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不同参数序列下线性函数关系最大似然估计的改进AI 解读

We propose an improvement of the maximum likelihood (ML) estimate in linear functional relationships. The improved estimate is a linear combination of the ML and the least squares estimate so as to remove the bias of the former. Approximations to the distribution of the estimate are derived for two alternative parameter sequences: a sequence in which the noncentrality parameter (the spread of the true values) increases while the number of observations stays fixed, and that…

部分系统抽样中的方差估计AI 解读

Systematic sampling is very convenient in many practical situations, but does not provide a satisfactory estimator of the variance of the sample mean except when additional assumptions are made. A method is proposed to estimate the mean of a finite population and to estimate the variance of this estimate, using a systematic sample and a simple random sample drawn from the remaining population. It is shown that both estimators are unbiased. This method provides also an…

对数周期图的自动平滑AI 解读

We develop an objective optimum smoothing procedure for an estimate of the log spectral density, based on smoothing the log periodogram with a smoothing spline. We call the result the optimally smoothed spline (OSS) estimate. We show that an unbiased estimate [Rcirc](λ) of the expected integrated mean square error can be obtained as a function of the smoothing, or “bandwidth” parameter λ. The smoothing parameter then is chosen as that λ that minimizes [Rcirc](λ). The degree…

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线性判别分析中实际误判率的分布AI 解读

Some results concerning the distributions of the actual error rates in linear discriminant analysis, under various assumptions about the parameters, are discussed. To determine the form in the one-variable case, formulas for the exact distribution and density functions of the actual error rates are presented. Formulas for the asymptotic distribution and asymptotic moments of the actual error rates in both the univariate and multivariate cases are also given.

非线性回归中参数函数的显式估计量AI 解读

When repetitive estimations are to be made under field conditions using data that follow a nonlinear regression law, a simple polynomial function of the observations has considerable appeal as an estimator. The polynomial estimator of finite degree with smallest average mean squared error is found. Conditions are given such that as degree increases it converges in probability to the Bayes estimator and its average mean squared error converges to the lower bound of all square…

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离散噪声中二项分布信号的最大似然估计AI 解读

Let X be the sum of independent variables Y and Z, where Y is binomially distributed and Z is a nonnegative integer-valued variable whose distribution does not depend on the binomial parameter p. Convoluted binomial distributions describing variables like X are characterized by regularity conditions and equations of the form ∂/∂p P(X = x)=c[P(X = x − 1) − P(X = x)]. The characterization, together with a monotonicity property for probability ratios, is shown to facilitate…

随访研究中产后闭经时长选择偏差的调整AI 解读

In a prospective study in which females giving birth in a specified small interval of time are followed to obtain the distribution of the duration of postpartum amenorrhea (PPA), the observed distribution involves a selection bias because of an overrepresentation of smaller PPA. In this article, the nature of this selection bias is investigated and an analytical procedure is outlined to adjust the observed distribution of PPA in order to obtain the true distribution. The…

大规模调查的一类稳健抽样设计AI 解读

A combined estimation and selection scheme is proposed for use in the context of large-scale enterprise and establishment surveys. The estimator is asymptotically design unbiased and subject to this constraint has minimum expected variance under a superpopulation model. The main advantage of this scheme over current practice is the removal of the need for size stratification. The relation of both the current and the proposed schemes to the Royall and Hereon (1973a,b)…

简单线性模型百分位数曲线的紧置信带与容忍带AI 解读

This article develops sharp confidence bands for percentiles of regression functions over finite intervals. Attention is focused on one-sided (upper) bands for these percentiles, but a simple extension allows construction of two-sided bands. These upper bands are useful for tolerance bands, since a 100-γ percent confidence band for the 100/βth percentile is also a γ coefficient β-tolerance band.

方差加性模型稳健检验的一般方差分析方法AI 解读

Linearly combining Levene's z 2 variable with the jackknife pseudo-values of s 2 produces a family of variables that allows for analysis of variance (ANOVA) tests of additive models for the variances in fixed effects designs. Some distributional theory is developed, and a new robust homogeneity of variance test is advocated.

纳入复杂度成本时预检验估计量的可容许性AI 解读

Consider the problem of estimating the mean by using a random sample from a normal population. Let denote the sample mean and consider the estimator that assumes the value zero when and the value when . This is called a preliminary test estimator. For most of the usual loss functions it is inadmissible. In this article we show that for some loss functions, which include a complexity cost, the estimator is admissible. The results are related to Cohen's work on hybrid…

基于伽马分布的不同收入不平等指标性质分析AI 解读

The Gini, Theil entropy, and Pietra measures of inequality associated with the gamma distribution function are expressed in terms of the parameters defining the gamma distribution. Method of moments (MME) and maximum likelihood estimators (MLE) of these measures are obtained along with expressions for the asymptotic standard errors of the MLE measures. A table is presented that facilitates the calculation of MLE of inequality measures and the associated asymptotic standard…

单变量 ARMA 时间序列模型残差互相关的分布AI 解读

Cross-correlations between univariate autoregressive moving average (ARMA) time series residuals are useful in the examination of relationships between time series (Pierce 1977a) and in the identification of dynamic regression models (Haugh and Box 1977). In this article, the asymptotic distribution of these residual cross-correlations is derived, and its application to the problem of testing for lagged relationships in the presence of instantaneous causality is discussed.…

合并检验的渐近最优方法AI 解读

A criterion for the asymptotic optimality of combined independent tests is given. Methods other than Fisher's are shown to satisfy the criterion. Certain problems call for a weighted combination of tests. It is shown that many weighted procedures are optimal. In particular, a weighted procedure based on gamma transforms is optimal. This weighted procedure has the additional advantage that critical values are easily determined. Good's weighting procedure is shown not to be…

含伴随变量的单臂老虎机问题AI 解读

We consider a Bayesian sequential allocation problem that incorporates a concomitant variable in the model. Although the model is highly simplified, our results do have some mildly surprising aspects: (a) the approximate solution to the allocation problem is simpler in the presence of concomitant information than in its absence, (b) the exact value of the discount factor is less important than in previous work, and (c) the myopic procedure is asymptotically optimal.

利用复杂抽样设计的数据区分分布AI 解读

This article presents the statistical methodology for estimating stratum cumulative distribution functions (cdf's) when the sample is drawn according to a complex design. Justification for the use of this methodology is offered, and examples are presented to demonstrate the expanded inference possible when estimated cdf's are used in addition to stratum means. The methods are applied to data from a survey of the patterns of care in radiation therapy facilities in the United…

时间序列的决定系数度量AI 解读

With time series data, the conventional regression R 2 is a nebulous concept, as the explained variation consists in part of variation that can be attributed merely to past values of the dependent variable. Thus R 2 is extremely sensitive to prefiltering operations such as first differencing. This article develops and illustrates an alternative R 2 concept, which eliminates this ambiguity by measuring the explanatory power of a time series-regression model relative to that…

二项分布参数若干近似置信区间的比较AI 解读

We consider two confidence intervals for the binomial parameter that are frequently recommended for large samples. We show that one of these, which is in fact less popular in the literature, enjoys certain advantages over the other one. The criteria used for comparison are the confidence coefficients, the lengths, and the Neyman shortness of the intervals.

一类两样本尺度参数的分布自由检验AI 解读

A class of distribution-free statistics for testing equality of two scale parameters when the location parameters are equal is defined. When the two populations are identical, each statistic in this class is governed by the same distribution as that of the two-sample Wilcoxon statistic. A method for selecting which member of the class to use for a particular data set is described, the resulting adaptive procedure being relatively insensitive to small failures in the…

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