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位置参数的最优稳健线性估计量AI 解读

Efficiency-robust linear estimation as outlined in Birnbaum and Laska (JASA, 62 (1967) pp. 1230–1240) is applied, determining maximin-efficient linear unbiased estimators (MLUEs), and their efficiencies, for ordered samples of sizes 5 (5) 20 from a family of nine distributions. The results are compactly summarized because of the tendency of these distributions to admit simple orderings such that the MLUE over any subset of the distributions is just the MLUE over the extreme…

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计量经济学走向何方？AI 解读

To try to chart the future of development in econometrics during the 1970's, it is useful to review the origins of the subject before World War II and the modern era in which our present body of knowledge flowered, 1940–1970. New developments should be made in computer analysis of large data banks, more complete systems, control systems, and microeconometric applications. It is likely that the future of the subject will be less tied to the United States than in the past few…

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一类平稳与非平稳含噪信号的近似最优线性预测AI 解读

A technique for approximating the best linear predictor of a noise-distorted signal is presented. The technique is applicable when the signal is stationary with a spectrum which is highly concentrated around known or estimated frequencies, or when the signal is an accumulating sequence whose “spectrum” has poles at these frequencies. The noise must be stationary, but its spectrum need only be known or estimated at the above-mentioned frequencies. The time parameter is…

稳定季节模式估计中最小二乘法的效率AI 解读

In this article we investigate the efficiency of least squares (l.s.) in estimating a stable pattern. A model is proposed for an economic time series, which, after filtering, is a suitable basis for our investigation. The covariance structure of the disturbances is assumed known and several possible generating processes for the disturbances are considered. We contrast the variances of the l.s. estimates with those from the best linear unbiased (b.l.u.) procedure for four…

分组 Poisson 数据的极大似然估计AI 解读

In this article, sufficient conditions are given for the existence of a unique solution of the likelihood equation which results from a grouped data sample. The necessary and sufficient conditions for the convergence of a sequence defined by the method of successive approximations to this unique solution are also given. Finally, it is shown that when the groups from an underlying Poisson distribution are connected the method of successive approximations will converge to the…

对数正态分布与对数正态回归的贝叶斯及非贝叶斯分析AI 解读

In this article, Bayesian and non-Bayesian methods for estimating parameters of the log-normal distribution and of log-normal regression processes are considered. Posterior distributions for parameters of interest are derived and their properties are described. With respect to point estimation, a rather broad class of estimators is defined and, relative to this class, new minimal mean square error (MSE) estimators for the median and mean of the log-normal distribution and…

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极小极大实验设计AI 解读

When an experimenter is interested in more than one parameter in the regression model and tries to obtain a design that minimizes the maximum variance of the individual regression coefficients, he is looking for a minimax design with respect to the single parameter. In this article we explicitly present the minimax s.p. designs for the ordinary polynomial regression, when the degree is ≤4. For 5≤n ≤12 we present the minimax s.p. designs obtained through a computer. These are…

事故发生率潜势：泊松过程的多元回归分析AI 解读

Various accident frequency models have appeared in the literature which predict the distribution of future accidents based on the number of past accidents. This article presents a method for deriving such distributions using several predictive criteria. It is assumed that an individual's accident experience is a Poisson process with the parameter a linear function of criterion variables. An iterative weighted least-squares procedure is used to solve the system of maximum…

序贯概率比检验所需样本量的渐近分布AI 解读

The derivation is presented of the asymptotic distribution of the number N of observations required to terminate the classical sequential probability ratio test (SPRT) with bounds a, b (a > 0 > b) of a simple parametric hypothesis H: θ = θ1 against a simple parametric alternative K:θ=θ1+Δ(Δ>0) when Δ tends to zero. It is shown that if the common probability density function (p.d.f.) of the basic random variables belongs to the Darmois-Koopman exponential class and if the…

零截断二项分布若干估计量的小样本表现AI 解读

Estimation of the parameter of a binomial distribution with the zero class truncated is a classical problem in human genetics. Mathematically the problem is the estimation of p from n, independent observations with distribution, (r s)prqs-r/(1 - qs) where r = 1, 2, ··· s, q = 1 - p and s ≥ 2 is a known integer. This article gives exact results which show the simple estimator of Mantel [17] to be less biased, both asymptotically and in small samples, than either the ML…

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分段线性损失下简单次序统计量估计的效率AI 解读

When losses are piecewise linear, optimal decision-making hinges on estimating a specified fractile of a probability distribution. In this article we investigate, through examples, the operating characteristics of an estimation procedure which utilizes simple linear combinations of one or two values in the order statistic generated by an observation vector. Such estimates appear to be remarkably efficient compared to the estimates generated by simple parametric procedures;…

回归分析中利用不完整观测的进一步建议AI 解读

The purpose of this article is to suggest a method of estimating parameters of linear regressions containing two independent variables, when data is missing among these variables. The problem envisaged concerns the case where: (1) the independent variables are considered as fixed numbers; (2) each observation contains the values of the dependent variable and at least one of the independent variables; (3) some observations are complete. In contrast with other approaches…

回归分析中扰动项的新估计量AI 解读

In this article, an alternative v for the vector û of least-squares residuals in the linear model is derived. It is best in the class of all linear unbiased estimators' of u having a certain fixed covariance matrix chosen a priori. Under the normality assumption, the distribution of the Von Neumann Ratio based on v is independent of the regression vectors, so that v is particularly useful for testing on serial correlation of the disturbances. It is pointed out that the…

职业流动的典型相关分析AI 解读

The method of canonical correlation between sets of dummy variables is used to assign weights to the categories of occupational mobility tables, in order to test two assumptions: 1. The socioeconomic distance between occupations determines the correlation across individuals in a mobility table. 2. The relative status of occupations has remained constant over time. The weights which yield the maximum correlation are found to correlate very highly with measures of…

利用平均绝对离差构造置信限和进行 t 类检验的 H 分布分位点AI 解读

A table to three decimal places is provided for the percentage points of the variate , where d is the mean absolute deviation from the mean of a normal sample of size n, and μ is the population mean. The table is analogous to the table of Student's t-distribution. It makes it possible to compute confidence limits for the mean and to perform various tests of significance by way of the mean absolute deviation instead of the standard deviation. This method is almost as accurate…

非参数选择程序的效率：最大位置参数情形AI 解读

Suppose that X1, ···, Xk are mutually independent observations from populations π1, ···, πk and that Xi has a density fxi(·)(1 ≤ i ≤ k). For i = 1, ···, k let pi = P[Xi > maxj ≠ i Xj], and let p[k] = max (p1, ···, pk). Bechhofer and Sobel [4] have proposed a nonparametric selection procedure based on multinomial random variables for the problem of selecting a population which has the highest probability, p[k], of producing the largest observation. (The density fxi(·) may be…

双指数分布族中非参数位置检验的小样本功效函数AI 解读

Eight nonparametric tests of location are examined in a small sample setting. Power functions are presented for samples drawn from the double exponential distribution. The results provide an example where the asymptotically most powerful rank test (the Mood median test) performs poorly for alternatives which are not very close to the null hypothesis.

通过识别法求取抽样分布AI 解读

Let [ttilde] be a statistic sufficient for a parameter θ and let L[θ;t) be the likelihood function of θ for given t. Suppose we recognize a function φ(t) such that L(θ;t) φ(t) regarded as a function of t for a given θ, is a density function. We show here that this is the sampling density of [ttilde] if the family of recognized densities is complete. Examples are given to illustrate that in many situations this recognition method provides a neat way of finding sampling…