头企业的市场行为研究——从产品纵向差异的角度分析

**总被引：1，自引：0，他引：1**从产品纵向差异的角度分析了垄断市场中双寡头企业的短期市场行为和长期市场行为.具体来说,从短期的角度出发,将产品质量视为外生变量,研究高质量企业和低质量企业的定价策略和利润状况,并对均衡结果进行比较静态分析.研究结果表明,两个企业都有提高或降低各自产品质量的动机,这取决于双方现有的质量水平.从长期的角度出发,将产品质量视为内生变量,研究企业的质量与价格决策.研究结果表明,产品质量存在唯一均衡,但均衡质量并没有表现出较大的差异化,而是表现出较小的差异化.此外,无论从短期还是长期的角度来看,企业都不存在高质量优势,而仅存在低质量优势. 相似文献

7.

Bayesian analysis of a Tobit quantile regression model

**总被引：1，自引：0，他引：1**This paper develops a Bayesian framework for Tobit quantile regression. Our approach is organized around a likelihood function that is based on the asymmetric Laplace distribution, a choice that turns out to be natural in this context. We discuss families of prior distributions on the quantile regression vector that lead to proper posterior distributions with finite moments. We show how the posterior distribution can be sampled and summarized by Markov chain Monte Carlo methods. A method for comparing alternative quantile regression models is also developed and illustrated. The techniques are illustrated with both simulated and real data. In particular, in an empirical comparison, our approach out-performed two other common classical estimators. 相似文献

8.

Robust normal reference bandwidth for kernel density estimation

**总被引：1，自引：0，他引：1**Bandwidth selection is the main problem of kernel density estimation, the most popular method of density estimation. The classical normal reference bandwidth usually oversmoothes the density estimate. The existing hi-tech bandwidths have computational problems (even may not exist) and are not robust against outliers in the sample. A highly robust normal reference bandwidth is proposed, which adapts to different types of densities. 相似文献

9.

Preliminary test ridge regression estimators with student’s

*t*errors and conflicting test-statisticsThe preliminary test ridge regression estimators (

*P**T**R**R**E*) based on the Wald (*W*), Likelihood Ratio (*L**R*) and Lagrangian Multiplier (*L**M*) tests for estimating the regression parameters has been considered in this paper. Here we consider the multiple regression model with student*t*error distribution. The bias and the mean square errors (*M**S**E*) of the proposed estimators are derived under both null and alternative hypothesis. By studying the*M**S**E*criterion, the regions of optimality of the estimators are determined. Under the null hypothesis, the*P**T**R**R**E*based on*L**M*test has the smallest risk followed by the estimators based on*L**R*and*W*tests. However, the*P**T**R**R**E*based on*W*test performs the best followed by the*L**R*and*L**M*based estimators when the parameter moves away from the subspace of the restrictions. The conditions of superiority of the proposed estimators for both shrinkage parameter,*k*and the departure parameter, are provided. Some tables for the maximum and minimum guaranteed efficiency of the proposed estimators have been given, which allows us to determine the optimum level of significance corresponding to the optimum estimator. Finally, we conclude that the estimator based on Wald test dominates the other two estimators in the sense of having highest minimum guaranteed efficiency. 相似文献10.

In this paper, we discuss the properties of preliminary test estimators (PTE) of the parameters of simple linear model with
measurement error (ME model) when the slope of the linear model is suspected to be zero. Expressions of the bias, MSE and
efficiencies are obtained under conditional as well as unconditional situations with known reliability coefficient. Conditional
model results are compared to the standard model without measurement error. We also provide the unconditional model analysis
in finite samples. Asymptotic theory under local alternatives is developed when the variance of measurement error or the ratio
of the variance of the model error relative to the variance of the measurement error is known. Asymptotic expressions of bias
and MSE of the estimators along with their efficiencies are obtained. In every case, it is shown that the measurement error
tend to increase the variability of the estimators compared to the estimators without measurement error. Graphs and tables
are provided to see these results and to determine optimum level of significance for minimum guaranteed efficiency.
Received October 2001
RID="*"
ID="*" A. K. Md. E. Saleh is a Distinguished Research Professor and H. M. Kim is a Ph.D. candidate in the School of Mathematics
and Statistics, Carleton University, Ottawa.

*Acknowledgment.*The authors gratefully acknowledge the constructive suggestion of the referees to improve the paper. The research is supported by NSERC grant A3088. 相似文献