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混合分布的非参数极大似然估计AI 解读

The nonparametric maximum likelihood estimate of a mixing distribution is shown to be self-consistent, a property which characterizes the nonparametric maximum likelihood estimate of a distribution function in incomplete data problems. Under various conditions the estimate is a step function, with a finite number of steps. Its computation is illustrated with a small example.

典型分析：比较有限离散分布函数的因子分析方法AI 解读

The methods of factor analysis are adapted to the comparison of finite discrete distribution functions. Each element of a finite class of distribution functions is presented in a canonical form in which components differentiating and uniting the functions are easily distinguished and are readily calculated using factor-analysis algorithms. This technique, which we call canonical analysis, has uses in heterogeneity and goodness-of-fit analysis and in the classification of…

成对比较中的处理对比：大样本结果、应用与部分最优设计AI 解读

Treatment contrasts in paired comparison experiments are considered. Given that specified orthonormal treatment contrasts are null, remaining treatment parameters, orthonormal contrasts among them, and their logarithms are estimated. The estimators are shown to be consistent and, when suitably scaled and centered, to have distribution functions that are normal in the limit for large sample sizes. Hypothesis tests on treatment contrasts are obtained. The limiting distribution…

典型分析：比较有限离散分布函数的因子分析方法AI 解读

The methods of factor analysis are adapted to the comparison of finite discrete distribution functions. Each element of a finite class of distribution functions is presented in a canonical form in which components differentiating and uniting the functions are easily distinguished and are readily calculated using factor-analysis algorithms. This technique, which we call canonical analysis, has uses in heterogeneity and goodness-of-fit analysis and in the classification of…

摘要暂缺

关于拟合优度检验的半样本方法AI 解读

Summary Two interesting processes, related to the empirical distribution function, have been pointed out by Rao (1972) and by Durbin (1973). The second, in particular, leads to the half-sample method, an elegant and simple technique for dealing with unknown parameters in goodness-of-fit testing, without the necessity of new tables of percentage points for each distribution tested. to those who have spent some effort in producing such tables, it is natural to wonder whether…

有限总体抽样分布的渐近展开AI 解读

An asymptotic expansion is obtained for the distribution function of the standardized mean of a sample of $s$ observations taken randomly without replacement from a finite population of $n$ numbers. The expansion is given to order $1/n$ and agrees with the formal Edgeworth expansion. The proof of the result is obtained using an approximation to the characteristic function of the standardized sum.

检测均值系统性变化的二变量检验AI 解读

Let (xi, yi ), i = 1, …, n, be a sequence of observations such that yi = bi + cxi + ui , where bi and c are unknown parameters, and {ui } and {xi } are independent sequences of independent, identically distributed random variables. The likelihood ratio test is derived for the hypothesis that bi = b (i = 1, …, n), against the alternative that bi = b (i ≤ i 0) and bi = b + d (i > i 0) for some b, i 0, and d ≠ 0, assuming the ui 's are normal. Quantiles of the test statistic…

百分位数回归：参数化方法AI 解读

For situations in which no assumptions are explicitly made about error distributions, other model assumptions may imply constraints on the form of the residual distribution. This is true of regression models which assume that percentiles are functions of the regressor variable. Hogg (1975) used a procedure based on signs of residuals to fit linear percentile models. Advantages of making (and testing!) explicit parametric assumptions in this context are illustrated using a…

最小绝对误差回归的渐近理论AI 解读

In the general linear model with independent and identically distributed errors and distribution function F, the estimator which minimizes the sum of absolute residuals is demonstrated to be consistent and asymptotically Gaussian with covariance matrix ω2 Q -1, where Q = lim T -1 X'X and ω2 is the asymptotic variance of the ordinary sample median from samples with distribution F. Thus the least absolute error estimator has strictly smaller asymptotic confidence ellipsoids…

百分位回归：参数化方法AI 解读

For situations in which no assumptions are explicitly made about error distributions, other model assumptions may imply constraints on the form of the residual distribution. This is true of regression models which assume that percentiles are functions of the regressor variable. Hogg (1975) used a procedure based on signs of residuals to fit linear percentile models. Advantages of making (and testing!) explicit parametric assumptions in this context are illustrated using a…

一类截断分布中回归系数解释的说明AI 解读

DESPITE THE INTENSE ACTIVITY in the area of estimation of limited dependent variable (LDV) models (see, for example, the Fall 1976 issue of the Annals of Economic and Social Measurement), the interpretation of regression coefficients in truncated regression models has been largely ignored. This issue should not be taken lightly since the obvious interpretation which equates regression coefficients to partial derivatives of the conditional mean of the dependent variable is…

Kendall秩相关系数的Edgeworth展开札记AI 解读

In this note it is shown how to some extent the Edgeworth expansion for the distribution function of Kendall's $\\tau$ can be established by using a well-known general result on such expansions.

强渐近中位数无偏估计量的渐近效率AI 解读

It is shown that the problem of asymptotic efficiency (in the Wolfowitz-sense) admits a satisfactory solution for the class of strongly asymptotically median unbiased estimators. The concept of strongly asymptotic median unbiasedness furthermore links up the classical approach (concerning estimator-sequences whose distribution functions converge) with Pfanzagl's concept of median unbiasedness.

分位数过程的强逼近AI 解读

Let $q_n(y), 0 < y < 1,$ be a quantile process based on a sequence of i.i.d. rv with distribution function $F$ and density function $f.$ Given some regularity conditions on $F$ the distance of $q_n(y)$ and the uniform quantile process $u_n(y),$ respectively defined in terms of the order statistics $X_{k:n}$ and $U_{k:n} = F(X_{k:n}),$ is computed with rates. As a consequence we have an extension of Kiefer's result on the distance between the empirical and quantile processes,…

右删失观测下分布与生存函数的经验贝叶斯估计AI 解读

This paper provides an empirical Bayes approach to the problem of nonparametric estimation of a distribution (or survival) function when the observations are censored on the right. The results use the notion of a Dirichlet process prior introduced by Ferguson. The paper presents a generalization to the case of right censored observations of the rate result of an empirical Bayes nonparametric estimator of a distribution function of Korwar and Hollander in the uncensored case.…

若干非线性模型中的估计AI 解读

Extensions of linear model contrasts to general and location-scale models are proposed. These extensions are defined in terms of shift functions which measure how much the variables from one population must be shifted to be aligned in distribution with the variables from another. A general estimate based on empirical distribution functions and three estimates appropriate for the location-scale model are considered and compared in terms of asymptotic relative efficiencies. An…

若干非线性模型中的估计AI 解读

Extensions of linear model contrasts to general and location-scale models are proposed. These extensions are defined in terms of shift functions which measure how much the variables from one population must be shifted to be aligned in distribution with the variables from another. A general estimate based on empirical distribution functions and three estimates appropriate for the location-scale model are considered and compared in terms of asymptotic relative efficiencies. An…

分布函数的贝叶斯置信带AI 解读

A set of recurrences is developed for computing the probability content of any prior or posterior confidence bands for a distribution function assuming the parameter of the prior Dirichlet process known. When the prior parameter is unknown and is estimated from the sample, nonparametric estimates of the probability content of the posterior bands are obtained.

加权中位数回归估计AI 解读

In the simple linear regression problem $\{Y_i = \alpha + \beta x_i + e_i i = 1,\cdots, n, e_i$ i.i.d. $\sim F$ continuous, $x_1 \leqq \cdots \leqq x_n$ known, $\alpha, \beta$ unknown$\}$ we investigate the following type of estimator: To each $s_{ij} = (Y_j - Y_i)/(x_j - x_i)$ with $x_i < x_j$ attach weight $w_{ij}$ and as estimator for $\beta$ consider the median of this weight distribution over the $s_{ij}$. A confidence interval for $\beta$ is found by taking certain…

形式 Edgeworth 展开的有效性AI 解读

Let $\{Y_n\}_{n\geqq 1}$ be a sequence of i.i.d. $m$-dimensional random vectors, and let $f_1,\cdots, f_k$ be real-valued Borel measurable functions on $R^m$. Assume that $Z_n = (f_1(Y_n),\cdots, f_k(Y_n))$ has finite moments of order $s \geqq 3$. Rates of convergence to normality and asymptotic expansions of distributions of statistics of the form $W_n = n^{\frac{1}{2}}\lbrack H(\bar{Z}) - H(\mu)\rbrack$ are obtained for functions $H$ on $R^k$ having continuous derivatives…

比较两个相依分布的非参数检验AI 解读

Summary Using a sample from an unknown bivariate distribution, we propose a test for the hypothesis that one marginal distribution is stochastically larger than the other. We show that the test statistic has an asymptotic normal distribution, and that the proposed test is asymptotically non-parametric. This test is compared to the paired t-test for large samples in terms of asymptotic relative efficiency and for samples of size 20 by simulation estimates of size and power.…

有限总体分位数的置信区间：简单随机抽样与分层简单随机抽样AI 解读

Summary Given a finite population consisting of N units, it is desired to have a confidence interval for the (t/N)th quantile, Y (t), of the population. Assuming simple random sampling, a confidence interval procedure is suggested and several expressions for the associated confidence coefficient are given. With stratified simple random sampling, for L = 2 strata, three confidence interval procedures are suggested. The associated confidence coefficients are derived under each…

混合生成的离散时间序列（二）：渐近性质AI 解读

Summary The darma (discrete mixed autoregressive-moving average) processes are a broad but parametrically simple class of models for a stationary sequence of dependent discrete random variables. A darma process is formed as a random linear combination of independent identically distributed discrete random variables. The process is specified by the distribution of the independent variables, which is also the marginal distribution of the random process, and several other…