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单纯形约束模型中遗传距离及其他量的估计偏差AI 解读

The genetic distance between two loci on a chromosome is defined as the mean number of crossovers between the loci. The parameters of the crossover distribution are constrained by the parameters of the distribution of chiasmata. Ott (1996) derived the maximum likelihood estimator (MLE) of the parameters of the crossover distribution and the MLE of the mean. We demonstrate that the MLE of the mean is pointwise less than or equal to the empirical mean number of crossovers. It…

多元模型中单侧备择的方向性检验AI 解读

Consider one-sided testing problems for a multivariate exponential family model. Through conditioning or other considerations, the problem oftentimes reduces to testing a null hypothesis that the natural parameter is a zero vector against the alternative that the natural parameter lies in a closed convex cone $\mathscr{C}$. The problems include testing homogeneity of parameters, testing independence in contingency tables, testing stochastic ordering of distributions and many…

锥序关联、随机锥排序及其在序约束检验中的应用AI 解读

Cohen, Sackrowitz and Samuel-Cahn introduced the notion of cone order association and established a necessary and sufficient condition for a normal random vector to be cone order associated (COA). In this paper we provide the following: (1) a necessary and sufficient condition for a multinomial distribution to be COA when the cone is a pairwise contrast cone; (2) a relationship between COA and regular association; (3) a notion of stochastic cone ordering (SCO) of random…

利用先导样本构造置信下界及其审计应用AI 解读

A pilot study is often done prior to a more thorough study, to determine whether a larger-scale effort is likely to yield useful results. In one sense, the pilot study can discourage or encourage further investigation. This is true in many situations in auditing. For example, an auditor seeks to determine that amount an insurance provider overpays. Often the provider makes few mistakes and overpays little. On the other hand, occasionally a provider overpays a lot. Because…

利用先导样本构造置信下界及其审计应用AI 解读

A pilot study is often done prior to a more thorough study, to determine whether a larger-scale effort is likely to yield useful results. In one sense, the pilot study can discourage or encourage further investigation. This is true in many situations in auditing. For example, an auditor seeks to determine that amount an insurance provider overpays. Often the provider makes few mistakes and overpays little. On the other hand, occasionally a provider overpays a lot. Because…

均匀分布尺度同质性的双侧与单侧检验AI 解读

Consider the model where Xij, i = 1, 2, …, k; j = 1, …, n i are independent uniform random variables with scale parameter θ i > 0. Test H 0: θl = ··· = θ k versus H 2: not H 0. Also consider the alternative H 1: θl ≤ ··· ≤ θ k . For H 0 versus H 2 and n i = n, we obtain a complete class of constant-size permutation invariant tests and show that each test in the class is unbiased. The likelihood ratio test and others are in this class. For H 0 versus H 1 we obtain a complete…

均匀分布尺度同质性检验：双侧与有序单侧备择AI 解读

Consider the model where Xij, i = 1, 2, …, k; j = 1, …, n i are independent uniform random variables with scale parameter θ i > 0. Test H 0: θl = ··· = θ k versus H 2: not H 0. Also consider the alternative H 1: θl ≤ ··· ≤ θ k . For H 0 versus H 2 and n i = n, we obtain a complete class of constant-size permutation invariant tests and show that each test in the class is unbiased. The likelihood ratio test and others are in this class. For H 0 versus H 1 we obtain a complete…

指数族回归中的无偏检验AI 解读

Let $(X_{ij}, \mathbf{z}_i), i = 1, 2, \ldots, k, j = 1, 2, \ldots, n_i$, be independent observations such that $\mathbf{z}_i$ is a fixed $r \times 1$ vector $\lbrack r$ can be 0 (no $\mathbf{z}$'s observed) or $1, 2, \ldots, k - 1\rbrack$, and $X_{ij}$ is distributed according to a one-parameter exponential family which is log concave with natural parameter $\theta_i$. We test the hypothesis that $\theta = \mathbf{Z}\beta$, where $\theta = (\theta_1, \ldots, \theta_k)', \mathbf{Z}$…

Consider the one-way fixed and balanced analysis of variance model under the assumptions of independence and normality. The problem is to test for homogeneity of variances. A necessary and sufficient condition for admissibility of a test among the class of scale invariant tests is given. Hartley's test and Cochran's test are not in the class and therefore are inadmissible. Various scale invariant tests are examined for parameter consistency. Parameter consistency in this…

模型选择后推断：变换型与自适应推断的决策论方法AI 解读

A decision-theory approach is formulated for inference following model selection. Inference here refers to either testing, point estimation, or confidence estimation. The loss function includes components for model selection as well as for inference and allows for flexibility in emphasis on one or the other, if such emphasis is desired. A general prescription for Bayes and generalized Bayes procedures is given. A procedure consists of model selection and inference. The…

同质性检验的无偏性AI 解读

Let $X_i, i = 1, 2, \ldots, k$, be independent random variables distributed according to a one-parameter exponential family with parameter $\theta_i$. Assume also that the probability density function of $X_i$ is a Polya frequency function of order two $(PF_2)$. Consider the null hypothesis $H_0: \theta_1 = \theta_2 = \cdots = \theta_k$ against the alternative $K$: not $H_0$. We show that any permutation invariant test of size $\alpha$, whose conditional (on $T = \sum^k_{i = 1}X_i)$…

对称分布的分位数估计AI 解读

The problem is to estimate a quantile of a symmetric distribution. The cases of known and unknown center are studied for small and large samples. The estimators for known center are the sample quantile, the symmetrized sample quantile, the sample quantile from flipped over data, the Rao-Blackwellized sample quantile, and a Bayes estimator using a Dirichlet prior. For center unknown, we study the analogues of the first four estimators listed above. For small samples and…

二项分布双重抽样估计的若干结果AI 解读

A complete class result is obtained for double sample estimation of a binomial parameter. The complete class leads to some inadmissibility results for some procedures that are likely to be used in practice. It is also shown that the sample proportion as a true double estimator is not unbiased.

贝叶斯两阶段抽样估计程序AI 解读

Bayes double sample procedures are given for estimating the mean of exponential family distributions. The distribution can be multiparameter and so the case of normal mean with unknown variance is included. Linear combination loss functions are usually assumed. Stein's double sample procedure, and other intuitive double sample procedures for estimating a binomial parameter, are studied. Recommendations are given, including guidelines for the size of the initial samples.

条件独立的 2×2×2 列联表中边际概率的假设检验AI 解读

Consider a 2 × 2 × 2 contingency model with factors A, B, and C. Assume factors A and B are conditionally independent given factor C. We are interested in testing the null hypothesis that the marginal probabilities of the second level of B are the same across the levels of A. Small-sample and large-sample tests are studied.

摘要暂缺

条件独立列联表中边际均值的统计推断AI 解读

Consider a three-way contingency table with factors A, B, and C. Assume factors A and B are independent for each given level of factor C. Inference procedures concerning the marginal means of the levels of factor A are studied. Maximum likelihood estimators, unbiased estimators, and uniformly minimum variance unbiased estimators are obtained. Exact variance formulas for the estimators are obtained. Large sample theory is developed and used for testing and confidence…

条件独立列联表中边际均值的推断AI 解读

Consider a three-way contingency table with factors A, B, and C. Assume factors A and B are independent for each given level of factor C. Inference procedures concerning the marginal means of the levels of factor A are studied. Maximum likelihood estimators, unbiased estimators, and uniformly minimum variance unbiased estimators are obtained. Exact variance formulas for the estimators are obtained. Large sample theory is developed and used for testing and confidence…

序贯假设检验的完全类AI 解读

We consider problems of sequential testing when the loss function is the sum of a component due to an error in the terminal decision and a cost of observation component. In all cases we establish a characterization of a complete class or an essentially complete class. In order to obtain such results for testing a null hypothesis against an alternative hypothesis we establish complete class results for testing the closure of the null hypothesis against the closure of the…

合并检验的渐近最优方法AI 解读

A criterion for the asymptotic optimality of combined independent tests is given. Methods other than Fisher's are shown to satisfy the criterion. Certain problems call for a weighted combination of tests. It is shown that many weighted procedures are optimal. In particular, a weighted procedure based on gamma transforms is optimal. This weighted procedure has the additional advantage that critical values are easily determined. Good's weighting procedure is shown not to be…

严格单调似然比下的完全类定理及其应用AI 解读

Suppose a random variable has a density belonging to a one parameter family which has strict monotone likelihood ratio. For inference regarding the parameter (or a monotone function of the parameter) consider the loss function to be bowl shaped for each fixed parameter and also to have each action be a "point of increase" or a "point of decrease" for some value of the parameter. Under these conditions, given any nonmonotone decision procedure, a unique monotone procedure is…

等单元概率情形下卡方、似然比及其他拟合优度检验的无偏性AI 解读

The chi-square test, likelihood ratio test, and other goodness of fit tests in a family are shown to have monotonic power functions, and hence are unbiased, for testing a simple hypothesis that all cell probabilities are equal. The chi-square test is also shown to be Type D for this situation.

两个正态分布共同均值的估计AI 解读

Consider the problem of estimating the common mean of two normal distributions. Two new unbiased estimators of the common mean are offered for the equal sample size case. Both are better than the sample mean based on one population for sample sizes of 5 or more. A slight modification of one of the estimators is better than either sample mean simultaneously for sample sizes of 10 or more. This same estimator has desirable large sample properties and an explicit simple upper…

共同均值的点估计、置信估计与区组间信息的回收AI 解读

Consider the problem of estimating a common mean of two independent normal distributions, each with unknown variances. Note that the problem of recovery of interblock information in balanced incomplete blocks designs is such a problem. Suppose a random sample of size $m$ is drawn from the first population and a random sample of size $n$ is drawn from the second population. We first show that the sample mean of the first population can be improved on (with an unbiased…