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用傅里叶级数估计概率密度与累积分布AI 解读

A class of estimators (referred to as the Fourier estimators m and m) of the probability density function f and the associated cumulative distribution function F are considered. Here m = Σmk=0 âkψk and m = Σmk=0 Âk ψk where the functions {ψk} comprise an orthogonal set with respect to weight function w(x), and the statistics âk and Âk are formed from the n unordered observations.Simple expressions are found for the mean integrated square errors, M.I.S.E., of the estimators m…

双端删失样本下第一类极值渐近分布参数的最大似然估计AI 解读

Let X be a random variable having the first asymptotic distribution of smallest (largest) values, with location parameter u and scale parameter b, b > 0. The natural logarithm of the likelihood function of a sample of size n from such a distribution, the lowest r1 and the highest r2 sample values having been censored, is written down and its first and second partial derivatives with respect to the parameters are worked out. The likelihood equations, obtained by equating to…

利用样本分位数分析超大样本极值数据AI 解读

This paper deals with estimating the location and the scale parameters of the extreme value distribution when the sample size is very large, using sample quantiles. An estimator is given for the location parameter when the scale parameter is known, based on one or more (up to 15) order statistics. Also given is an estimator for the scale parameter when the location parameter is known, built on two order statistics. An iterative procedure is utilized to estimate the…

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多元指数分布的参数估计AI 解读

Simple consistent estimates are derived for the parameters of a multivariate exponential distribution. The mean squared error of the estimates is computed, and a lower bound for their efficiency is derived. A precise lower bound for the efficiency is computed in the bivariate case. It does not seem feasible to compute the efficiency precisely in the multivariate case. Some attention is given to the behavior of the estimates when observations are rounded prior to analysis.

经典占位问题的统计推断：类别数的无偏估计AI 解读

A random sample of N observations is obtained from a multinomial distribution with an unknown number θ of equiprobable cells. The existence and asymptotic properties of the unbiased estimator based on the number of occupied cells is given. The related problem in which observations are made sequentially, stopping after L repeated cells have been observed, is also discussed. In the fixed sample size case, if θ is known not to exceed N, the unbiased estimator is a ratio of…

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若干互不相关的非参数检验统计量AI 解读

It is shown that odd translation invariant two sample statistics are uncorrelated with even translation invariant two sample statistics when the distribution function of the combined sample is equally symmetric. This is a generalization of a result of Hogg. It is used to establish conditions under which certain dispersion test statistics (including ones proposed by Lehmann, Mood, Ansari-Bradley-Freund-Barton-David, Klotz and Moses) are uncorrelated with certain location test…

第一中位数检验：控制中位数检验的双侧版本AI 解读

Consider two independent samples (called x's and y's) of mutually independent observations from populations with c.d.f.'s F(x) and G(x) respectively. Let υ be the number of x's which are smaller than the median of the y-sample and let u be the number of y's which are less than the median of the x-sample. If the x-sample is regarded as the control group, then the control median test proposed by Kimball et al. [9], rejects the hypothesis that F(x) ≡ G(x) if u is small. The…

In this study of robustness the insensitivity of the F-test between means to its underlying assumptions (normally distributed populations with equal variances) is investigated. Using two nonnormal distributions (exponential and lognormal), it is found that the test is fairly insensitive for moderate and equal sample size (n = 32) when the variances are equal. Further, for small samples (n < 32), the test is conservative with respect to Type I error. It is also conservative…

This paper presents the region of coverage of the curve shape characteristics, α23 and δ = (2α4 −3α23 −6) /(α4+3), for a certain general system of distributions, Burr (1942). These curve-shape characteristics were chosen for comparison with the Pearson system because of the simplicity with which they map the members of the latter system, Craig (1936). It is here shown that the present system covers almost all of the regions of the main Pearson Types IV and VI, and an…

Two nonparametric tests are presented for analyzing data from a one-way layout. Their principal characteristic is ease in computation. One test is intended for k samples of equal size n, and the other is for k samples of possibly unequal sample sizes. Both tests may be regarded as generalizations of Mosteller's slippage test. Multiple decision aspects of both tests are discussed. Monte Carlo studies show the first test to be more powerful than the F test in some situations,…

BLS 与人口普查局修订季节调整程序的谱评价AI 解读

This paper presents spectral criteria to evaluate seasonal adjustment procedures, and applies them to the estimated spectral properties of the monthly unemployment series, as adjusted by past and present methods of the Bureau of Labor Statistics (BLS) and of the Census Bureau. It also re-examines some conclusions reported in the Gordon Committee Report (1962) and in Nerlove (1964) on past methods of adjustment. The paper concludes that (1) the loss in spectral power between…

人口普查局与 BLS 季节调整方法的线性近似AI 解读

The Census and BLS ratio-to-moving-average seasonal adjustment methods are usually specified by procedural steps. They can be written mathematically as combinations of linear and non-linear operations on the logarithms of the original series. For some purposes the non-linear operations can be ignored. The Census and BLS historical seasonal factors are almost identical to those from a simpler model using ratios to a centered 12-term moving average. They also closely resemble…

百分位数的后验分布：有限总体抽样中的贝叶斯推断AI 解读

A Bayesian approach to inference about the percentiles and other characteristics of a finite population is proposed. The approach does not depend upon, though it need not exclude, the use of parametric models.Some related questions concerning the existence of exchangeable distributions are considered. It is shown that there are no countably additive exchangeable distributions on the space of observations which give ties probability 0 and for which a next observation is…

线性回归系数的改进估计量AI 解读

Point estimators for the coefficients in orthogonal linear regression which are better than the ordinary least squares estimator are obtained when at least three coefficients are to be estimated. The measure of goodness of an estimator is the sum, or weighted sum, of the componentwise mean squared errors. Some of the new estimators have interpretations as estimators which depend upon preliminary tests of significance. These estimators may be especially appropriate when the…

随机系数线性模型的若干估计量AI 解读

The linear model given by is considered. The βk represent average responses of yt the dependent variable to unit changes in the independent variables, ztk. The vtk are independently distributed random errors. A number of consistent estimators of the coefficients, βk, and the variances of the errors are developed and a few properties of the estimators are noted. Further investigations of sampling properties are needed.

分室模型的偏和联合估计方法AI 解读

An estimation procedure is presented that may be used to simultaneously estimate the parameters in a multiple equation regression model. The regression models considered are shown to arise from radioactive tracer experiments using compartmental models. For such models the regression equations are shown to be linear combinations of the same exponential parameters, and the number of independent regression equations is also shown to be the same as the number of exponential…

线性回归中参数约束均方误差准则的检验AI 解读

The objectives of this paper are to examine the mean square error criterion for rejecting or adopting restrictions on the parameter space in a regression model, and to develop a uniformly most powerful testing procedure for the criterion. We present a tabulation of critical points for the test for one restriction and selected points of the power function. The mean square error criterion suggests a framework for thinking about the problem of multicollinearity in a linear…

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复杂抽样所得指数的标准误AI 解读

Methods of computing standard errors were developed and applied for several statistics of importance in economic and social surveys. These statistics are based on ratio means r = y/x; x is often the variable sample size of complex samples. Some statistics involve weighted sums σWjrj, others concern the relatives R1 = r1/r0 = (y1/x1)/(y0/x0), the ratio of current (1) to base (0) mean. From these relatives the indexes are constructed, and changes, I2 – I1, in the index. We…

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