论文检索

摘要暂缺

可能具有不同方差的正态总体共同均值估计：模拟研究AI 解读

Relative efficiency of estimators of the common mean of possibly different normal populations N(μ, σ i 2) is investigated empirically. A weighted least squares estimator , with weights based on a modification of minimum norm quadratic unbiased (MINQU) estimators of the σ i 2, is found to be substantially more efficient than the maximum likelihood (ML) estimator of μ when the heterogeneity in the σ i , is small to moderate and the number of sample observations from a…

摘要暂缺

摘要暂缺

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…

正态与非正态扰动下联立方程估计量的小样本蒙特卡洛比较AI 解读

In this paper we consider four alternative forms of two-parameter normal and nonnormal error distributions and report on a Monte Carlo study of the small-sample properties of least squares, two-stage least squares, three-stage least squares and full information maximum likelihood estimators. On the basis of 1,000 replications of sample size 20 in two experiments on an overidentified model, we found that the small-sample rankings of econometric estimators of both structural…

用于对称性检验的 Cramér–von Mises 型统计量AI 解读

A Cramér-von Mises-type statistic for testing symmetry, proposed independently by Orlov (1972) and Rothman and Woodroofe (1972), is decomposed into components in the manner of Durbin and Knott (1972); the components are found to be related to Fourier series expansions of the underlying distribution function. Asymptotic power properties of the statistic and its components in testing symmetry about the origin against location shift alternatives when observations have double…

小样本因子模型中似然比统计量的解释AI 解读

The use of the likelihood ratio statistic in testing the goodness of fit of the exploratory factor model has no formal justification when, as is often the case in practice, the usual regularity conditions are not met. In a Monte Carlo experiment it is found that the asymptotic theory seems to be appropriate when the regularity conditions obtain and sample size is at least 30. When the regularity conditions are not satisfied, the asymptotic theory seems to be misleading in…

离散噪声中二项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…

线性回归模型中非正态性的若干大样本检验AI 解读

This study provides conditions under which several well-known and easily computable statistics for testing nonnormality (√b 1, b 2, D, W′, W) can be modified for large-sample use in the classical linear regression framework by replacing the true stochastic error with the least squares residual. Monte Carlo simulations indicate that the modified statistics perform acceptably well even for n = 35. None of the tests clearly dominates the others, although the modified version of…

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…

线性判别分析中实际错误率的分布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.

混合线性模型的多变量方法AI 解读

The usual treatment of the two-way mixed model parallels that of the fixed models, with the usual sums of squares appearing in the F ratios. In this article, we argue in favor of a multivariate approach. We propose a new criterion for testing a general hypothesis under general conditions and offer an expression for the asymptotic expansion of the distribution function.

非线性回归中参数函数的显式估计量AI 解读

Abstract 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…

协方差矩阵与参数向量存在函数关系时的最小二乘估计AI 解读

Estimation for the linear model y = Xβ + e with unknown diagonal covariance matrix G is considered. The diagonal elements of G are assumed to be known functions of the explanatory variables X and an unknown parameter vector Θ, where Θ is permitted to contain elements of β. A weighted joint least squares estimator is developed that is asymptotically equivalent to the maximum likelihood estimator. Asymptotic properties of the simple least squares estimator and of the weighted…

对称性对非对称性的渐近分布无关检验AI 解读

An asymptotically distribution-free procedure is proposed for testing whether a univariate population is symmetric about some unknown value versus a broad class of asymmetric distribution alternatives. The consistency class of the test is discussed and two competing tests are described, one based on the sample skewness, and the other on Gupta's nonparametric procedure. A Monte Carlo study shows that the proposed test is superior to either competitor since it maintains the…

分类程序错误率的一般分布及其在逻辑回归判别中的应用AI 解读

The large-sample distribution of the error rate of an arbitrary estimator of the optimal classification rule is given. The asymptotic distribution of the logistic regression estimator is found. These results are used to show that the efficiency of logistic regression classification in some nonnormal cases is low. This suggests that maximum likelihood discrimination should be used whenever possible.

硬限幅后平稳自回归过程的参数估计AI 解读

Estimates of the parameters in normal autoregressive (AR(p)) processes may be obtained as functions of certain runs and subsequences in the associated clipped 0 − 1 processes. For example, the parameter in AR (1) is a function of the number of 1 runs only. Equivalently, this parameter can be estimated by counting only the number of axis crossings by the process. The estimates are obtained by a modification of the likelihood function of the clipped data. The loss of…

由 M 估计构造近似置信区间的新方法AI 解读

The empirical function used to define M estimates of location is similar to a distribution function when Ψ is nondecreasing. This similarity allows approximate confidence intervals to be constructed from the “percentiles” of the defining function.

两种序列相关检验的稳健性性质AI 解读

We compare Geary's test based on the number of sign changes in residuals with the Durbin-Watson (DW) test for serial correlation. We derive the asymptotic distribution of Geary's statistic for the special case of identically distributed random variables and show that it is asymptotically distribution free for symmetric errors. Monte Carlo simulations show that the DW procedure is generally more powerful and robust than Geary's test.

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…

对若干岭回归方法的批评AI 解读

Ridge estimates seem motivated by a belief that least squares estimates tend to be too large, particularly when there is multicollinearity. The ridge solution is to supplement the data by stochastically shrinking the estimates toward zero. Although flexibility is provided by the abstention from exact exclusion restrictions, ridge regression retains many weaknesses of similarly motivated procedures : a neglect of the basic fact that linear transformations should not change…

惩罚似然密度估计与峰值识别：散射及陨石数据示例AI 解读

The (maximum) penalized-likelihood method of probability density estimation and bump-hunting is improved and exemplified by applications to scattering and chondrite data. We show how the hyperparameter in the method can be satisfactorily estimated by using statistics of goodness of fit. A Fourier expansion is found to be usually more expeditious than a Hermite expansion but a compromise is useful. The best fit to the scattering data has 13 bumps, all of which are evaluated…

出生人数时间序列模型及其结构解释AI 解读

Saboia (1977) has developed a theory relating a particular type of births autoregressive moving average (ARMA) model to the classical deterministic cohort model of population growth. Reexamination of the data used by Saboia indicates that his estimated births models contain common factors and insignificant coefficients and cannot be regarded as evidence in favor of his argument. It is shown, however, that well-known theory on the relationship between deterministic and…