购销广告中的数学学问

本文通过对需求市场的分析，得出人们的潜在购买量随广告费的增加而增大。但实际需求量是随机的。为使问题简化，并做出定量分析，本文假定实际需求量服从均匀分布，并用数学方法确定广告费和购进量的最优值。     

THE BIVARIATE EXPONENTIAL DISTRIBUTION; A REVIEW AND SOME NEW RESULTS

Various models have been proposed as bivariate forms of the exponential distribution. A brief but comprehensive review is presented which classifies, interrelates and contrasts the different models and outlines what is known about distributional properties, applicability and estimation and testing of parameters (particularly the association parameter). Some new results are presented for one particular model. Maximum likelihood, and moment–type, estimators of the association parameter are examined. Asymptotic variances are derived and attention is given to the relative efficiency of the estimators and to problems of their evaluation.     

基于单元星形光纤网的最大总光程及其求解方法

研究了单元星形光纤网中,最多光路数目与最大允许光链路损耗间的关系,推出了在给定最大允许光链路损耗、不同光路数目时各路总光程的求解方法,进而得到最佳光路数目与最大总光程,最终得出六条结论。     

Developing effective e-recruiting websites: Insights for managers from marketers

In recent years, the practice of using corporate websites to recruit job applicants has increased steadily. Despite this trend, however, studies show that approximately 75% of job seekers find the sites too complicated to use successfully [Brown, D. (2004). Unwanted online job seekers swamp HR staff. Canadian HR Reporter, 17(7), 1-2] and that more than 20% have rejected job opportunities based on poorly designed websites [Pastore, M. (2000, March 29). http://www.clickz.com/showPage.html?page=330331]. To address this problem, this article joins Internet marketing and employee recruitment research to offer six development implications for creating an effective “e-recruitment” source on a corporate website. Based on a job marketing approach to the recruitment process and consumer behavior research on persuasive communication and decision making, we present considerations important to creating an online recruiting website that effectively influences the search decisions and behaviors of a target market of desired job candidates.     

Volatility Estimation with Price Quanta

Volatility estimators based on high, low, opening and closing prices have been developed, and perform well on simulated data, but on real data they frequently give lower values for volatility than the simple open–close estimator. This may be due to the fact that for real data, the maximum (or minimum) price is often at the beginning or end of the day. While this could not happen if the observed process was log Brownian, it could happen if the observed process were log Brownian, but observed only to the nearest penny. We develop the theory of such approximations to derive the corrected versions of the basic estimators.     

VAN DE HULST ON ROBUST STATISTICS: A HISTORICAL NOTE

This paper provides a discussion of an unpublished set of notes written in 1942 by the Dutch astronomer H.C. VAN DE HULST. In these notes VAN DE HULST derives the asymptotic variances of M– estimators as well as trimmed means and concludes that the asymptotic variance of what is now called HUBER'S estimator is the same as that of a trimmed mean. This conclusion is usually ascribed to BICKEL (1965). A letter written by D. VAN DANTZIG in 1943 providing a critical evaluation of. VAN DE HULST'S results, adds interest to this suprisingly early contribution to the theory of robust statistics.     

Poisson Regression for Clustered Data

We compare five methods for parameter estimation of a Poisson regression model for clustered data: (1) ordinary (naive) Poisson regression (OP), which ignores intracluster correlation, (2) Poisson regression with fixed cluster‐specific intercepts (FI), (3) a generalized estimating equations (GEE) approach with an equi‐correlation matrix, (4) an exact generalized estimating equations (EGEE) approach with an exact covariance matrix, and (5) maximum likelihood (ML). Special attention is given to the simplest case of the Poisson regression with a cluster‐specific intercept random when the asymptotic covariance matrix is obtained in closed form. We prove that methods 1–5, except GEE, produce the same estimates of slope coefficients for balanced data (an equal number of observations in each cluster and the same vectors of covariates). All five methods lead to consistent estimates of slopes but have different efficiency for unbalanced data design. It is shown that the FI approach can be derived as a limiting case of maximum likelihood when the cluster variance increases to infinity. Exact asymptotic covariance matrices are derived for each method. In terms of asymptotic efficiency, the methods split into two groups: OP & GEE and EGEE & FI & ML. Thus, contrary to the existing practice, there is no advantage in using GEE because it is substantially outperformed by EGEE and FI. In particular, EGEE does not require integration and is easy to compute with the asymptotic variances of the slope estimates close to those of the ML.     

EMPIRICAL ESTIMATION OF NON-LINEAR INPUT–OUTPUT MODELS: AN ENTROPY ECONOMETRICS APPROACH

Despite theoretical advances, non-linear input–output models have been empirically applied only to a limited extent. This is mainly due to the fact that the number of parameters to be estimated is much higher than the number of available data points. Taking advantage of the recent proliferation of input–output databases and by applying an estimation strategy that relies on entropy econometrics, this paper suggests a way to estimate the parameters that characterize non-linear relationships between inputs and output. This non-linear modelling allows for considering time-specific input coefficients, instead of fixed ones. Several types of multipliers can be derived from this non-linear model, and the proposed generalized maximum entropy (GME) estimator allows estimating them from time series or cross-sectional datasets of input–output tables. The proposed GME technique is illustrated by means of an empirical application that estimates the parameters that characterize a non-linear input–output model for the Spanish economy over the period 1995–2011.