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二项可探测性模型中的种群规模推断AI 解读

Many models for biological populations, including simple mark-recapture models and distance sampling models, involve a binomially distributed number, n, of observations x1, …, xn on members of a population of size N. Two popular estimators of (N, θ), where θ is a vector parameter, are the maximum likelihood estimator and the conditional maximum likelihood estimator based on the conditional distribution of x1, …, xn given n. We derive the large-N asymptotic distributions of…

紧黎曼流形上均匀性的数据驱动 Sobolev 检验AI 解读

Data-driven versions of Sobolev tests of uniformity on compact Riemannian manifolds are proposed. These tests are invariant under isometries and are consistent against all alternatives. The large-sample asymptotic null distributions are given.

同质总体规模的植入捕获估计AI 解读

We consider maximum likelihood estimation of the size of a target population to which has been added a known number of planted individuals. The standard equal-catchability model used in mark-recapture is assumed to be applicable to the augmented population. After proving the unimodality of the profile likelihood for the target population size, we obtain both the maximum likelihood estimator of this size and interval estimators based on its asymptotic distribution.

紧致黎曼流形上分布拟合优度的 Sobolev 检验AI 解读

Classes of coordinate-invariant omnibus goodness-of-fit tests on compact Riemannian manifolds are proposed. The tests are based on Giné’s Sobolev tests of uniformity. A condition for consistency is given. The tests are illustrated by an example on the rotation group SO(3).

捕获—再捕获实验中泊松与多项模型的推断AI 解读

Capture-recapture models have been formulated both as Poisson and as multinomial distributions. Maximum likelihood estimates of parameters under the two models are compared. For parameters which do not involve the population size the asymptotic covariances are shown to be the same.

捕获—再捕获实验的Poisson与多项式模型推断AI 解读

Capture-recapture models have been formulated both as Poisson and as multinomial distributions. Maximum likelihood estimates of parameters under the two models are compared. For parameters which do not involve the population size the asymptotic covariances are shown to be the same.

微分几何、剖面似然、L 充分性与复合变换模型AI 解读

Let $\Omega$ denote the parameter space of a statistical model and let $\mathscr{K}$ be the domain of variation of the parameter of interest. Various differential-geometric structures on $\Omega$ are considered, including the expected information metric and the $\alpha$-connections studied by Chentsov and Amari, as well as the observed information metric and the observed $\alpha$-connections introduced by Barndorff-Nielsen. Under certain conditions these geometric objects on…

随机向量或方向数据的非参数相关系数与两样本检验AI 解读

For multivariate or directional data a nonparametric correlation coefficient and a two-sample statistic are proposed. Both of these statistics are coordinate-free, resistant and unchanged under almost all small perturbations of the data. The correlation coefficient generalizes Kendall's tau and the angular-angular correlation coefficient of Fisher & Lee (1982). The two-sample statistic is related to the Cramér-von Mises statistic and to Watson's (1962) U2. A numerical…

随机向量或方向数据的非参数相关系数与双样本检验AI 解读

For multivariate or directional data a nonparametric correlation coefficient and a two-sample statistic are proposed. Both of these statistics are coordinate-free, resistant and unchanged under almost all small perturbations of the data. The correlation coefficient generalizes Kendall's tau and the angular-angular correlation coefficient of Fisher & Lee (1982). The two-sample statistic is related to the Cramér-von Mises statistic and to Watson's (1962) U2. A numerical…

方向变量独立性的 Sobolev 检验AI 解读

Two families of invariant tests for independence of random variables on compact Riemannian manifolds are proposed and studied. The tests are based on Gine's Sobolev norms which are obtained by mapping the manifolds into Hilbert spaces. For general compact manifolds, randomization tests are suggested. For the bivariate circular case, distribution-free tests based on uniform scores are considered.

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方向数据的一般相关系数及相关回归问题AI 解读

A correlation coefficient ρ2 is proposed for bivariate angular distributions and for bivariate distributions on general manifolds. In the cylindrical case ρ2 is the coefficient of Mardia (1976), and for the bivariate angular case it is a modified version of the correlation coefficient of Mardia & Puri (1978). Some properties of ρ2 are examined and compared with those of other bidirectional correlation coefficients. In particular, this coefficient is found to be closely…

矩阵 von Mises–Fisher 与 Bingham 分布的极大似然估计AI 解读

It has been conjectured by Khatri and Mardia that with probability one MLEs for the parameters of the von Mises-Fisher matrix distribution exist and are unique. We prove that, except for small sample sizes, this conjecture is true, both in the case where the parameter matrix has known rank and in the unrestricted case. The corresponding result for the matrix Bingham distribution is proven also.