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基于曲线长度的拟合优度检验AI 解读

The length of the graph of an estimate of the distribution function is used as a measure of goodness of fit. The asymptotic theory of tests which are based on such a measure is studied and, in addition, tables of critical values for these tests are given. In the context of time series analysis, the proposed test rejects the null hypothesis of white noise whenever the length of the linearly interpolated cumulative periodogram, or of some smoothed version of it, is too large.

计量经济估计量的Imhof分布近似AI 解读

The article develops new approximations to the distribution function of a general econometric estimator or test statistic from a linear model. The method relies heavily on the general arguments for the validity of Edgeworth approximations, and produces formulae of a similar type, except that, instead of using the cumulative normal distribution, an Imhof distribution is used derived from the exact distribution of a linear combination of the sample data second moments. On…

L-矩：利用次序统计量的线性组合分析与估计分布AI 解读

SUMMARY L-moments are expectations of certain linear combinations of order statistics. They can be defined for any random variable whose mean exists and form the basis of a general theory which covers the summarization and description of theoretical probability distributions, the summarization and description of observed data samples, estimation of parameters and quantiles of probability distributions, and hypothesis tests for probability distributions. The theory involves…

基于贝塔过程的生命历程数据非参数贝叶斯估计AI 解读

Several authors have constructed nonparametric Bayes estimators for a cumulative distribution function based on (possibly right-censored) data. The prior distributions have, for example, been Dirichlet processes or, more generally, processes neutral to the right. The present article studies the related problem of finding Bayes estimators for cumulative hazard rates and related quantities, w.r.t. prior distributions that correspond to cumulative hazard rate processes with…

广类平稳、可能具有无限方差的线性过程经验分位数的 Bahadur 型表示AI 解读

Bahadur has obtained an asymptotic almost sure representation for empirical quantiles of independent and identically distributed random variables. In this paper we present an analogous result for a large class of stationary linear processes.

离子通道的更新理论性质AI 解读

The membranes of cells, such as those found in heart and nerve tissue, contain structures known as ion channels. The current produced by an ion channel in a cell membrane has been modelled as a finite state-space Markov process. Statistical analysis of ion channels has been largely limited to the case where a single channel is observed, or where the stimulus to the channel is so slight that only one channel at a time is emitting current. In many experiments, however, several…

条件分位数的核估计与近邻估计AI 解读

Let $(X_1, Z_1), (X_2, Z_2), \ldots, (X_n, Z_n)$ be iid as $(X, Z), Z$ taking values in $R^1$, and for $0 < p < 1$, let $\xi_p(x)$ denote the conditional $p$-quantile of $Z$ given $X = x,$ i.e., $P(Z \leq \xi_p(x)\mid X = x) = p$. In this paper, kernel and nearest-neighbor estimators of $\xi_p(x)$ are proposed. In order to study the asymptotics of these estimates, Bahadur-type representations of the sample conditional quantiles are obtained. These representations are used to…

时间序列回归中 Durbin–Watson 等不变检验统计量分布的快速计算AI 解读

A method is given for evaluating p values in O(n) operations for a general class of invariant test statistics that can be expressed as the ratio of quadratic forms in time series regression residuals. The best known of these is the Durbin-Watson statistic, although several others have been discussed in the literature. The method is numerically exact in the sense that the user specifies the error tolerance at the outset. As with existing exact methods, the problem is…

多元方差分量秩检验的分位点AI 解读

In the balanced one-way multivariate analysis of variance with random effects the likelihood ratio criterion for testing that the rank of the covariance matrix of the effect vector is not greater than a specified number is considered. The limiting distribution of −2 times the logarithm of the criterion is the distribution of the sum of squares of the positive characteristic roots of a certain random symmetric matrix. This paper presents exact and simulated quantiles of this…

摘要暂缺

Roy 模型的经验内容AI 解读

This paper explores the robustness of the essential economic conclusions of the Roy model of self-selection and income inequality to relaxation of its normality assumptions. A log concave version of the model reproduces most of the main results. Log convex cases offer counterexamples. The authors show that in a Roy economy, random assignment is inegalitarian and Pareto inefficient. They consider nonparametric identifiability of latent skill distributions with cross-section…

条件分位数约束下线性与一型删失回归模型的有效估计AI 解读

We consider the linear regression model with censored dependent variable, where the disturbance terms are restricted only to have zero conditional median (or other prespecified quantile) given the regressors and the censoring point. Thus, the functional form of the conditional distribution of the disturbances is unrestricted, permitting heteroskedasticity of unknown form. For this model, a lower bound for the asymptotic covariance matrix for regular estimators of the…

工具变量估计量精确小样本性质的进一步结果AI 解读

New results on the exact small sample distribution of the instrumental variable estimator are presented by studying an important special case. The exact closed forms for the probability density and cumulative distribution functions are given. There are a number of surprising findings. The small sample distribution is bimodal. with a point of zero probability mass. As the asymptotic variance grows large, the true distribution becomes concentrated around this point of zero…

格点分布的 Edgeworth 展开AI 解读

This paper investigates the use of Edgeworth expansions for approximating the distribution function of the normalized sum of $n$ independent and identically distributed lattice-valued random variables. We prove that the continuity-corrected Edgeworth series, using Sheppard-adjusted cumulants, is accurate to the same order in $n$ as the usual Edgeworth approximation for continuous random variables. Finally, as a partial justification of the Sheppard adjustments, it is shown…

估计混合密度与混合分布的傅里叶方法AI 解读

Let $X_1, X_2, \cdots$ be iid observations from a mixture density $f(x) = \int f(x \mid \theta)dG(\theta)$, where $f(x \mid \theta)$ is a known parametric family of density functions and $G$ is an unknown distribution function. This paper concerns estimating the mixing density $g = G'$ and the mixing distribution $G$. Fourier methods are used to derive kernel estimators, upper bounds for their rates of convergence and lower bounds for the optimal rate of convergence.…

对数样条模型的大样本推断AI 解读

Let $f$ be a continuous and positive unknown density on a known compact interval $\mathscr{Y}$. Let $F$ denote the distribution function of $f$ and let $Q = F^{-1}$ denote its quantile function. A finite-parameter exponential family model based on $B$-splines is constructed. Maximum-likelihood estimation of the parameters of the model based on a random sample of size $n$ from $f$ yields estimates $\hat{f, F}$ and $\hat{Q}$ of $f, F$ and $Q$, respectively. Under mild…

随机截断模型与马尔可夫过程AI 解读

Random left truncation is modelled by the conditional distribution of the random variable $X$ of interest, given that it is larger than the truncating random variable $Y$; usually $X$ and $Y$ are assumed independent. The present paper is based on a simple reparametrization of the left truncation model as a three-state Markov process. The derivation of a nonparametric estimator is a distribution function under random truncation is then a special case of results on the…

利用 S 系统微分方程计算统计密度、累积分布、分位数与功效AI 解读

A comprehensive approach for the analysis of statistical univariate distributions is advanced. The method is based on recasting a distribution in a canonical set of first-order nonlinear differential equations called an S system, in which the derivative of each variable equals a difference of products of power-law functions. The recasting techniques are illustrated with some examples from central and noncentral probability distributions. The density and the cumulative,…

基于单样本程序的删失生存时间中位数双样本推断AI 解读

Confidence intervals for median survival times are derived for censored survival data. The intervals are obtained by using the quantiles of the Kaplan-Meier product-limit estimator and have the same Pitman efficiency as the intervals found by inverting the sign test. Two-sample tests and confidence intervals for the difference in median survival times are then developed based on the comparison of the one-sample confidence intervals. Several methods for choosing the…

二项分布参数近似置信区间的准确性AI 解读

This article considers the uniform convergence of the coverage probabilities of some approximate confidence intervals for the binomial parameter p, induced by central limit arguments. A uniform upper bound on the coverage probabilities of any such interval obtained by transformation of the sample proportion [pcirc] n is derived. The coverage probability of the interval induced by the arcsine transformation turns out to be very close to the upper bound. Replacing [pcirc] n by…

核分位数估计量AI 解读

For an estimator of quantiles, the efficiency of the sample quantile can be improved by considering linear combinations of order statistics, that is, L estimators. A variety of such methods have appeared in the literature; an important aspect of this article is that asymptotically several of these are shown to be kernel estimators with a Guassian kernel, and the bandwidths are identified. It is seen that some implicit choices of the smoothing parameter are asymptotically…

分位数—分位数图的多元推广AI 解读

In this article we present a multivariate generalization of quantile-quantile (Q-Q) plots. Like univariate Q-Q plots, these plots are useful for examining the distributional shape of multivariate point clouds. These plots are based on finding a matching between the points of the data set whose shape is being examined and a reference sample. Graphical displays of how well the point clouds match are then developed. The reference sample used as the basis for comparison is…

摘要暂缺

分位数—分位数图的多元推广AI 解读

In this article we present a multivariate generalization of quantile-quantile (Q-Q) plots. Like univariate Q-Q plots, these plots are useful for examining the distributional shape of multivariate point clouds. These plots are based on finding a matching between the points of the data set whose shape is being examined and a reference sample. Graphical displays of how well the point clouds match are then developed. The reference sample used as the basis for comparison is…