The effect of nonnormality on near-replicate lack-of-fit tests

We examine the effect of nonnormality on the distributions of near-replicate lack-of-fit F-tests. We show that when the number of clusters is large, the distributions of the lack-of-fit tests depend on the kurtosis of the error distribution, and that heavy-tailed error distributions can inflate significantly the sizes of the tests. This behaviour is also evident in small samples, where some lack-of-fit tests are clearly more affected than others by nonnormality. Two modifications of the F-tests are suggested to eliminate the effect of the kurtosis on the limiting null distributions, and their behaviour is studied for small samples.     

Testing the disturbance variance after a pre-test for a linear hypothesis on coefficients in a linear regression

In this paper, we examine the sampling performance of a two-stage test which consists of a pre-test for a linear hypothesis on regression coeffiecients followed by a main-test for a disturbance variance in a linear regression. It is shown that the actual size of the two-stage test can be well-controlled around the normal size if the suggested sizes presented in this paper are used in the pre-test. It is also shown that the two-stage test when the suggested sizes are used in the preferable to the usual test for the disturbance variable which incorporates no pre-test in terms of the power.     

论当代科学前沿背景下实验方法的转向

在传统科学活动中，科学探索以物质实验为主、思想实验为辅。在现代科学中，由于客观条件限制，物质实验在微观领域和宏观世界中难以发挥作用，而思想实验的作用逐渐显现，物质实验仅仅是整个科学活动的验证步骤。以不确定性原理的产生为界，思想实验和物质实验在科学活动的主要领地中的主次关系发生了变化。这种情况存在于相对论、量子力学和宇宙学的研究中。     

A note on umvu estimation in the transformed chi-square family

The transformed chi-square family includes many common one-parameter continuous distributions. In that family, we give conditions under which a given function of the mean admits a minimum variance unbiased estimator and an orthogonal expansion for this estimator in terms of the generalized Laguerre polynomials. We show that such expansion is useful for obtaining bounds for the variance and for the study of the asymptotic properties of the unbiased estimators.     

Roundoff error for floating point representation of real data

In the present paper we define aprobabilistic model for the study ofthe relative roundoff error in the floating point representation ofreal data. In particular, starting from the assumption that real data is uniformly distributed in the interval (0,1), each floating point is assigned aprobability value corresponding to the proportion of real data assigned this floating point value. For each real number x～ U(0,1), we compute the relative roundoff error in the floating point representation and we calculate i t s expected value and variance.     

Short confidence intervals for variance components

Four approximate methods are proposed to construct confidence intervals for the estimation of variance components in unbalanced mixed models. The first three methods are modifications of the Wald, arithmetic and harmonic mean procedures, see Harville and Fenech (1985), while the fourth is an adaptive approach, combining the arithmetic and harmonic mean procedures. The performances of the proposed methods were assessed by a Monte Carlo simulation study. It was found that the intervals based on Wald's method maintained the nominal confidence levels across all designs and values of the parameters under study. On the other hand, the arithmetic (harmonic) mean method performed well for small (large) values of the variance component, relative to the error variance component. The adaptive procedure performed rather well except for extremely unbalanced designs. Further, compared with equal tails intervals, the intervals which use special tables, e.g., Table 678 of Tate and Klett (1959), provided adequate coverage while having much shorter lengths and are thus recommended for use in practice.     

The Time-Varying-Parameter Model for Modeling Changing Conditional Variance: The Case of the Lucas Hypothesis

The main econometric issue in testing the Lucas (1973) hypothesis in a time series context is estimation of the forecast-error variance conditional on past information. The conditional variance may vary through time as monetary policy evolves and agents are obliged to infer its present state. Under the assumption that a monetary policy regime is continuously changing, a time-varying-parameter model is proposed for the monetary-growth function. Based on Kalman-filtering estimation of recursive forecast errors and their conditional variances, the Lucas hypothesis is tested for the U.S. economy (1964:1–1985:4) using monetary growth as aggregate demand variable. The Lucas hypothesis is rejected in favor of Friedman's (1977) hypothesis—the conditional variance of monetary growth affects real output directly, not through the coefficients on the forecast-error term in the Lucas-type output equation.     

基于多属性决策的未动用油气储量评价方法研究

未动用油气储量综合评价是油田确定区块开发序列,降低开发风险、提高开发效益的关键问题之一,多属性决策为解决该问题提供了理论与方法基础。提出一种集结决策者或专家打分与均方差最大化的组合赋权法,并结合加权算术平均算子构建了基于多属性决策的未动用油气储量评价方法。依据未动用油气储量特征,分析选择11个指标构成评价指标体系。最后,通过中国西北某区26个已探明未动用区块的实证分析,说明该方法合理有效。     

Robust sampling strategies for regression estimation

For probability linear regression estimation, conditions are derived where sampling will be robust against violations of the commonly assumed heterogeneous variance model. Stratified pps (spps) and stratified random sampling (spscx) are shown to satisfy these conditions approximately and are more efficient generally than restricted simple random sampling (RSRS) for some real populations and for artificial populations with weights of k = 0, 0.5, 1.0, 1.5 and 2.0. The criteria needs some additional refinement to better predict relative efficiency of spps and spscx.