Maximum integrated likelihood estimator of the interest parameter when the nuisance parameter is location or scale

The problem of estimation of an interest parameter in the presence of a nuisance parameter, which is either location or scale, is studied. Two estimators are considered: the usual maximum likelihood estimator and the estimator based on maximization of the integrated likelihood function. The estimators are compared, asymptotically, with respect to the bias and with respect to the mean squared error. The examples are given.     

A new method for the estimation of variance components directly from the sample covariance matrix

Statistical techniques for the estimation of variance components are usually associated with methodological and computational difficulties. In this paper a new computational method for the estimation of variance components directly from the sample covariance matrix is proposed. A comparison between this method and the maximum likelihood method for variance component estimation, based on their computational performance, is made. Cases for balanced and unbalanced simulated data assuming a two-way nixed model with correlated errors are considered, and a real-life application in animal breeding is presented.     

Estimation of a common parameter for pooled samples from the uniform distributions

Summary The problem to estimate a common parameter for the pooled sample from the uniform distributions is discussed in the presence of nuisance parameters. The maximum likelihood estimator (MLE) and others are compared and it is shown that the MLE based on the pooled sample is not (asymptotically) efficient.     

On the bounds of maximal entries in the principal eigenvector of symmetric nonnegative matrix

The upper bound of maximal entries in the principal eigenvector of a simple undirected connected graph is investigated in [Linear Algebra Appl. 310 (2000) 129]. We further investigate the maximal entry y^max_p in the principle eigenvector of symmetric nonnegative matrix with zero trace and obtain both sharp upper and lower bounds on the y^max_p. Particularly, this result answers the open question given in the above-mentioned reference     

Two-sample inference for normal mean vectors based on monotone missing data

Inferential procedures for the difference between two multivariate normal mean vectors based on incomplete data matrices with different monotone patterns are developed. Assuming that the population covariance matrices are equal, a pivotal quantity, similar to the Hotelling T² statistic, is proposed, and its approximate distribution is derived. Hypothesis testing and confidence estimation of the difference between the mean vectors based on the approximate distribution are outlined. The validity of the approximation is investigated using Monte Carlo simulation. Monte Carlo studies indicate that the approximate method is very satisfactory even for small samples. A multiple comparison procedure is outlined and the proposed methods are illustrated using an example.     

Using principal eigenvectors of adjacency matrices with added diagonal weights to compose centrality measures and identify bowtie structures for a digraph

Principal eigenvectors of adjacency matrices are often adopted as measures of centrality for a graph or digraph. However, previous principal-eigenvector-like measures for a digraph usually consider only the strongly connected component whose adjacency submatrix has the largest eigenvalue. In this paper, for each and every strongly connected component in a digraph, we add weights to diagonal elements of its member nodes in the adjacency matrix such that the modified matrix will have the new unique largest eigenvalue and corresponding principal eigenvectors. Consequently, we use the new principal eigenvectors of the modified matrices, based on different strongly connected components, not only to compose centrality measures but also to identify bowtie structures for a digraph.     

A two-step estimator of the extreme value index

In this paper, we build a two-step estimator , which satisfies , where is the well-known maximum likelihood estimator of the extreme value index. Since the two-step estimator can be calculated easily as a function of the observations, it is much simpler to use in practice. By properly choosing the first step estimator, such as the Pickands estimator, we can even get a shift and scale invariant estimator with the above property. The author thanks Laurens de Haan for motivating this work and giving helpful comments. The author also thanks two anonymous referees for their useful comments.     

Sharp Error Estimate for Maximum Likelihood Estimator of Nonstationary Diffusion Processes

We consider the maximum likelihood estimator of the unknown parameter in a class of nonstationary diffusion processes. We give further a precise estimate for the error of the estimator.     

A matrix formula for the skewness of maximum likelihood estimators

We give a general matrix formula for computing the second-order skewness of maximum likelihood estimators. The formula was firstly presented in a tensorial version by Bowman and Shenton (1998). Our matrix formulation has numerical advantages, since it requires only simple operations on matrices and vectors. We apply the second-order skewness formula to a normal model with a generalized parametrization and to an ARMA model.     

Approximate method for eigensensitivity analysis of a defective matrix

Based on the exact modal expansion method, an arbitrary high-order approximate method is developed for calculating the second-order eigenvalue derivatives and the first-order eigenvector derivatives of a defective matrix. The numerical example shows the validity of the method. If the different eigenvalues μ(1),…,μ(q) of the matrix are arranged so that |μ(1)|≤?≤|μ(q)| and satisfy the condition that |μ(q₁)|<|μ(q₁+1)| for some q₁<q, and if the approximate method only uses the left and right principal eigenvectors associated with μ(1),…,μ(q₁), then associated with μ(h)(h≤q₁) the errors of the eigenvalue and eigenvector derivatives by the pth-order approximate method are nearly proportional to |μ(h)/μ(q₁+1)|^p+1.     

Interval estimation for the mean of lognormal data with excess zeros

This paper considered interval estimations for the mean of lognormal distribution with excess zeros. We proposed two methods for interval estimation based on an approximate generalized pivotal quantity and a fiducial quantity. Simulation results show that the fiducial approach has highly accurate coverage probability and fairly low bias.     

Asymptotic normality of the principal components of functional time series

We establish the asymptotic normality of the sample principal components of functional stochastic processes under nonrestrictive assumptions which admit nonlinear functional time series models. We show that the aforementioned asymptotic depends only on the asymptotic normality of the sample covariance operator, and that the latter condition holds for weakly dependent functional time series which admit expansions as Bernoulli shifts. The weak dependence is quantified by the condition of L⁴$L^4$-m$m$-approximability which includes all functional time series models in practical use. We also demonstrate convergence of the cross covariance operators of the sample functional principal components to their counterparts in the normal limit.     

Second order asymptotic comparison of estimators of a common parameter in the double exponential case

Summary The problem to estimate a common parameter for the pooled sample from the double exponential distributions is discussed in the presence of nuisance parameters. The maximum likelihood estimator, a weighted median, a weighted mean and others are asymptotically compared up to the second order, i.e. the ordern ^−1/2 with the asymptotic expansions of their distributions. University of Electro-communications     

Border estimation of a disc observed with random errors solved in two steps

The problem of estimating the boundary of a uniform distribution on a disc is considered when data are measured with normally distributed additive random error. The problem is solved in two steps. In the first step the domain is subdivided into thin slices and the endpoints of slices are obtained within the framework of a corresponding one-dimensional problem. For the estimations implemented in that step the moment method and the maximum likelihood method are used. As there are numerical problems with calculating the variance of the estimator in the maximum likelihood approach, its good approximation is also given.     

Maximal and minimal entry in the principal eigenvector for the distance matrix of a graph

Let G=(V,E) be a simple, connected and undirected graph with vertex set V(G) and edge set E(G). Also let D(G) be the distance matrix of a graph G (Jane?i? et al., 2007) [13]. Here we obtain Nordhaus–Gaddum-type result for the spectral radius of distance matrix of a graph.A sharp upper bound on the maximal entry in the principal eigenvector of an adjacency matrix and signless Laplacian matrix of a simple, connected and undirected graph are investigated in Das (2009) [4] and Papendieck and Recht (2000) [15]. Generally, an upper bound on the maximal entry in the principal eigenvector of a symmetric nonnegative matrix with zero diagonal entries and without zero diagonal entries are investigated in Zhao and Hong (2002) [21] and Das (2009) [4], respectively. In this paper, we obtain an upper bound on minimal entry in the principal eigenvector for the distance matrix of a graph and characterize extremal graphs. Moreover, we present the lower and upper bounds on maximal entry in the principal eigenvector for the distance matrix of a graph and characterize extremal graphs.     

Logistic响应分布分位数的鞍点近似置信区间

论文基于响应数据，应用鞍点近似方法，给出构造Logistic响应分布分位数的近似置信区间的方法. 论文还对这种置信区间进行了模拟，并将该方法应用于QD8电雷管. 模拟和实例结果表明，当样本量较小时，该方法能够较好地推断Logistic响应分布的分位数     

Asymptotic Improvement of the Usual Confidence Set in a Multivariate Normal Distribution with Unknown Variance

We consider confidence sets for the mean of a multivariate normal distribution with unknown covariance matrix of the formσ²I. The coverage probability of the usual confidence set is shown to be improved asymptotically by centering at a shrinkage estimator.     

The precise asymptotic behavior of parameter estimators in Ornstein-Uhlenbeck process

In the present paper, we study the asymptotic behavior for estimator of the drift parameter in an Ornstein-Uhlenbeck process. The Lr-convergence rate and the precise asymptotics in the law of iterated logarithm and in the law of logarithm for the estimator are obtained. Moreover, we also get the complete moment convergence of this estimator. The main method of this paper is the deviation inequality for the quadratic functional.