Parameter estimation based upon nonparametric function estimators

By considering the solution to a linear approximation of a nonlinear regression problem, a procedure for developing a para¬meter estimator, based upon a nonpammetric estimator of a para¬metric function, is given. The resulting estimators, which are determinable in closed form, are asymptotically normally distri¬buted and are optimal among the class of estimators based upon the function estimator. Further, in many cases, the estimator will have the same asymptotic distribution theory as the correspond¬ing maximum likelihood estimator. Estimators based upon the Kaplan-Meier quantile function are developed for randomly censored samples.     

Order-restricted goodness-of-fit tests based on spacings

Goodness-of-fit tests are proposed for unimodal densities and U-shaped hazards. The tests are based on maximum-product-of-spacings estimators, and incorporate unimodality or U-shapedness using order restrictions. A slightly improved “maximum violator” algorithm is given for computing the order-restricted estimates and test statistics. Modified spacings such as “k-spacings”, which may actually increase power, ensure computational feasibility when sample sizes are large. Simulations demonstrate that for samples of size less than twenty, the use of order restrictions can increase power, even with modified spacings. The proposed methods can be used as approximations in cases of null hypotheses that are specified only up to unknown parameters that are estimated.     

Modified maximum likelihood estimation for rayleigh distribution

For defining a Modified Maximum Likelihood Estimate of the scale parameter of Rayleigh distribution, a hyperbolic approximation is used instead of linear approximation for a function which appears in the Maximum Likelihood equation. This estimate is shown to perform better, in the sense of accuracy and simplicity of calculation, than the one based on linear approximation for the same function. Also the estimate of the scale parameter obtained is shown to be asymptotically unbiased. Numerical computation for random samples of different sizes from Rayleigh distribution, using type I1 censoring is done and is shown to be better than that obtained by Lee et al. (1980)     

On the efficiency of nonparametric variance estimation in sequential dose-finding

Dose-finding in clinical studies is typically formulated as a quantile estimation problem, for which a correct specification of the variance function of the outcomes is important. This is especially true for sequential study where the variance assumption directly involves in the generation of the design points and hence sensitivity analysis may not be performed after the data are collected. In this light, there is a strong reason for avoiding parametric assumptions on the variance function, although this may incur efficiency loss. In this paper, we investigate how much information one may retrieve by making additional parametric assumptions on the variance in the context of a sequential least squares recursion. By asymptotic comparison, we demonstrate that assuming homoscedasticity achieves only a modest efficiency gain when compared to nonparametric variance estimation: when homoscedasticity in truth holds, the latter is at worst 88% as efficient as the former in the limiting case, and often achieves well over 90% efficiency for most practical situations. Extensive simulation studies concur with this observation under a wide range of scenarios.     

TESTS FOR EQUALITY OF TWO DISTRIBUTIONS WITH CORRELATED INTERVAL CENSORED LIFE-TIMES

ABSTRACT

Large sample properties of Life-Table estimator are discussed for interval censored bivariate survival data. We restrict our attention to the situation where response times within pairs are not distinguishable, and the univariate survival distribution is the same for any individual within any pair. The large sample properties are applied to test for equality of two distributions with correlated response times where treatments are applied to different independent sets of cohorts. Data, which can be separated into two independent sets, from an angioplasty study where more than one procedure is performed on some patients are used to illustrate this methodology.     

兼业Ⅰ农户与雇主雇佣生产合约的模型及实证分析

在优化多任务委托一代理的基础上,通过建立相对激励强度,假设任务2的分享系数不变,建立农业雇佣生产合约模型,分析影响兼业I农户（雇工）与雇主达成固定工资合约的因素。研究表明固定工资合约与任务1可观测性、绝对风险厌恶系数呈负相关,与任务1比重正相关,与两项任务替代弹性关系不确定。利用“互惠性”非理性行为的新委托代理模型,发现在村落社会中互惠性有利于降低道德风险。     

Procurement strategies in the presence of the spot market—an analytical framework

This paper investigates a problem in which a buyer can procure from a regular supplier as well as from a supplier in a spot market, possibly formed over the Internet. The contract with the regular supplier specifies a predetermined order volume and price, while the spot market has unlimited supply but a varying spot price. We analyse this problem from a buyer/supplier perspective, and an analytical model is developed to analyse two distinctive procurement strategies: the pure procurement system (PS) and the mixed procurement system of regular supplier with a supplier in spot markets (MS). Without loss of generality, we obtained a closed-forms solution that enabled us to provide numerical analysis on the procurement strategies, and allowed us to compare further the different characteristics between PS and MS. The results of our analysis demonstrate that the use of spot market could effectively mitigate the risk associated with demand uncertainty facing the buyer. The results also show that adopting MS can generate a higher buyer's profit than the PS, and significant supply-chain profit improvements can indeed be achieved through buyer/supplier coordination. Furthermore, spot price volatility leads to the facilitation of the use of spot markets, improving the buyer and the supply-chain profitability.     

Who Chooses Which Private Education? Theory and International Evidence

Private school students do not always perform better in standardized tests. We suggest that this may be explained by choice of private schooling by less capable students in countries where government schools are better suited to talented students. To assess the empirical relevance of this mechanism, we exploit cross‐country variation in the Program for International Student Assessment (PISA) 2009 survey of differences between private and state school regarding organizational features that are differently suitable for students with different learning ability. We seek and find evidence of this mechanism's empirical relevance in controlled regressions that treat within‐country variation of PISA scores as an indicator of unobserved ability to learn.     

WHAT GOOD IS WEALTH WITHOUT HEALTH? THE EFFECT OF HEALTH ON THE MARGINAL UTILITY OF CONSUMPTION

We estimate how the marginal utility of consumption varies with health. To do so, we develop a simple model in which the impact of health on the marginal utility of consumption can be estimated from data on permanent income, health, and utility proxies. We estimate the model using the Health and Retirement Study's panel data on the elderly and near‐elderly, and proxy for utility with measures of subjective well‐being. Across a wide range of alternative specifications and assumptions, we find that the marginal utility of consumption declines as health deteriorates, and we are able to clearly reject the null of no state dependence. Our point estimates indicate that a one‐standard‐deviation increase in the number of chronic diseases is associated with a 10%–25% decline in the marginal utility of consumption relative to this marginal utility when the individual has no chronic diseases. We present some simple, illustrative calibration results that suggest that state dependence of the magnitude we estimate can have a substantial effect on important economic problems such as the optimal level of health insurance benefits and the optimal level of life‐cycle savings.     

A formula for Type III sums of squares

Abstract

Type III methods were introduced by SAS to address difficulties in dummy-variable models for effects of multiple factors and covariates. They are widely used in practice; they are the default method in several statistical computing packages. Type III sums of squares (SSs) are defined by a set of instructions; an explicit mathematical formulation does not seem to exist.

An explicit formulation is derived in this paper. It is used to illustrate Type III SSs and to establish their properties in the two-factor ANOVA model.