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分位数回归估计量的 BootstrapAI 解读

The asymptotic variance matrix of the quantile regression estimator depends on the density of the error. For both deterministic and random regressors, the bootstrap distribution is shown to converge weakly to the limit distribution of the quantile regression estimator in probability. Thus, the confidence intervals constructed by the bootstrap percentile method have asymptotically correct coverage probabilities.

分位数回归、Box–Cox 变换模型与美国工资结构：1963—1987年AI 解读

This study examines changes in the increments (‘returns’) to education and experience at different points of the wage distribution. It also examines changes in within-group wage inequality. Newly developed quantile regression techniques are applied to the Box-Cox transformation model using the Current Population Survey data. The increments differ, but they changed in similar pattern at different points of the wage distribution. They are larger at the low end of the…

依赖数据自助法的分块选择规则AI 解读

SUMMARY: We address the issue of optimal block choice in applications of the block bootstrap to dependent data. It is shown that optimal block size depends significantly on context, being equal to n1/3, n1/4 and n1/5 in the cases of variance or bias estimation, estimation of a onesided distribution function, and estimation of a two-sided distribution function, respectively. A clear intuitive explanation of this phenomenon is given, together with outlines of theoretical…

双参数指数族后验分布的可积展开AI 解读

Asymptotic expansions of posterior distributions are derived for a two-dimensional exponential family, which includes normal, gamma, inverse gamma and inverse Gaussian distributions. Reparameterization allows us to use a data-dependent transformation, convert the likelihood function to the two-dimensional standard normal density and apply a version of Stein's identity to assess the posterior distributions. Applications are given to characterize optimal noninformative priors…

通过逐次替代抽样进行不完整数据的贝叶斯非参数估计AI 解读

In the problem of estimating an unknown distribution function $F$ in the presence of censoring, one can use a nonparametric estimator such as the Kaplan-Meier estimator, or one can consider parametric modeling. There are many situations where physical reasons indicate that a certain parametric model holds approximately. In these cases a nonparametric estimator may be very inefficient relative to a parametric estimator. On the other hand, if the parametric model is only a…

生存数据中的充分随访与异常值检验AI 解读

A situation in which a sample of failure times with many of the largest times censored may be taken as evidence of a proportion of “immune” or “cured” individuals, who are not subject to failure, in the population. A plot of the Kaplan-Meier empirical distribution function for such data will tend to level off near its right extreme, provided that follow-up of individuals has been continued for long enough. This article develops a diagnostic test for sufficient follow-up in…

Cox模型中若干Bootstrap置信区间的比较AI 解读

We study bootstrap confidence intervals for three types of parameters in Cox's proportional hazards model: the regression parameter, the survival function at fixed time points, and the median survival time at fixed values of a covariate. Several types of bootstrap confidence intervals are studied, and the type of interval is determined by two factors. One factor is the method of drawing the bootstrap sample. We consider three such methods: (1) ordinary resampling from the…

两个分布的二阶随机占优检验AI 解读

A distribution function F is said to stochastically dominate another distribution function G in the second-order sense if , for all x . Second-order stochastic dominance plays an important role in economics, finance, and accounting. Here a statistical test has been constructed to test , for some x ∈ [ a , b ], against the hypothesis , for all x ∈ [ a , b ], where a and b are any two real numbers. The test has been shown to be consistent and has an upper bound α on the…

三参数 Weibull 分布的估计与拟合检验AI 解读

SUMMARY Estimation techniques are given for the three-parameter Weibull distribution, with all parameters unknown. Tables are given for the empirical distribution function statistics W 2, U 2 and A 2, for testing for the distribution.

GI/G/1 队列平稳等待时间分布函数的非参数估计AI 解读

The $GI/G/1$ queueing model is regarded as a functional that maps the service and interarrival time distribution functions onto the stationary waiting time distribution function. By considering the output of the functional when it is applied to nonparametric estimators of the input distribution functions, we obtain a nonparametric estimator of the stationary waiting time distribution function. Using appropriate continuity and differentiability properties of the functional,…

右删失两样本问题中位移函数的推断及应用AI 解读

For two distribution functions, F and G, the shift function is defined by Δ(t) = G −1 · F(t) - t. The shift function is the distance from the 45° line and the quantity plotted in Q-Q plots. In the analysis of lifetime data, A represents the difference between two treatments. The shift function can also be used to find crossing points of two distribution functions. The large-sample distribution theory for estimates of Δ is studied for right-censored data. It turns out that…

右删失两样本问题中位移函数的推断及应用AI 解读

For two distribution functions, F and G, the shift function is defined by Δ(t) = G −1 · F(t) - t. The shift function is the distance from the 45° line and the quantity plotted in Q-Q plots. In the analysis of lifetime data, A represents the difference between two treatments. The shift function can also be used to find crossing points of two distribution functions. The large-sample distribution theory for estimates of Δ is studied for right-censored data. It turns out that…

以平稳性为原假设的残差检验及美国宏观时间序列应用AI 解读

This paper proposes residual-based tests for the null of level- and trend-stationarity, which are analogs of the LM test for an MA unit root. Asymptotic distributions of the tests are nonstandard, but they are expressed in a unified manner by expressing stochastic integrals. In addition, the tests are shown to be consistent. By expressing the distributions expressed as a function of a chi-square variable with one degree of freedom, the exact limiting probability density and…

多元 M 估计量的经验鞍点近似AI 解读

SUMMARY In this paper, we investigate the use of the empirical distribution function in place of the underlying distribution function F to construct an empirical saddlepoint approximation to the density fn of a general multivariate M-estimator. We obtain an explicit form for the error term in the approximation, investigate the effect of renormalizing the estimator, carry out some numerical comparisons and discuss the regression problem.

极化的测量AI 解读

Suppose that the authors are interested in the distribution of a set of characteristics over a population. They study a precise sense in which this distribution can be said to be polarized and provide a theory of measurement. Polarization, as conceptualized here, is closely related to the generation of social tensions, to the possibilities of revolution and revolt, and to the existence of social unrest in general. The authors take special care to distinguish their theory…

带移入的临界分枝过程中 Bootstrap 的无效性AI 解读

This article considers a case of parametric bootstrap when the observations consist of generation sizes of the branching process with immigration together with the immigration component of each generation. Suppose we estimate the offspring mean $m$ by the maximum likelihood estimator (m.l.e.). It is then shown that the bootstrap version of the standardized m.l.e. does not have the same limiting distribution as the standardized m.l.e., under the assumption that $m = 1$ (critic…

复杂调查抽样中的 L 统计量AI 解读

We study linear combinations of order statistics ($L$-statistics) in survey problems with a stratified multistage sampling design. Two general types of $L$-statistics are considered: smooth $L$-statistics with weights generated by a smooth function and nonsmooth $L$-statistics (sample quantiles). The trimmed sample mean, the decile mean and variance, the sample Lorenz curve and the sample Gini's family parameters are examples of smooth $L$-statistics or functions of smooth $L$…

通过最小化平均绝对偏差估计曲线及其含义AI 解读

The local median regression method has long been known as a robustified alternative to methods such as local mean regression. Yet, its optimal statistical properties are largely unknown. In this paper, we show via decision-theoretic arguments that a local weighted median estimator is the best least absolute deviation estimator in an asymptotic minimax sense, under $L_1$-loss. We also study asymptotic efficiency of the local median estimator in the class of all possible…

利用 Gibbs 抽样进行指数族近似条件推断AI 解读

This article presents the Gibbs-Skovgaard algorithm for approximate frequentist inference. The method makes use of the double saddlepoint approximation of Skovgaard to the conditional cumulative distribution function of a sufficient statistic given the remaining sufficient statistics. This approximation is then used in the Gibbs sampler to generate a Markov chain. The equilibrium distribution of this chain approximates the joint distribution of the sufficient statistics…

基于枢轴估计函数的重抽样方法AI 解读

Suppose that, under a semiparametric model setting, one is interested in drawing inferences about a finite-dimensional parameter vector β based on an estimating function. Generally a consistent point estimator β^ for βo, the true value for β, can be easily obtained by finding a root of the corresponding estimating equation. To estimate the variance of β^, however, may involve complicated and subjective nonparametric functional estimates. In this paper, a general and simple…

基于核方法的参数密度拟合优度检验AI 解读

Let F denote a distribution function defined on the probability space (Ω, , P ), which is absolutely continuous with respect to the Lebesgue measure in R d with probability density function f . Let f 0 (·,β) be a parametric density function that depends on an unknown p × 1 vector β. In this paper, we consider tests of the goodness-of-fit of f 0 (·,β) for f (·) for some β based on (i) the integrated squared difference between a kernel estimate of f (·) and the quasimaximum…

单位根与协整检验的近似渐近分布函数AI 解读

Monte Carlo experiments and response surface regressions are used to calculate approximate asymptotic distribution functions for a number of well-known unit root and cointegration test statistics. These allow empirical workers to calculate approximate P values for these tests. The results of the paper are based on an extensive set of Monte Carlo experiments, which yield finite-sample quantiles for several sample sizes. Response surface regressions are then used to obtain…

利用一阶累积特征识别非线性时间序列AI 解读

A new approach to the problem of identifying a nonlinear time series model is considered. We argue that cumulative lagged conditional mean and variance functions are the appropriate "signatures" of a nonlinear time series for the purpose of model identification, being analogous to cumulative distribution functions or cumulative hazard functions in iid models. We introduce estimators of the cumulative lagged conditional mean and variance functions and study their asymptotic…

异方差回归模型的拟合AI 解读

In heteroscedastic regression models assumptions about the error distribution determine the method of consistent estimation of parameters. For example, consider the case where the model specifies the regression and dispersion functions for the data but robustness is of concern and one wishes to use least absolute error regressions. Except in certain special circumstances, parameter estimates obtained in this way are inconsistent. In this article we expand the heteroscedastic…