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使用迭代自助法对广义基尼指数进行推断AI 解读

Inference using the iterated-bootstrap method proposed by Hall is appealing for cases in which the percentile method needs to be used but the nominal level of a confidence interval has to be adjusted. One natural application is for generalized Gini indices of income inequality. When applying these theoretical inequality measures directly to sample data for the purpose of statistical inference, economists must come up with some measure of sampling variation. This is…

非高斯观测的状态空间时间序列分析：经典与贝叶斯视角AI 解读

Summary The analysis of non-Gaussian time series by using state space models is considered from both classical and Bayesian perspectives. The treatment in both cases is based on simulation using importance sampling and antithetic variables; Markov chain Monte Carlo methods are not employed. Non-Gaussian disturbances for the state equation as well as for the observation equation are considered. Methods for estimating conditional and posterior means of functions of the state…

一般条件下的两样本分位数检验AI 解读

A simple, nonparametric two-sample test for equality of a given collection of quantiles is developed which can be applied to a variety of empirical distribution functions, including the Kaplan-Meier estimator, a self-consistent estimator for doubly-censored data and an estimator for repeated measures data. The null hypothesis tested is that the quantiles are equal but other aspects of the distributions may differ between the two samples. This procedure can also be applied to…

分位数回归的拟合优度及相关推断过程AI 解读

We introduce a goodness-of-fit process for quantile regression analogous to the conventional R2 statistic of least squares regression. Several related inference processes designed to test composite hypotheses about the combined effect of several covariates over an entire range of conditional quantile functions are also formulated. The asymptotic behavior of the inference processes is shown to be closely related to earlier p-sample goodness-of-fit theory involving Bessel…

删失回归模型中的尾部信息迁移AI 解读

Consider a heteroscedastic regression model $Y = m(X) + \sigma(X)\varepsilon$, where the functions $m$ and $\sigma$ are “smooth,” and $\varepsilon$ is independent of $X$. The response variable $Y$ is subject to random censoring, but it is assumed that there exists a region of the covariate $X$ where the censoring of $Y$ is “light.” Under this condition, it is shown that the assumed nonparametric regression model can be used to transfer tail information from regions of light…

允许零支付意愿的二元选择条件估值模型AI 解读

Dichotomous-choice contingent-valuation data are modeled using a mixture distribution. The standard parametric survival model is modified such that respondents in the lowest willingness-to-pay category may have either zero willingness to pay or a small positive willingness to pay. In comparison to the standard model, the mixture model leads to a dramatic reduction in estimates of mean willingness to pay. Covariates such as income are found to be more significant in…

杂论：分位数估计与马尔可夫链蒙特卡洛收敛AI 解读

In this paper we examine the method of Raftery & Lewis (1992) for estimating the convergence of Markov chain Monte Carlo, samplers when functionals of interest are in the form of parameter quantiles. Although popular, the method is commonly mis-applied to problems where quantiles are not of primary interest. We show how the method can be misleading in this case, and that it can seriously underestimate the true length of the burn-in. We provide a number of examples, comparing…

分位数比较函数的半参数推断及其在受试者工作特征曲线中的应用AI 解读

In studies to compare two samples, more information may be available on one treatment than the other. When one population is modelled parametrically and the other nonparmetrically, we study large sample properties of a semiparametric sample quantile comparison function and show that it can have substantially smaller asymptotic variance than its nonparametric counterpart, especially near the boundaries. We describe applications to both two-sample tests and receiver operating…

次序统计量之差与学生化样本分位数的鞍点近似AI 解读

Summary For a sample from a given distribution the difference of two order statistics and the Studentized quantile are statistics whose distribution is needed to obtain tests and confidence intervals for quantiles and quantile differences. This paper gives saddlepoint approximations for densities and saddlepoint approximations of the Lugannani–Rice form for tail probabilities of these statistics. The relative errors of the approximations are n −1 uniformly in a neighbourhood…

协整似然比检验的数值分布函数AI 解读

This paper employs response surface regressions based on simulation experiments to calculate asymptotic distribution functions for the Johansen-type likelihood ratio tests for cointegration. These are carried out in the context of the models recently proposed by Pesaran, Shin, and Smith (1997) that allow for the possibility of exogenous variables integrated of order one. The paper calculates critical values that are very much more accurate than those available previously.…

基于自回归秩得分的自回归模型最优检验AI 解读

Locally asymptotically optimal tests based on autoregression rank scores are constructed for testing linear constraints on the structural parameters of AR processes. Such tests are asymptotically distribution free and do not require the estimation of nuisance parameters. They constitute robust, flexible and quite powerful alternatives to existing methods such as the classical correlogram-based parametric tests, the Gaussian Lagrange multiplier tests, the optimal non-Gaussian…

基于经验似然的多重分位数图置信管AI 解读

The nonparametric empirical likelihood approach is used to obtain simultaneous confidence tubes for multiple quantile plots based on $k$ independent (possibly right-censored) samples. These tubes are asymptotically distribution free, except when both $k \geq 3$ and censoring is present. Pointwise versions of the confidence tubes, however, are asymptotically distribution free in all cases. The various confidence tubes are valid under minimal conditions. The proposed methods…

高维中的集中性与拟合优度：渐近分布无关方法AI 解读

A novel approach for constructing goodness-of-fit techniques in arbitrary finite dimensions is presented. Testing problems are considered as well as the construction of diagnostic plots. The approach is based on some new notions of mass concentration, and in fact, our basic testing problems are formulated as problems of ‘‘goodness-of-concentration.’’ It is this connection to concentration of measure that makes the approach conceptually simple. The presented test statistics…

基于经验似然比的混合比例置信区间AI 解读

We consider the problem of estimating a mixture proportion using data from two different distributions as well as from a mixture of them. Under the model assumption that the log-likelihood ratio of the two densities is linear in the observations, we develop an empirical likelihood ratio based statistic for constructing confidence intervals for the mixture proportion. Under some regularity conditions, it is shown that this statistic converges to a chi-squared random variable.…

基于 L₂-Wasserstein 距离的拟合优度检验AI 解读

We consider the Wasserstein distance between a sample distribution and the set of normal distributions as a measure of nonnormality. By considering the standardized version of this distance we obtain a version of Shapiro–Wilk’s test of normality. The asymptotic behavior of the statistic is studied using approximations of the quantile process by Brownian bridges. This method differs from the “ad hoc” method of de Wet and Venter and permits a similar analysis for testing other…

从当前居住时长推断家庭总居住时长的分布AI 解读

Estimates of households' expected duration of residence are important to private and public decisionmakers. The common methods of estimation have been shown to be unreliable. This article presents a measurement framework for estimating total time of residence using five large sets of published government census data on the housing market. By developing a moving-behavior model, the distribution of total residence duration can be estimated from the census data on the age of…

双典型相关分析中的秩似然比检验AI 解读

The likelihood-ratio test for the hypothesis that the smallest of two canonical correlations is zero is Bartlett adjustable. This theoretical property says that the moments of the test criterion and of a scaled version of the asymptotic distribution have the same second-order expansion. Simulations show that scaling with the exact expectation improves the asymptotic distribution, but the expectation is approximated poorly by its second-order expansion. This can be explained…

洛伦兹曲线排序的统计推断AI 解读

In this paper we consider the issue of performing statistical inference for Lorenz curve orderings. This involves testing for an ordered relationship in a multivariate context and making comparisons among more than two population distributions. Our approach is to frame the hypotheses of interest as sets of linear inequality constraints on the vector of Lorenz curve ordinates, and apply order-restricted statistical inference to derive test statistics and their sampling…

三条及以上回归直线所有对比的精确置信界AI 解读

It is desired to compare κ ≥ 3 treatments. Under the assumption of iid normal errors, it is well known that the Scheffé method produces exact simultaneous confidence bounds for all contrasts of the treatment means. Furthermore, it is known that the Scheffé method is conservative when one desires confidence bounds for a specific subset of contrasts of means. Exact methods, such as those due to Tukey and Dunnett, yield tighter bounds than the Scheffé method for specific…

回归深度AI 解读

In this article we introduce a notion of depth in the regression setting. It provides the “rank” of any line (plane), rather than ranks of observations or residuals. In simple regression we can compute the depth of any line by a fast algorithm. For any bivariate dataset Z n of size n there exists a line with depth at least n/3. The largest depth in Z n can be used as a measure of linearity versus convexity. In both simple and multiple regression we introduce the deepest…

重尾实用指南：统计技术与应用AI 解读

Part 1 Applications: heavy tailed probability distributions in the World Wide Web, M.E. Crovella et al self-similarity and heavy tails - structural modelling of network traffic, W. Willinger et al heavy tails in high-frequency financial data, U.A. Muller et al stable paretian modelling in finance - some empirical and theoretical aspects, S. Mittnik et al risk management and quantile estimation, F. Bassi et al. Part 2 Time series: analyzing stable time series, R.J. Adler et…

三条及以上回归直线所有对比的精确置信界AI 解读

It is desired to compare κ ≥ 3 treatments. Under the assumption of iid normal errors, it is well known that the Scheffé method produces exact simultaneous confidence bounds for all contrasts of the treatment means. Furthermore, it is known that the Scheffé method is conservative when one desires confidence bounds for a specific subset of contrasts of means. Exact methods, such as those due to Tukey and Dunnett, yield tighter bounds than the Scheffé method for specific…

稀有事件概率的估计AI 解读

Let $(X_{1},Y_{1}), (X_{2},Y_{2}),\dots,(X_{n},Y_{n})$ be a random sample from a bivariate distribution function $F$ which is in the domain of attraction of a bivariate extreme value distribution function $G$. A subset $C$ of $\mathbb{R}^{2}$ is given, which contains none of the observations. We shall give an asymptotic confidence interval for $\Pr((X_{i},Y_{i}) \in C)$ under certain conditions.