日期精度：到日 5104 篇 · 到月 0 篇 · 到年 0 篇
Minimax interval estimators of location parameters analogous to the Pitman point estimators are found by employing invariance in decision theory. The half normal distribution is used as an illustrative example.
位置向量单个坐标最优不变估计量的可容许性
In 1960, Charles Stein conjectured that the best invariant estimate of a single co-ordinate of a $p$-dimensional location parameter would be admissible if $p \leqq 3$ but inadmissible if $p \geqq 4$. This appear present a class of examples which supports Stein's conjecture.
线性假设检验的正态理论近似
Let $\{\mathbf{y}_1, \cdots, \mathbf{y}_N\}$ be $N$ independent repetitions of an experiment for which $\mathscr{E}\mathbf{y} = \mathbf{X\beta}$ and $\mathscr{E}(\mathbf{y} - \mathbf{X\beta})(\mathbf{y} - \mathbf{X\beta} ' = \sigma^2\mathbf{I}$, where $\mathbf{X}$ is nonstochastic of full rank and $\mathbf{\beta'} = \lbrack \mathbf{\beta_1'}, \cdot, \mathbf{\beta}_r'\rbrack$ and $\sigma^2$ are unknown parameters. We investigate some large-sample properties of $N^{\frac{1}{2}} (\hat{\mathbf{\beta}}_N - \mathbf{\beta})$…
趋势二次秩检验的局部渐近功效
A general class of quadratic rank tests for randomness versus trend is introduced and studied in this paper. Included within this class are the Cramer-von Mises two sample test, the Watson two-sample test, and their extensions to trend alternatives. Analytical study is made of the asymptotic power and efficiency of such tests in a neighborhood of the null hypothesis.
检验对称性的序贯符号秩检验
A sequential procedure for testing the hypothesis that the distribution of a sequence of i.i.d. random variables is symmetric about zero is given, where the test statistic is a function of the signs and the rank of the absolute values of the observations. Necessary and sufficient conditions that the individual signed ranks be independent are given. The critical region, power, and expected sample size of the test are determined approximately by using the fact that the test…
生灭过程中的最大似然估计
Maximum likelihood estimation of the parameters $\lambda$ and $\mu$ of a simple (linear) birth-and-death process observed continuously over a fixed time interval is studied. Asymptotic distributions for large initial populations and for large periods of observation are derived and some nonstandard results appear. The result problem of estimation from the discrete skeleton of the process is also discussed.
排序与选择问题中的受限子集选择方法
Let $\pi_1,\cdots, \pi_k$ be $k$ populations with $\pi_i$ characterized by a scalar $\lambda_i \in \Lambda$, a specified interval on the real line. The object of the problem is to make some inference about $\pi_{(k)}$, the population with largest $\lambda_i$. The present work studies rules which select a random number of populations between one and $m$ where the upper bound, $m$, is imposed by inherent setup restrictions of the subset selection and indifference zone…
受随机扰动与尺度因子影响的经验分布函数弱收敛
The weak convergence of empirical distribution functions subject to random perturbations and scale factors to a Gaussian process is established. This result is used to study the efficiencies of tests based on spacings in goodness-of-fit problems.
位置参数的渐近有效估计量序列
An asymptotically efficient sequence of estimators for the location parameter of an (unknown) symmetric density $f$ is given under weak conditions on the tails of $f$. The estimators are related to the usual linear combination of order statistics except that the unknown $f$ has to be estimated and only some of the order statistics are used.
位置参数的自适应最大似然估计
Consider estimators $\hat{\theta}_n$ of the location parameter $\theta$ based on a sample of size $n$ from $\theta + X$, where the random variable $X$ has an unknown distribution $F$ which is symmetric about the origin but otherwise arbitrary. Let $\mathscr{F}$ denote the Fisher information on $\theta$ contained in $\theta + X$. We show that there is a nonrandomized translation and scale invariant adaptive maximum likelihood estimator $\hat{\theta}_n$ of $\theta$ which doe…
广义保序回归的一致性
Suppose $T$ is a partially ordered set and that associated with each $t$ in $T$ we have a distribution with "location parameter" $m(t)$. In this paper we discuss consistency properties of estimates of $m(\cdot)$ which are isotonic with respect to a partial order. The results extend results in the literature, some of which are contained in Brunk (1970) (Estimation of isotonic regression in Nonparametric Techniques in Statistical Inference, Cambridge University Press,…
对称狄利克雷先验下反对多项总体等概率的贝叶斯因子
A sample $(n_1, n_2,\cdots, n_t)$ is taken from a $t$-category multinomial population. The hypothesis of equiprobability, that the $t$ physical probabilities associated with the cells are all equal to $1/t$, is called the null hypothesis. Conditional on the non-null hypothesis, a symmetric Dirichlet prior of parameter $k$ is assumed $(k \geqq 0)$ and the Bayes factor against the null hypothesis, with this assumption, is denoted by $F(k)$. A conjecture made in 1965 is almost…
删失数据独立性检验的局部最强秩检验
In this paper locally most powerful rank tests for independence with censored data for a one-parameter family are derived. The statistic derived has discrete score functions and its asymptotic normality follows from a theorem essentially given by Ruymgaart [6].
一致点估计量的收敛速率
The rate at which the probability $P_\theta\{|t_n - \theta| \geqq \varepsilon\}$ of consistent estimator $t_n$ tends to zero is of great importance in large sample theory of point estimation. The main tools available at present for finding the rate are Bernstein-Chernoff-Bahadur's theorem and Sanov's theorem. In this paper, we give two new techniques for finding the rate of convergence of certain consistent estimators. By using these techniques, we have obtained an upper…
点估计量矩的下界
We consider the problem of estimating an unknown parameter $\theta$ on the basis of independent identically distributed observations with a common density $f(x,\theta)$ and give some lower bounds for the accuracy of estimates of $\theta$ expressed in terms of the Hellinger distance $\rho(\theta; \theta') = \int_\mathscr{X} (f^{\frac{1}{2}}(x; \theta) - f^{\frac{1}{2}}(x; \theta'))^2 d\nu.$
指数模型后验分布的渐近正态性
Let $f(x)$ be a $\operatorname{pdf}$ of exponential form with respect to the measure $\mu$. Suppose a prior $\operatorname{pdf}$ $\pi$ has been placed on the natural parameter space $\Omega$, where $\pi$ is a density (with respect to $m$-dimensional Lebesgue measure) which is both positive and continuous at $\tau^\ast$, the true but unknown parameter value. Using basic properties of exponential families and certain associated convex functions, it is shown that the posterior…
正态回归中的一个外推判据
In a full rank normal regression model, the existence of an unbiased estimate of the distribution associated to any "future" observation is studied. A necessary and sufficient condition in terms of the point at which the "future" observation will be taken is given for such an estimate to exist. This criterion is introduced to consider the validity of extrapolation.
多元正态分布均值的极小极大估计量
An extension of Strawderman's results yields minimax admissible estimates for the mean of a $p$-variate normal distribution where the known nonsingular covariance matrix is not necessarily the identity and $p > 2$. Minimax estimators for the case where the covariance matrix is unknown are also given.
多项分布函数和的中心极限定理
Let $(N_1, \cdots, N_k)$ be a multinomial vector with $n = \sum N_i$ and with parameter $(p_1, \cdots, p_k), \sum p_i = 1$. Let $f_1, \cdots, f_k$ be real-valued functions defined on the integers $\{0, 1, \cdots, n\}$, and let $S_k = \sum^k_{i=1} f_i(N_i)$. Suppose $k \rightarrow \infty$, and as $k \rightarrow \infty$, that $n \rightarrow \infty$ and $\max_{1\leqq i \leqq k}p_i \rightarrow 0$. Conditions on the $\{f_i\}$ are given which guarantee that $S_k$, suitably…
经验贝叶斯估计问题的收敛速度：连续情形
In this paper we construct sequences of estimators for a density function and its derivatives, which are not assumed to be uniformly bounded, using classes of kernel functions. Utilizing these estimators, a sequence of empirical Bayes estimators is proposed. It is found that this sequence is asymptotically optimal in the sense of Robbins (Ann. Math. Statist. 35 (1964) 1-20). The rates of convergence of the Bayes risks associated with the proposed empirical Bayes estimators…
不变正态模型
Many hypotheses in the multidimensional normal distribution are given or can be given by symmetries or, in other words, invariance. This means that the variances are invariant under a given subgroup of the general linear group in the vector space of observations. In this paper we define a class of hypotheses, the Invariant Normal Models, including all symmetry hypotheses. We derive the maximum likelihood estimator of the mean and variance and its distribution under the…
检测均值变化的检验
Procedures are considered for testing whether the means of each variable in a sequence of independent random variables can be taken to be the same, against alternatives that a shift might have occurred after some point $r$. Bayesian test statistics as well as some statistics depending on estimates of $r$ are presented and their powers compared. Exact and asymptotic distribution functions are derived for some of the Bayesian statistics.
分段回归中的对数似然比
This paper deals with the asymptotic distribution of the log likelihood ratio statistic in regression models which have different analytical forms in different regions of the domain of the independent variable. It is shown that under suitable identifiability conditions, the asymptotic chi square results of Wilks and Chernoff are applicable. It is shown by example that if there are actually fewer segments than the number assumed in the model, then the least squares estimates…
分段回归问题的渐近分布理论：可识别情形
This paper deals with the asymptotic distribution theory of least squares estimators in regression models having different analytical forms in different regions of the domain of the independent variable. An important special case is that of broken line regression, in which each segment of the regression function is a different straight line. The residual sum of squares function has many corners, and so classical least squares techniques cannot be directly applied. It is…