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删失数据下若干两样本秩检验的蒙特卡洛比较AI 解读

The powers of several nonparametric tests for the two-sample problem with censored data are compared by simulation. The tests studied include Gehan's, Efron's, and Peto's, and Prentice's generalized Wilcoxon tests, along with the logrank test. The test with the greatest power changes with the sample sizes, censoring mechanism, and distribution of the random variables. The test that performed the best overall was the Peto-Prentice generalized Wilcoxon statistic with an…

序贯概率比检验停止时间的方差与高阶中心矩札记AI 解读

Results are obtained on the limiting distribution and corresponding moment convergence for the (normalized) stopping time of an SPRT, as the boundaries of the continuation region become infinite. These asymptotic results suggest a certain approximation for the variance of the stopping time, which is compared with some Monte Carlo results of Cox and Roseberry (1966) and an approximation due to Ghosh (1969), in the case of testing a normal mean with known variance. The…

位置参数与拟合优度的最小距离估计AI 解读

A weighted Cramér-von Mises distance between the empirical distribution function and the assumed model F0(x - θ) is minimized to produce estimators θ n that are asymptotically normal. If the weight function is taken proportional to (- ln f 0)″/f 0 , then θ n is asymptotically efficient and the minimized distance has the appropriate loss of one degree of freedom. Special attention is focused on the limiting distribution of this latter goodness-of-fit statistic in both null…

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二项分布试验次数的估计方法比较AI 解读

Estimating the number, n, of trials, given a sequence of independent success counts obtained by replicating the n-trial experiment is less studied and a considerably harder problem than estimating p for the binomial distribution. Both the method of moments and the maximum likelihood estimators of n are considered. When p is unknown and small, while n is large, both estimators become highly unstable. Stabilized versions of these estimators are proposed, and their performance…

核型密度估计尺度参数的估计AI 解读

An algorithm is given for estimation of the scaling parameter Λ in the kernel-type density estimate derived from the Fourier integral. A Monte Carlo study of five different densities compares the integrated square error (ISE) for the resulting estimate to the ISE for the Fourier integral estimate (FIE) with mean integrated squared error (MISE) optimal Λ and to the ISE for the normal kernel with asymptotically MISE optimal Λ. The study shows the FIE with estimated Λ compares…

正稳定分布的高效率估计AI 解读

A moment method based on the sample averages of X -t and X -2t (with suitably chosen t) is suggested for estimating the index a and scale parameter c 1/α of the positive stable distribution with Laplace transform E exp(-ΛX) = exp(-cΛα). The corresponding Cramér-Rao lower bounds are computed by using a new and simple Fourier technique, which is based on an idea of Jarrett. It is found that the asymptotic efficiencies of the proposed estimators exceed .97 for all values of α…

未知自回归阶数对预测均方误差的影响（一）AI 解读

Given a realization of T consecutive observations of an autoregressive process, x, of unknown order m, a process of an arbitrary order p is assumed to be fitted for predicting the future values of another process [xtilde](t), where [xtilde](t) is independent of xt but otherwise has identical probabilistic structure. The mean squared error of prediction when the autoregressive coefficients are estimated by least squares is obtained to terms of order T -1. The bias in…

大量时间序列的预测AI 解读

Principles for constructing estimators of the Stein type (shrinkage estimators) are discussed in general terms, with emphasis on underlying assumptions. The problem of parameter estimation and prediction for multiple time series is examined with these principles in mind, particularly for the case in which the number of time series is large and the number of observations from each series is small. Our results are applied to the problem of demand estimation in an inventory…

极值与 Weibull 分布拟合检验的 Kolmogorov 统计量AI 解读

Percentage points are given for the Kolmogorov-Smirnov statistics D +, D -, and D and for the Kuiper statistic V for testing fit to the extreme-value distribution with unknown parameters. The statistics may also be used for tests for the Weibull distribution.

独立指数寿命下 k-out-of-m 系统可靠性估计量的近似均方误差AI 解读

Suppose S is a system with m independent components such that the system functions if and only if at least k components operate. Assume that the component lifetimes are identically exponentially distributed. This work provides simple approximation formulas for the mean squared errors of the minimum variance unbiased and the maximum likelihood estimators of reliability of this system. The performance of the proposed approximation formulas is investigated.

导致似然无界的一类变量变换AI 解读

Hill (1963) proved the existence of paths in the parameter space of the three-parameter lognormal distribution along which the likelihood for any given sample tends to infinity. Lambert (1970) considered a similar phenomenon in the case of the four-parameter lognormal distribution. It is shown that this anomaly is caused by the nature of the variate transformations used and not by the normal distribution itself.

通过潜变量估计实现多指标多原因模型的 EM 方法AI 解读

This article considers both likelihood and Bayesian estimation procedures for a model with multiple indicators and multiple causes of a single unobservable latent variable. The model is complicated by its reduced form, which displays a mixture of econometric and psychometric themes. We avoid this complexity via the estimation of the unobservable latent variable through direct use of the original structural form. This approach not only provides maximum likelihood estimates…

含大值单位的简单随机样本总体总量估计AI 解读

The problem considered is the estimation of the population total of some characteristic from a simple random sample containing a few large or extreme observations. The effect of these large units in the sample is to distort the estimate of the population total. It is therefore important to correct the weights for such units or deflate their values at the estimation stage once they have been sampled and identified as unusually large units. In this paper, three estimators that…

整群抽样数据的回归分析AI 解读

For the case of different regression relationships in different subgroups of a finite population, only part of which are sampled, the extended least squares estimator of any weighted average of the distinct coefficients is derived, under assumptions relating only to the first two moments of the distribution of the coefficients. Under these assumptions, the estimator is shown to be the best linear ξ-unbiased estimator, while under further distributional assumptions, it is…

方差变化曲线与最优再下降型 M 估计量AI 解读

We define the change-of-variance curve (CVC) of location M-estimators in order to investigate the infinitesimal stability of the asymptotic variance. We also construct the so-called hyperbolic tangent estimators, proving their existence and performing certain numerical computations of their defining constants. Their introduction is motivated by a theorem that shows they are the optimally robust redescending M-estimators in the sense of the CVC.

一般 Gauss–Markov 线性模型的约束最小二乘方法AI 解读

The task of estimating the vector of parameters β in the general Gauss-Markov model (y, Xβ, σ2 W) with no restrictions on the design matrix X or the covariance matrix σ2 W is formulated as a constrained linear least squares problem. A BLUE of any estimable function of β is obtained directly by solving this problem. The use of matrix decompositions leads to numerically stable algorithms for computing the solution. The approach is theoretically easy and is shown to be…

含误差成分动态模型的估计AI 解读

Observations on N cross-section units at T time points are used to estimate a simple statistical model involving an autoregressive process with an additive term specific to the unit. Different assumptions about the initial conditions are (a) initial state fixed, (b) initial state random, (c) the unobserved individual effect independent of the unobserved dynamic process with the initial value fixed, and (d) the unobserved individual effect independent of the unobserved…

S 阵列与 Box–Jenkins ARMA 模型识别方法的关系AI 解读

This paper investigates an extension of the partial autocorrelation function, which we call the generalized partial autocorrelation function. These generalized partial autocorrelations, which are not true correlations except when p = 0, are useful in examining the relationship between the S array method of Gray, Kelley, and McIntire (1978) and the Box-Jenkins approach to ARMA model identification. Also, the generalized partial autocorrelation is shown to be a useful model…

预测均方误差估计中的偏差AI 解读

We examine the forecasting problem for a finite series of observations from either a nonseasonal or a seasonal autoregressive-moving average process. Four sources of bias in the usual estimator of forecast mean squared error are identified and analyzed for particular models using maximum likelihood and least squares parameter estimates. The usual estimator is found to be biased downwards, especially near the boundary of a stationary or invertible region, and the bias is…

存在缺失数据时的时间序列模型估计AI 解读

A method is proposed for the estimation of models for discrete time series in the presence of missing data. Some justification is given for the use of this method over alternatives; the choice of estimator is likely to be governed by the pattern of missing data, the nature of the time series model, and computational considerations. The method's performance in estimating simple models is studied by simulations, and it is applied to a time series of pollution levels containing…

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