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逆高斯模型下双因素实验的分析AI 解读

This article treats the analysis of factorial experiments under an inverse Gaussian distribution for the failure times. A reciprocal-linear model for the factor effects is motivated from the context of the underlying Wiener process. Explicit solutions to the likelihood equations are derived, and important properties such as strong consistency and limiting normality are established. A least squares approach using the reciprocals of the sample cell means is also studied and…

逆高斯模型下的双因素实验分析AI 解读

This article treats the analysis of factorial experiments under an inverse Gaussian distribution for the failure times. A reciprocal-linear model for the factor effects is motivated from the context of the underlying Wiener process. Explicit solutions to the likelihood equations are derived, and important properties such as strong consistency and limiting normality are established. A least squares approach using the reciprocals of the sample cell means is also studied and…

摘要暂缺

无需预先知道函数形式也能一致估计弹性AI 解读

We consider an open question in applied price theory: Without a priori knowledge of a firm's cost function or a consumer's indirect utility function, is it possible to estimate price and substitution elasticities consistently by observing a demand system? As the work of White [30], Guilkey, Lovell, and Sickles [19], and others has shown, ordinary flexible functional forms such as the translog cannot achieve this objective. We find that if one is prepared to assume that…

摘要暂缺

学习曲线的估计与检验AI 解读

This article describes a new approach to learning curve estimation. Our approach is to formulate statistical procedures that conform to alternative learning curve theories. This leads to the development of nonlinear statistical models of the learning curves. For the three data sets analyzed, autocorrelation seems to be an important problem. Parameter estimates were derived using the maximum likelihood principle in the presence of first-order autocorrelation. Nonnested tests…

美国复合食品需求系统的估计AI 解读

This study develops statistical procedures for computing the parameters of a complete demand system. A constrained maximum likelihood method has been applied, and parametric restrictions derived from classical demand theory are introduced by a substitution approach. The procedures are then applied to U.S. data for estimating a composite food demand system covering 12 food categories and one nonfood sector.

回归中的舍入误差：Sheppard 修正的适用性AI 解读

SUMMARY We consider three simple approaches to rounding error in least squares regression. The first treats the rounded data as if they were unrounded, the second adds an adjustment to the diagonal of the covariance matrix of the variables and the third subtracts an adjustment from the diagonal. The third, Sheppard's corrections, can be motivated as maximum likelihood with small rounding error and either (1) joint normal data or (2) normal residuals, “regular” independent…

缺失数据下单总体多元正态结构化均值与协方差的检验和估计AI 解读

In this paper the multivariate normal linear patterned mean and covariance matrix testing and estimation problem is studied in the presence of missing data for general one-population hypotheses. The Newton-Raphson, Method of Scoring and EM algorithms are given for finding the maximum likelihood estimates. The asymptotic joint distribution of the maximum likelihood estimates under null and alternative hypotheses are derived along with the form of the likelihood ratio…

极端中程统计量的联合渐近分布AI 解读

We derive the joint asymptotic distribution of the $k$ midranges formed by averaging the $i$th smallest normalized order statistic with the $i$th largest normalized order statistic, $i = 1, \cdots, k$. We then derive the distribution of the maximum midrange among these $k$ extreme midranges and the limiting distribution of this maximum as $k \rightarrow \infty$. These results imply that, even in infinite samples, different distributions in the class of symmetric, unimodal…

删失数据下双参数递减风险率分布的最大似然估计AI 解读

Problems of maximum likelihood estimation are discussed for shape and scale parameters from certain decreasing hazard rate distributions, typically either mixed-exponential or “work-hardened.” Sufficient conditions on the mixing distribution are given that guarantee regular behavior of the hazard rate and that ensure, even with highly censored data, that the MLE's exist from such DHR distributions whenever the sample satisfies a certain condition; otherwise a constant hazard…

信息不足时的估计AI 解读

As a possible explanation for the existence of absurd UMVU estimators, a class of estimation problems is defined: estimating the probability of an “unobservable” event, for example, estimating the probability of an event of interest occurring over a long period of time from observations over a much shorter period. It is pointed out that in typical cases of this kind, no reasonable unbiased estimator can exist. Consideration of the maximum likelihood estimator suggests the…

删失数据下双参数递减风险率分布的极大似然估计AI 解读

Problems of maximum likelihood estimation are discussed for shape and scale parameters from certain decreasing hazard rate distributions, typically either mixed-exponential or “work-hardened.” Sufficient conditions on the mixing distribution are given that guarantee regular behavior of the hazard rate and that ensure, even with highly censored data, that the MLE's exist from such DHR distributions whenever the sample satisfies a certain condition; otherwise a constant hazard…

最大似然估计量分布的一个公式AI 解读

Abstract A simple formula for the conditional distribution of the maximum likelihood estimator given a maximal ancillary statistic is discussed and exemplified. The formula is generally accurate to order $ O(n^{-1}) $ or even $ O(n^{-{3}/{2}}) $, and for many important models it is, in fact, exact. After some preliminary discussion of the formula and of certain relevant aspects of likelihood, the formula is used to motivate the definition of a modified profile likelihood…

最大似然估计量分布的一个公式AI 解读

A simple formula for the conditional distribution of the maximum likelihood estimator given a maximal ancillary statistic is discussed and exemplified. The formula is generally accurate to order O(n−θθl) or even O(n−θθ3/2), and for many important models it is, in fact, exact. After some preliminary discussion of the formula and of certain relevant aspects of likelihood, the formula is used to motivate the definition of a modified profile likelihood whose inferential…

平稳随机过程的 m 阶最大似然估计AI 解读

SUMMARY Sometimes the likelihood cannot be computed even introducing approximations whose effect is asymptotically negligible. To overcome this problem for inference from a stochastic process, we approximate the log likelihood by a sum whose generic term is the density function of the corresponding sample element conditional on the m most recent observations, for some m ≥ 0. General results on the asymptotic properties of the associated estimates are given, and numerical…

论 Sprent 的广义最小二乘估计量AI 解读

Summary This paper studies the asymptotic properties of Sprent's (1966) generalized least-squares estimator of the slope parameter in a functional relationship model which allows errors at different data points be correlated. Consistency is established and the asymptotic variance derived. When the Joint distribution of the errors is normal, in which case Sprent's estimator coincides with the maximum likelihood estimator, the asymptotic variance formula is further simplified…

原点未知平移的连续单变量分布参数估计AI 解读

Summary A general method of estimating parameters in continuous univariate distributions is proposed. It is especially suited to cases where one of the parameters is an unknown shifted origin. This occurs, for example, in the three-parameter lognormal, gamma and Weibull models. For such distributions it is known that maximum likelihood (ML) estimation can break down because the likelihood is unbounded and this can lead to inconsistent estimators. Properties of the proposed…

动态非线性理性预期模型的求解与极大似然估计AI 解读

A solution method and an estimation method for nonlinear rational expectations models are presented in this paper.The solution method can be used in forecasting and policy applications and can handle models with serial correlation and multiple viewpoint dates.When applied to linear models, the solution method yields the same results as those obtained from currently available methods that are designed specifically for linear models.It is, however, more flexible and general…

用普通最小二乘进行 Logistic 回归与判别分析AI 解读

If the observations for fitting a polytomous logistic regression model satisfy certain normality assumptions, the maximum likelihood estimates of the regression coefficients are the discriminant function estimates. This article shows that these estimates, their unbiased counterparts, and associated test statistics for variable selection can be calculated using ordinary least squares regression techniques, thereby providing a convenient method for fitting logistic regression…

估计中的中偏差理论AI 解读

The performance of a sequence of estimators $\{T_n\}$ of $\theta$ can be measured by the probability concentration of the estimator in an $\varepsilon_n$-neighborhood of $\theta$. Classical choices of $\varepsilon_n$ are $\varepsilon_n = cn^{-1/2}$ (contiguous case) and $\varepsilon_n = \varepsilon$ fixed for all $n$ (non-local case). In this article all sequences $\{\varepsilon_n\}$ with $\lim_{n\rightarrow\infty} \varepsilon_n = 0$ and $\lim_{n\rightarrow\infty} \varepsilon_nn^{1/2} = \infty$…

多元统计分析中的特征值分布AI 解读

Ten invariant multivariate testing problems involving the real, complex, or quaternion structure of covariance matrices are considered. In each problem the maximal invariant statistic and its distribution are described, as well as the maximum likelihood estimators and likelihood ratio test statistics. These results are obtained by means of a new, unified method based on invariance arguments.

离散多元冲击模型的最大似然估计AI 解读

A k-variate Bernoulli distribution with k + 1 parameters is obtained as a shock model in which shocks are fatal to single components only or to all components simultaneously in a k-component system. The maximum likelihood estimator (MLE) for model parameters is fully characterized. In the most complex case, the MLE is displayed as a simple function of the smallest positive root of a kth degree polynomial. An iterative scheme that converges monotonically to the desired root…

随机配对的检验AI 解读

The analysis of contingency tables in which both margins have the same polychotomy is considered. These tables arise when members from categories form pairs. Pairs cannot be between members of the same category. Appropriate models for pairing are introduced. A maximum likelihood algorithm is developed and asymptotic covariance formulas are derived. An empirical example illustrates the procedures.