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均值线性组合的区间估计AI 解读

The simultaneous interval estimation for a given set of linear combinations of means whose estimates are jointly normally distributed is treated. In order to give the exact confidence intervals, t 2 M , the maximum of several quasi-independent t 2-statistics, is introduced. Using the inclusion-exclusion formula, a procedure and tables are given for obtaining a good approximation to the exact upper percentage point of t 2 M . As illustrative examples, the procedure is applied…

最优替代区间估计量的评价准则及其正态分布应用AI 解读

The following criteria for determining best substitute interval estimators of a given class for a population parameter are considered in this paper: (1) minimizing the expected length of the confidence interval (maximizing the effectiveness); (2) minimizing the sum of the mean (absolute) deviations of the upper and lower confidence bounds from the true value (maximizing the effectivity); and (3) minimizing the sum of the mean squared deviations of the upper and lower…

变化季节模式的估计AI 解读

A model is constructed for an economic time series with a changing seasonal pattern. This represents the seasonal component as itself a stationary time series with almost all of the spectral mass very near to the six (angular) frequencies, (πj/6). The problem of “predicting” this seasonal component at the time point n – μ (μ positive, zero or negative) is then solved on the basis of a reasonable model for this spectrum. The unspecified parameters are basically the signal to…

在估计中利用已知变异系数AI 解读

An estimator, γ, of μ is developed which utilizes a priori information concerning the value of the population coefficient of variation. γ′ is shown to have a smaller mean squared error than the sample mean, γ. A table of relative efficiencies for various coefficients of variation and sample sizes is presented.

线性结构关系的极大似然估计札记AI 解读

It is shown that the maximum likelihood estimate of a structural relationship line with uncorrelated errors is usually the same when both error variances are known as when only the ratio is known though exceptionally the slope of the line may be indeterminate. It is also shown how the equations given by Madansky [2] for the maximum likelihood estimates in the case when one error variance is known needs to be modified when, under certain circumstances, they are inconsistent.

两个变量均含误差时线性回归的区间估计AI 解读

Define the linear functional relationship with parameters, α, β, by μ = α + βv. This paper considers the problem of confidence interval estimation of α and β separately, based on a sample of independent pairs, (x i , y i ), i = 1, 2, ···, n, with Ex i = vi, Ey i = μ i . The pairs, (x i , y i ), are assumed to be independent (i ≠ i′), to have a common (unknown) covariance matrix Σ, and to follow the bivariate normal distribution. It is known that under these circumstances…

观测不足时的最小二乘法AI 解读

The optimality of the method of least squares is reconsidered when multicollinearity is present. An analysis is presented of the relationship between estimability and identifiability. The criterion of best linear minimum bias is developed, and shown to be equivalent to that of best linear conditionally unbiased estimation subject to complementary (non-estimable) linear restrictions. Imposition of erroneous estimable linear restrictions is shown to lower variances of…

双向分层总体中的样本选择与估计量选择AI 解读

The paper studies the effect on variance of the method of sample selection and the choice of estimator in a two-way stratified population. Three methods of sampling, simple random and one and two-way stratified, are studied in conjunction with estimators which use no population information, one and two sets of marginal frequencies and cell frequencies. It is shown that whether the information in the population frequencies is used in the sample draw or in the estimator, the…

若干非参数分布的统一推导AI 解读

This paper presents a unified derivation of a number of parameter-free distributions, some of which have appeared earlier in the literature. The starting point is the information provided by a random sample drawn from a certain population and the frequencies observed in a number of mutually exclusive classes. Several types of populations and several ways of defining the classes are considered. The distributions derived concern the unknown class frequencies and the unknown…

调查回答方差及其估计AI 解读

The mathematical model developed by Hansen, Hurwitz, and Bershad for the sampling and response errors of surveys is further analysed and also extended to cover the repetition of the original survey. This extension of the mathematical model provides a framework for the joint application of the two devices traditionally used to measure response variance: interpenetrating samples and re-enumeration. The joint application of these two methods facilitates the estimation of more…

消费者态度、股票价格与非态度变量的预测能力AI 解读

This article reports on tests of the comparative usefulness of consumer attitudes, stock prices, and some non-attitudinal variables for short-term forecasting of the value and number of motor vehicle sales. Both levels and changes of the variables are analyzed for a variety of time spans between 1952 and 1962. The work suggests that stock prices and some non-attitudinal variables, like the length of the work week, share the predictive ability of consumer attitudes, except…

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逐步回归的效率AI 解读

Much attention has been paid to bias of coefficients resulting from stepwise regressions. Looking at bias alone implies that stepwise estimates are inferior. However, using the criterion of relative mean square errors, it is shown for the two variable case that under certain circumstances, stepwise estimators are “better” than direct least squares estimators.

最佳替代区间估计量的准则：兼论正态分布的应用AI 解读

The following criteria for determining best substitute interval estimators of a given class for a population parameter are considered in this paper: (1) minimizing the expected length of the confidence interval (maximizing the effectiveness); (2) minimizing the sum of the mean (absolute) deviations of the upper and lower confidence bounds from the true value (maximizing the effectivity); and (3) minimizing the sum of the mean squared deviations of the upper and lower…

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奇异协方差矩阵下正态变量的条件均值与协方差AI 解读

This note gives formulas for conditional means and covariances—formulas which are valid even when the joint distribution is singular. The method is algebraic; it applies to any joint distribution for which independence and zero correlation are equivalent.

有效访员的识别AI 解读

In studies where validation data is not available, effective interviewers are identified on the basis of various measures of interviewing performance. Yet little is known about the validity of these measures. In the study reported, sample addresses were selected on a probability basis from the records of financial institutions and the holdings reported to the interviewer were compared with institution records for the day of the interview. The frequency with which an…

均值线性组合的区间估计AI 解读

The simultaneous interval estimation for a given set of linear combinations of means whose estimates are jointly normally distributed is treated. In order to give the exact confidence intervals, t 2 M , the maximum of several quasi-independent t 2-statistics, is introduced. Using the inclusion-exclusion formula, a procedure and tables are given for obtaining a good approximation to the exact upper percentage point of t 2 M . As illustrative examples, the procedure is applied…

摘要暂缺

双向分层总体中的抽样方式与估计量选择AI 解读

The paper studies the effect on variance of the method of sample selection and the choice of estimator in a two-way stratified population. Three methods of sampling, simple random and one and two-way stratified, are studied in conjunction with estimators which use no population information, one and two sets of marginal frequencies and cell frequencies. It is shown that whether the information in the population frequencies is used in the sample draw or in the estimator, the…

摘要暂缺

消费者态度、股票价格与非态度变量的预测能力AI 解读

This article reports on tests of the comparative usefulness of consumer attitudes, stock prices, and some non-attitudinal variables for short-term forecasting of the value and number of motor vehicle sales. Both levels and changes of the variables are analyzed for a variety of time spans between 1952 and 1962. The work suggests that stock prices and some non-attitudinal variables, like the length of the work week, share the predictive ability of consumer attitudes, except…