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非线性联立系统中基于残差的预测与估计程序AI 解读

This paper proposes the residual-based stochastic predictor as an alternative procedure for obtaining forecasts with a static nonlinear econometric model. This procedure modifies the usual Monte Carlo approach to stochastic simulations of the model in that calculated residuals over the sample period are used as proxies for disturbances instead of random draws from some assumed parametric distribution. In compar-ison with the Monte Carlo predictor, the residual-based should…

事件的估计AI 解读

The problem of estimating an event, having positive probability content, based on a sample of $n$ observations is considered. A natural metric is shown to exist on the space of possible values for the event. This leads to the definition of optimal estimators. We derive optimal estimators for events which correspond to quantiles for the univariate exponential model. Further optimal estimators are derived for the events bounded by the ellipsoidal contours of the density…

样本谱分布泛函的极限行为AI 解读

The parameters of a stationary process can be viewed as functions of the spectral distribution function. This work concerns (estimators) parameters defined as integrals of $m (\geq 1)$-dimensional kernel functions with respect to the (sample) spectral distribution function. Conditions for asymptotic normality, almost sure convergence, and probability one bounds are derived for such estimators. The approach taken is based upon the reduction of an $m$-dimensional problem to…

位置参数R估计量的极小极大性质AI 解读

Consider the problem of estimating the unknown location parameter $\theta$ based on a random sample from $F(x - \theta)$, where $F$ is an unknown member of the class of distribution functions $\mathscr{F} = \{F: F$ is symmetric about 0 and $\sup_x |F(x) - \Phi(x)| \leq \varepsilon\}$, where $\Phi$ denotes the standard normal distribution function. Huber (1964) showed that $M$-estimation has a minimax property for this model, whereas Sacks and Ylvisaker (1972) showed that $L$-…

摘要暂缺

分布不连续与缺失个体：最低工资与失业青年AI 解读

The effects of minimum wage legislation on the employment and wage rates of youth are estimated using a new statistical approach.We find that without the minimum, not only would the percent of out-of-school youth who are employed be 4 to 6 percent higher than it is, but also that these youth would earn more.In particular, the expected hourly earnings of youth with market wage rates below the 1978 minimum are 10 percent lower with the minimum than they would be without…

基于洛伦兹曲线与收入份额的分布无关统计推断AI 解读

The paper considers the problem of statistical inference with estimated Lorenz curves and income shares. The full variance-covariance structure of the (asymptotic) normal distribution of a vector of Lorenz curve ordinates is derived and shown to depend only on conditional first and second moments that can be estimated consistently without prior specification of the population density underlying the sample data. Lorenz curves and income shares can thus be used as tools for…

分布函数的正交级数估计及其应用AI 解读

SUMMARY Motivated by applications to the non-parametric estimation of mixture proportions, we develop techniques for multivariate orthogonal series estimation of distribution functions. We approximate the empiric distribution function, rather than the true distribution function. This enables us to use trigonometric series methods to estimate distribution functions with unbounded support.

混合比例的最小距离非参数估计AI 解读

SUMMARY Hall (1981a) develops a method of estimating mixture proportions using empirical distribution functions and a distance measure. A similar approach is suggested here based on density estimates. The method is applicable to general discrete data and multivariate data as well as to univariate continuous data and to ordered categorical data. For convenient quadratic distance measures the asymptotic theory is developed and remarks are made about practical implementation.…

准线性均值的推广：收入不平等度量与解决阿莱悖论的决策理论应用AI 解读

Chew Soo Hong, A Generalization of the Quasilinear Mean with Applications to the Measurement of Income Inequality and Decision Theory Resolving the Allais Paradox, Econometrica, Vol. 51, No. 4 (Jul., 1983), pp. 1065-1092

Ferguson 分布函数贝叶斯估计量的稳健性AI 解读

We derive an explicit expression for the Bayes risk (using weighted squared error loss) of Dalal's Bayes estimator of a symmetric distribution under a $\mathscr{G}$-invariant Dirichlet process prior. We compare this risk to the risk of Ferguson's estimator of an arbitrary distribution under the $\mathscr{G}$-invariant prior. This enables us to (i) assess the savings in risk attained by incorporating known symmetry structure in the model and (ii) provide information about the…

原假设下简单线性秩统计量的Edgeworth展开AI 解读

An Edgeworth expansion with remainder $o(N^{-1})$ is established for simple linear rank statistics under the null-hypothesis. The theorem is proved for a wide class of scores generating functions which includes the normal quantile function.

用 Sheffer 多项式计算 Takacs 拟合优度分布AI 解读

How often does the empirical distribution pass over an acceptance band around the hypothetical distribution function? Sheffer polynomials are applied to derive the exact distribution of this goodness-of-fit distribution and its two-sample analogue. This method leads to new proofs and extensions of Takacs's (1971) results.

经验分布正则泛函的分布与分位数展开及非参数置信区间AI 解读

Let $T(\cdot)$ be a suitably regular functional on the space of distribution functions, $F$, on $R^s$. A method is given for obtaining the derivatives of $T$ at $F$. This is used to obtain asymptotic expansions for the distribution and quantiles of $T(F_n)$ where $F_n$ is the empirical distribution of a random sample of size $n$ from a distribution $F$ with an absolutely continuous component. One- and two-sided confidence intervals for $T(F)$ are given of level $1 - \alpha + O(n^{-j/2})$…

利用核函数平滑计数过程强度AI 解读

The kernel function method developed during the last twenty-five years to estimate a probability density function essentially is a way of smoothing the empirical distribution function. This paper shows how one can generalize this method to estimate counting process intensities using kernel functions to smooth the nonparametric Nelson estimator for the cumulative intensity. The properties of the estimator for the intensity itself are investigated, and uniform consistency and…

二元选择模型的分布无关极大似然估计量AI 解读

is a given function of the exogenous variables z and unknown parameters 9, representing the systematic component of the utility difference, and F is the distribution function of the random component of the utility difference. This paper describes a method of estimating the parameters 9 without assuming any functional form for the distribution function F, and proves that this estimator is consistent. F is also consistently estimated. The method uses maximum likelihood…

收入分布模型的若干抽样性质AI 解读

A recently proposed model for describing the distribution of income over a population, based on the Burr distribution, has been shown to fit better than the commonly used lognormal or gamma distributions. The current article extends that analysis by deriving the large-sample properties of the maximum likelihood estimates for this three-parameter model. Consequently, resulting confidence intervals for some measures of income inequality (including the Gini index) are used to…

最近邻拟合优度检验的无限维近似AI 解读

Let $X_1, \cdots, X_n$ be i.i.d. $\mathbb{R}^m$-valued observations from a bounded density $g(x)$ continuous on its support. Let $W_i = \exp\{- ng(X_i)V(R_i)\}, i = 1, \cdots, n$, where $V(R_i)$ is the volume of the nearest neighbor sphere around $X_i$, and let $w(x)$ be any bounded continuous weight function on $\mathbb{R}^m$. An infinite-dimensional approximation to the asymptotic form of the weighted empirical distribution function of the $W_i$'s is presented. The…

基于最近邻统计量加权经验分布的多维拟合优度检验AI 解读

Let $X_1, \cdots, X_n$ be a random sample in $\mathbb{R}^m$ from an unknown density $f(x)$. Recently Bickel and Breiman have introduced a goodness of fit test for this situation based on the empirical distribution function of the variables $W_i = \exp\{-ng(X_i)V(R_i)\}, i = 1, \cdots, n$, where $g(x)$ is the hypothesized density and $V(R_i)$ represents the volume of the nearest neighbor sphere centered at $X_i$. Under the null hypothesis $H : f(x) = g(x)$, the empirical…

摘要暂缺

Logit生物测定中极端分位数的估计AI 解读

Suppose that we administer a low dose of a drug and if no response is observed, increase this dose by a fixed amount which is administered to a second experimental subject. This procedure continues until, at some dose level, a response is finally observed. This whole sequence may be repeated. We investigate the features of an experimental design of this kind for estimating the dose at which the expected response is small. This design is highly efficient when the number of…

空间模式的非参数最大似然估计AI 解读

Let $\mathbf{X}$ be an absolutely continuous random variable in $\mathbb{R}^k$ with distribution function $F(\mathbf{x})$ and density $f(\mathbf{x})$. Let $\mathbf{X}_1, \cdots, \mathbf{X}_n$ be independent random variables distributed according to $F$. Mapping the spatial distribution of $\mathbf{X}$ normally entails drawing a map of the isopleths, or level curves, of $f$. In this paper, it is shown how to map the isopleths of $f$ nonparametrically according to the…

更新过程中的非参数估计AI 解读

Data collected from many independent identically distributed renewal processes, each of which is observed for an arbitrary period of time, is usually affected by censoring coupled with length biased sampling. In this paper we derive an algorithm that produces the nonparametric maximum likelihood estimator (i.e., the analog of the single-sample empirical distribution function) of the common lifetime distribution, based on such data.

分布对称性的检验AI 解读

Tests for symmetry of a distribution function about an unknown value are investigated. The asymptotic distributions under symmetry as well as under near alternatives are given for two kinds of tests: trimmed Wilcoxon tests and tests based on gaps. It turns out that these procedures have a good stability of level under unimodal densities. In a special case (skewness to the left) the efficacies have been calculated. Monte Carlo results are also given.