论文检索

最小二乘回归中序列相关的局部稳健检验AI 解读

Kariya and Eaton and Kariya studied a robustness property of the usual tests for serial correlation against departure from normality. When the results were applied to a regression model $y = X \beta + u(X: nxk),$ it was assumed that the column space of $X$ is spanned by some $k$ latent vectors of the covariance matrix of error term $u.$ In this paper we delete this assumption and in a much broader class of distributions derive a locally best invariant test for a one-sided…

鞅差误差回归模型中最小二乘估计强一致性的一则说明AI 解读

Conditions for the pointwise consistency of weighted least squares estimators from multivariate regression models with martingale difference errors are given in terms of the relative rates at which certain quadratic forms diverge to infinity.

保序、凸及相关样条AI 解读

In this paper, we consider the estimation of isotonic, convex or related functions by means of splines. It is shown that certain classes of isotone or convex functions can be represented as a positive cone embedded in a Hilbert space. Using this representation, we give an existence and characterization theorem for isotonic or convex splines. Two special cases are examined showing the existence of a globally monotone cubic smoothing spline and a globally convex quintic…

参数估计下基于克拉美–冯·米塞斯统计量正交分量线性组合的检验AI 解读

In a previous work, the author showed how linear combinations of the orthogonal components of the Cramer-von Mises statistic could be used to test fit to a fully specified distribution function. In this paper, the results are extended to the case where $r$ parameters are estimated from the data. It is shown that if the coefficient vector of the linear combination is orthogonal to a specified $r$ dimensional subspace, then the asymptotic distribution of that combination is…

删失样本中平均生存时间估计量的大样本理论AI 解读

This paper introduces and studies the large sample properties of an estimator for the mean survival time from censored samples. Let $X_1, \cdots, X_n$ be independent identically distributed random variables with $F(x) = P\lbrack X_1 > x \rbrack.$ Let $Y_1, \cdots, Y_n$ be independent identically distributed (and independent of $X_1, \cdots, X_n$) censoring times with $G(y) = P\lbrack Y_1 > y\rbrack.$ Based on observing only $Z_i = \min(X_i, Y_i)$ and which observations are…

基于经验概率测度的拟合优度检验AI 解读

A goodness-of-fit test is proposed for the simple hypothesis specifying a continuous $p$-variate distribution. For a suitably defined empirical probability measure, the proposed test is based on the supremum of the absolute differences between hypothesized and empirical probabilities, the supremum being taken over all possible events. This test statistic is shown to be distribution free in the general $p$-variate case, its exact null distribution is indicated, and its…

总体参数具有任意重数时典型相关与MANOVA特征根密度的渐近表示AI 解读

Asymptotic representations of the joint densities of the canonical correlation coefficients, calculated from a sample from a multivariate normal population, and of the latent roots of $B(B + W)^{-1},$ where $B$ is $W_p(n_1, \Sigma, \Omega)$ and $W$ is $W_p(n_2, \Sigma),$ are obtained by deriving asymptotic representations of the hypergeometric functions in the joint densities. The results hold in the first case for large sample size and arbitrary values of the population…

岭回归估计的极小极大性质AI 解读

The technique of ridge regression, first proposed by Hoerl and Kennard, has become a popular tool for data analysts faced with a high degree of multicollinearity in their data. By using a ridge estimator, one hopes to both stabilize one's estimates (lower the condition number of the design matrix) and improve upon the squared error loss of the least squares estimator. Recently, much attention has been focused on the latter objective. Building on the work of Stein and others,…

多项式 monospline 回归的容许设计AI 解读

Admissible designs for polynomial monospline regression are shown to be a proper subset of the admissible designs for spline regression. Sufficient conditions are given for designs for polynomial monospline regression to be admissible, and examples are used to show that simply counting points in intervals does not determine admissibility for monospline functions.

多样本置换检验的渐近展开AI 解读

Let $V_n$ be the standardized sum of squares of the means of $r + 1$ random samples of sizes $s_0, s_1, \cdots, s_r$, where $n = s_0 + s_1 + \cdots + s_r$, taken without replacement from $n$ numbers. Then using an approximation to the characteristic function of the means, an asymptotic expansion is obtained for the distribution of $V_n$ with first term being the distribution function of $\chi^2_r$ and with error of approximation generally of smaller order than $1/n$. When…

两总体序贯检验中劣势总体期望样本量的渐近分析AI 解读

Let $X_1, \cdots$ be i.i.d. $\sim N(\mu_1,1)$ and $Y_1, \cdots$ be i.i.d. $\sim N(\mu_2,1)$. A symmetric sequential procedure for $H_0 : \mu_1 > \mu_2$ vs. $H_1 : \mu_1 < \mu_2$ is proposed in this paper. The expected number of observations taken from the inferior population is given in an asymptotic form, which is optimum in Farrell's sense.

泊松到达率的贝叶斯序贯估计：离散时间方法AI 解读

This paper provides explicit solutions to the problem of estimating the arrival rate $\lambda$ of a Poisson process using a Bayes sequential approach. The loss associated with estimating $\lambda$ by $d$ is assumed to be of the form $(\lambda - d)^2\lambda^{-p}$ and the cost of observation includes both a time cost and an event cost. A discrete time approach is taken in which decisions are made at the end of time intervals having length $t$. Limits of the procedures as $t$ ap…

似然比随机序性质的扩展AI 解读

Extensions in two directions are described of the well-known stochastic ordering property of likelihood ratios. 1. It is shown that the stochastic ordering property holds in a very general conditional sense. 2. It is shown that, for the usual setting occurring in sequential analysis, sequences of likelihood ratios possess the same stochastic ordering property in a multivariate sense. Applications to sequential analysis, and elsewhere, are described.

基于离散最大惩罚似然准则的非参数密度估计AI 解读

A nonparametric probability density estimator is proposed that is optimal with respect to a discretized form of a continuous penalized-likelihood criterion functional. Approximation results relating the discrete estimator to the estimate obtained by solving the corresponding infinite-dimensional problem are presented. The discrete estimator is shown to be consistent. The numerical implementation of this discrete estimator is outlined and examples displayed. A simulation…

平衡混合方差分析模型中的显式最大似然估计AI 解读

A result of Szatrowski, giving necessary and sufficient conditions for the existence of explicit maximum likelihood estimates for multivariate normal means and covariances with linear structure, can be applied to the problem of obtaining explicit maximum likelihood estimates in the mixed model of the analysis of variance. This application yields a simple procedure for checking whether or not explicit maximum likelihood estimates exist for the parameters in the balanced mixed…

结构化均值与协方差多元正态估计中显式解的充要条件AI 解读

The problem of finding maximum likelihood estimates for patterned means and covariance matrices in multivariate analysis is considered. Necessary and sufficient conditions are presented for the existence of explicit solutions and the obtaining of these explicit solutions in one iteration of the scoring equations from any positive definite starting point. Cases in which averaging yields the explicit maximum likelihood estimates are discussed. These results can be applied to…

最小二乘估计一致性方向的刻画AI 解读

Given a sequence of $p \times 1$ vectors $\mathbf{v} = \{\nu_i\}^\infty_{i=1}$ such that $M_n = \Sigma^n_{i=1} \nu_i\nu'_i$ is positive definite for some $n$, the linear space $\{u: u'M^{-1}_n u \rightarrow \infty\}$ is characterized in terms of the limiting properties of $\mathbf{v}$. This characterization result is applied to give a necessary and sufficient condition for the asymptotic consistency of any best linear unbiased estimator in terms of the limiting properties of…

线性回归模型中最小二乘估计量的强相合性AI 解读

For the linear regression model $y = X \beta + u$ with stochastic regressor matrix, strong consistency of the least squares estimator of $\beta$ is proved in the case of martingale difference errors and predetermined regressors and for the case where errors and regressors are orthogonal up to the second order. The results obtained are applied to parameter estimation in autoregressive processes, leading to strong consistency if the errors are quasi-independent up to the…

基于 ARMA 模型的递归估计AI 解读

A recursive estimate of the stochastic structure of a stationary time series is constructed based on the assumption that the true structure is ARMA, i.e., has a rational spectrum. The estimate is recursive in the sense that each successive estimate is obtained from the previous one by a relatively simple adjustment, that could be effected in a "real time" situation. The procedure is basically that of updating a regression when all variates involved are constructed from…

多元正态均值的稳健广义贝叶斯估计与置信域AI 解读

It is observed that in selecting an alternative to the usual maximum likelihood estimator, $\delta^0$, of a multivariate normal mean, it is important to take into account prior information. Prior information in the form of a prior mean and a prior covariance matrix is considered. A generalized Bayes estimator is developed which is significantly better than $\delta^0$ if this prior information is correct and yet is very robust with respect to misspecification of the prior…

非线性平滑器的若干理论AI 解读

In recent years J. W. Tukey has introduced several algorithms for nonlinear smoothing of time series, but theoretical development has been slow owing to the extreme difficulty of obtaining analytical results even in the simplest cases. We present here some desiderata for smoothers generally, and give a framework within which some detailed comparisons between different smoothers can be made.

一个 Edgeworth 奇例AI 解读

Taking the sample mean of a set of measurements need not be uniformly advantageous, even when $n = 2$ and all moments are finite. The examples presented include one given by Edgeworth in 1883.

众数的最优核估计AI 解读

Let $X_1, \cdots, X_n$ be independent observations with common density $f$. A kernel estimate of the mode is any value of $t$ which maximizes the kernel estimate of the density $f_n$. Conditions are given restricting the density, the kernel, and the bandwidth under which this estimate of the mode has an asymptotic normal distribution. By imposing sufficient restrictions, the rate at which the mean squared error of the estimator converges to zero can be decreased from $n^{-\frac{4}{7}}$…

摘要暂缺