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过度参数化结构模型的渐近理论AI 解读

A theory of overparameterized structural models is presented. In such a model some “redundant” parameters are involved; the parameter vector is not identified, and the information matrix is not nonsingular. The minimum discrepancy function (MDF) test statistic is shown to have an asymptotic chi-squared distribution almost everywhere for a wide class of discrepancy functions. Asymptotic distribution properties of the MDF estimators are investigated. The factor analysis model…

两阶段整群抽样中稳健方差估计的预测方法AI 解读

Robust statistics are derived for estimating the error variance when a finite population total or a ratio of totals is estimated from a two-stage cluster sample in which the first-stage sampling fraction is small. The analysis is based on prediction (superpopulation) models that allow for very general correlation structure within clusters. Results are obtained for when all cluster sizes are known and for when sizes are known only for sample clusters. Ratio, regression, and…

CPS 收入缺失值插补的替代方法AI 解读

The U.S. Bureau of the Census imputes missing income items in the income supplement of the Current Population Survey (CPS) by a technique commonly known as the CPS hot deck. This article compares CPS hot deck imputations of wages and salary amounts with alternatives based on regression models for the logarithm of wages and salary and for the wage rate. Comparisons are effected by comparing imputations with an Internal Revenue Service (IRS) wages and salary amount found by an…

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回归的 Bootstrap 预测区间AI 解读

Bootstrap prediction intervals provide a nonparametric measure of the probable error of forecasts from a standard linear regression model. These intervals approximate the nominal probability content in small samples without requiring specific assumptions about the sampling distribution. Empirical measures of the prediction error rate motivate the choice of these intervals, which are calculated by an application of the bootstrap. The intervals are contrasted to other…

N 个随机有序变量生存函数的极大似然估计AI 解读

Very often distributions will exist that logically should satisfy linear stochastic ordering requirements. For example, if a mechanical device is improved through N stages, the corresponding survival functions should be linearly stochastically ordered. Nevertheless, estimates may not totally reflect this stochastic ordering because of the inherent variability of the observations. Here we characterize the maximum likelihood estimates of the survival functions subject to…

潜在群体效应的估计AI 解读

Conventional methods of multivariate normal analysis do not apply when the variables of interest are not observed directly but must be inferred from fallible or incomplete data. A method of estimating such effects by marginal maximum likelihood, implemented by means of an EM algorithm, is proposed. Asymptotic standard errors and likelihood ratio tests of fit are provided. The procedures are illustrated with data from the administration of the Armed Services Vocational…

多个 2×2 列联表共同优势比精确置信区间的计算AI 解读

A quadratic time network algorithm is provided for computing an exact confidence interval for the common odds ratio in several 2×2 independent contingency tables. The algorithm is shown to be a considerable improvement on an existing algorithm developed by Thomas (1975), which relies on exhaustive enumeration. Problems that would formerly have consumed several CPU hours can now be solved in a few CPU seconds. The algorithm can easily handle sparse data sets where asymptotic…

误设自回归时间序列模型中预测量的性质AI 解读

This article investigates major effects of misspecification in stationary linear time series models when we fit a pth-order autoregressive model. The true model can be an autoregressive moving average model. We derive the formulas of bias and mean squared error (MSE) of the least squares estimator and the hth period ahead prediction MSE in the time domain. Contrary to previous studies, the process in estimation is not necessarily independent of the process in prediction, and…

谱估计的数据驱动选择：拓展交叉验证方法的适用范围AI 解读

I develop methods of objectively choosing a spectrum estimate from a general class C of available estimates. C can, for example, simultaneously include Blackman—Tukey and autoregressive estimates, so the statistician no longer needs to choose one type or the other arbitrarily. The methods work by extending the applicability of existing cross-validatory techniques through the introduction of generalized leave-out-one spectrum estimates. As special cases, I obtain new…

最小二乘与误差变量回归的比较：聚焦随机化协方差分析AI 解读

In an errors-in-variables regression model, the least squares estimate is generally inconsistent for the complete regression parameter but can be consistent for certain linear combinations of this parameter. We explore the conjecture that, when the least squares estimate is consistent for a linear combination of the regression parameter, it will be preferred to an errors-in-variables estimate, at least asymptotically. The conjecture is false, in general, but it is true for…

Hausman、Ramsey 与 Chow 设定检验之间的关系AI 解读

This article describes a relationship between the tests for specification error in regression models introduced by Ramsey (1969) and Hausman (1978). It also shows that the Chow (1960) test for structural shift can be viewed as a special case of specification error tests. This article shows the common structure of these tests. The common basis is the comparison of alternative estimators of regression coefficients. Under the null hypothesis, one estimator is efficient and…

复相关系数某一特定函数的估计AI 解读

Let R denote the sample multiple correlation coefficient formed from a sample from a normal distribution with population multiple correlation coefficient . This article considers the problem of estimating the parameter using quadratic loss. The best unbiased estimate of θ is a linear function of Y = R 2/(1 − R 2); it is shown that this is dominated by other linear estimates and that these, in turn, are dominated by nonlinear estimates. A Monte Carlo study indicates that such…

多阶段整群抽样中有限总体参数的贝叶斯推断AI 解读

Assuming a model appropriate for many multistage sample surveys, Bayesian predictive inference for a general linear function, ω, of the finite population elements is described. In a broad class of linear estimators of ω, the posterior mean, E″(ω), of ω is shown to have the optimal frequentist property of minimal bounded mean squared error. For the special case of three-stage sampling, E″(ω) is described in detail. Also presented are the results of an investigation of the…

抗异常值直线及相关回归方法AI 解读

In a bivariate (x, y) scatterplot the three-group resistant line is that line for which the median residual in each outer third of the data (ordered on x) is zero. It was proposed by Tukey as an exploratory method resistant to outliers in x and y and suited to hand calculation. A dual plot representation of the procedure yields a fast, convergent algorithm, nonparametric confidence intervals for the slope, consistency, influence function, and asymptotic normality results.…

通过局部极小极大均方误差构造有界影响回归AI 解读

The class of “general” M-estimators for the stochastic linear regression model is considered, and influence and change-of-variance functions are used to approximate the main term of the mean squared error (MSE). The estimator is then found in the class that minimizes the maximum of that approximate MSE over the ϵ-contamination neighborhood. This approach allows for additional flexibility of designing estimators optimal for prediction in specific regions of the factor space,…

分位数函数的平滑非参数估计AI 解读

A smooth alternative to the conventional sample quantile function as a nonparametric estimator of a population quantile function is proposed. The proposed estimator is essentially a kernel type of estimator and has the same asymptotic distribution as the conventional sample quantile. The mean squared convergence rate of the proposed estimator is also estimated. Monte Carlo studies are conducted to compare the proposed estimator with the sample quantile and the estimator…

非参数逐步多重比较程序AI 解读

Nonparametric multiple comparisons are discussed, with particular emphasis given to stepwise procedures. Nonparametric analogs of the stepwise all-subset procedure of Einot and Gabriel are presented, along with an ad hoc nonparametric analog of the Newman—Keuls procedure. These new procedures are compared among themselves and with nonstepwise procedures based on Type I error levels and comparisonwise power. It is shown that these stepwise nonparametric procedures control…

二元响应数据的高效序贯设计AI 解读

A class of sequential designs for estimating the percentiles of a quantal response curve is proposed. Its updating rule is based on an efficient summary of all of the data available via a parametric model. The logit-MLE version of the proposed designs can be viewed as a natural analog of the Robbins—Monro procedure in the case of binary data. It is shown to be asymptotically consistent, optimal, and nonparametric via its connection with the latter procedure. For certain…

卡方拟合优度检验中的分组数选择AI 解读

The power of Pearson chi-squared and likelihood ratio goodness-of-fit tests based on different partitions is studied by considering families of densities “between” the null density and fixed alternative densities. For sample sizes n → ∞, local asymptotic theory with respect to the number of classes k is developed for such families. Simple sufficient and almost necessary conditions are derived under which it is asymptotically optimal to let k tend to infinity with n. A…

不连续分布下 Kolmogorov 型拟合优度检验的精确功效AI 解读

Goodness-of-fit tests of Kolmogorov type reject a null hypothesis H 0 : F(x) = F*(x) whenever the graph of the sample cumulative distribution function crosses one of two boundary functions, G 1(x), G 2(x). The best-known example of a test of this type is the Kolmogorov—Smirnov test D. When the true cumulative distribution function F(x) is continuous, a number of algorithms are available for calculating the exact powers of such tests. In this article it is shown that such…