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Regression Techniques Applied to Seasonal Corrections and Adjustments for Calendar Shifts

回归技术在季节校正与日历变动调整中的应用

* The author wishes to acknowledge his indebtedness to Millard Hastay for suggesting the seasonal methods described below, and to Charlotte Boschan for intelligent assistance in all phases of the work.

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Distributions Possessing a Monotone Likelihood Ratio

具有单调似然比的分布

A sufficient condition for the validity of the commonly used one-sided tests is that the underlying density p(x, ω), where x is the observed variable and ω the unknown parameter, possess a “monotone likelihood ratio.” In estimation, only monotone functions of the observed variable x should be used as possible estimating functions of ω.

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Asymptotic Efficiencies of a Nonparametric Life Test for Smaller Percentiles of a Gamma Distribution

伽马分布较低分位点非参数寿命检验的渐近效率

This paper does not present new statistical methods. Rather, it shows that a well known nonparametric procedure which is valid under extremely general conditions also has high efficiency and other favorable properties for certain types of life testing situations. This nonparametric method is the sign test and its confidence interval and point estimate analogs. Sign test procedures and methods of applying them have already received extensive coverage in the literature (e.g.,…

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Asymptotic Efficiencies of a Nonparametric Life Test for Smaller Percentiles of a Gamma Distribution

伽马分布较低分位点非参数寿命检验的渐近效率

This paper does not present new statistical methods. Rather, it shows that a well known nonparametric procedure which is valid under extremely general conditions also has high efficiency and other favorable properties for certain types of life testing situations. This nonparametric method is the sign test and its confidence interval and point estimate analogs. Sign test procedures and methods of applying them have already received extensive coverage in the literature (e.g.,…

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On Approximating the Point Binomial

二项分布的近似方法比较

This paper presents the results of a systematic numerical investigation of the comparative accuracy of several approximations to the cumulative binomial distribution. The approximations studied include the normal, arcsine, Poisson, and six others. Two of the little-known approximations were found to be extremely good: the Poisson Gram-Charlier when the probability p is fairly small, and the Camp-Paulson approximation almost everywhere.

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Some Estimators in Sampling with Varying Probabilities without Replacement

不等概率不放回抽样中的若干估计量

The problem considered is estimation of the total value of a character for a finite population from a sample when the units are selected with varying probabilities without replacement. Several unbiased estimators are proposed. Exact expressions and unbiased estimators for the variances of the estimators are obtained. Certain properties of Yates and Grundy's estimator of variance are proved. Examples are included to study the relative performance of the various estimators.…

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A Sampling Procedure for Mailed Questionnaires

邮寄问卷的抽样程序

T HE mailed questionnaire is desirable in surveys because it is economical of money and effort, free from the interviewer's effect on the respondent, and able to reach individuals not accessible by visit or telephone. However, it has several drawbacks which can seriously limit its efficiency as a means of gathering reliable data. The mailed answers are often exposed to two kinds of bias: (1) bias arising from the respondents' misunderstanding the questions, resentment of…

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A Note on Matrix Inversion by the Square Root Method

关于平方根法求矩阵逆的说明

rT HE square root method, also known as Choleski's method in the nonstatistical literature, has been discussed recently by Duncan and Kenney [1, pp. 16-29], Dwyer [4; 5, Sec. 6.5, 13.4, 13.7, 13.8], Fox, et al. [7, p. 159], and others, with a bibliography in [5, p. 118]. The essence of the method is the reduction of a symmetric matrix A to the product S'S-in which S is a triangular matrix with zeros below the main diagonal, and S' is its transpose. Then, if A and hence S is…

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Table of Percentage Points of Kolmogorov Statistics

Kolmogorov统计量的分位点表

A simple method for testing the probability that a set of numbers is a sample from a known distribution consists of comparing the empirical cumulative distribution function of the sample, S n (x), with the known cumulative distribution function F(x). Both D n = maximum {S n (x) – F{x)} and D n * = maximum | S n (x) – F(x) | are random variables, independent of the special form of F(x), if F(x) is continuous. This paper contains more extensive tables of the percentage points…

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