Optimization in a multivariate generalized linear model situation

The purpose of this article is to find the settings of the factors which simultaneously optimize several mean responses in a multivariate generalized linear model (GLM) environment. The generalized distance approach, initially developed for the simultaneous optimization of several linear response surface models, is adapted to this multivariate GLM situation. An application of the proposed methodology is presented in the special case of a bivariate binary distribution resulting from a drug testing experiment concerning two responses, namely, the efficacy and toxicity of a particular drug combination. One of the objectives of this application is to find the dose levels of two drugs that simultaneously maximize their therapeutic effect and minimize any possible toxic effects. A second application is presented in the case of a multivariate gamma distribution.     

Approximation of solutions of generalized equations of Hammerstein type

Let $H$ be a real Hilbert space. For each $i=1,2,\dots ,m$, let $F_i,K_i:H\to H$ be bounded and monotone mappings. Assume that the generalized Hammerstein equation $u+{\sum }_{i=1}^m{K}_i{F}_{i}u=0$ has a solution in $H$. We construct a new explicit iterative sequence and prove strong convergence of the sequence to a solution of the generalized Hammerstein equation.     

One-sided tests in generalized linear dose–response models

This paper discusses the asymptotic null distribution of three asymptotically equivalent one-sided tests in generalized linear models with separate lines. Simple forms for the correlation coefficients, which appear in the weights of the asymptotic null distribution, that is a mixture of chi-squared distributions, are given. A particular structure is proposed for the experiments in order to simplify the correlations and consequently to allow the use of several approximations developed for the weights. It is showed that the hypothesis of synergism or antagonism between two compounds may be assessed, under parallelism, by one-sided tests. Finally, as illustration, the efficiency of a standard preparation is compared with the efficiency of four test preparations under a gamma log-linear model.     

The bivariate generalized linear failure rate distribution and its multivariate extension

The two-parameter linear failure rate distribution has been used quite successfully to analyze lifetime data. Recently, a new three-parameter distribution, known as the generalized linear failure rate distribution, has been introduced by exponentiating the linear failure rate distribution. The generalized linear failure rate distribution is a very flexible lifetime distribution, and the probability density function of the generalized linear failure rate distribution can take different shapes. Its hazard function also can be increasing, decreasing and bathtub shaped. The main aim of this paper is to introduce a bivariate generalized linear failure rate distribution, whose marginals are generalized linear failure rate distributions. It is obtained using the same approach as was adopted to obtain the Marshall-Olkin bivariate exponential distribution. Different properties of this new distribution are established. The bivariate generalized linear failure rate distribution has five parameters and the maximum likelihood estimators are obtained using the EM algorithm. A data set is analyzed for illustrative purposes. Finally, some generalizations to the multivariate case are proposed.     

Simplified specifications of a multivariate generalized autoregressive conditional heteroscedasticity model

Recent developments in multivariate volatility modeling suggest that the conditional correlation matrix can be described by a time series recursion, where the total number of parameters grows by the power-of-two of the dimension of financial returns. The power of two computational requirement makes high-dimensional multivariate volatility modeling very time consuming. In this paper, we propose two simplified specifications in a multivariate autoregressive conditional heteroscedasticity model. The first specification computes an unconditional correlation matrix from standardized residuals of the model. The second specification restricts the sum of the weights in a time-varying conditional correlation equation to be one. Applying a Bayesian sampling scheme allows the number of parameters to be reduced from the power of two of the dimension to the linear order of the dimension only and simultaneously provides us a framework for model comparison. We test our simplified specifications using simulated and real data from three sectoral indices in Hong Kong, three market indices and four exchange rates. The results suggest that our simplified specifications are more effective than the original formulation.     

A new statistic in the one-way multivariate analysis of variance

In the multivariate one-way analysis of variance a test statistic based solely on the rank orders of the data is proposed. In the two group case the statistic simplifies to a test of Puri and Sen [19]. Monte Carlo simulation techniques are used to evaluate the performance of the test statistic under various distributions. These evaluation include the simulated significance levels and power functions. By the nature of the proposed test it is evident that the new procedure is easier to implement than other existing rank based tests.     

Finite population estimation under generalized linear model assistance

Finite population estimation is the overall goal of sample surveys. When information regarding auxiliary variables are available, one may take advantage of general regression estimators (GREG) to improve sample estimates precision. GREG estimators may be derived when the relationship between interest and auxiliary variables is represented by a normal linear model. However, in some cases, such as when estimating class frequencies or counting processes means, Bernoulli or Poisson models are more suitable than linear normal ones. This paper focuses on building regression type estimators under a model-assisted approach, for the general case in which the relationship between interest and auxiliary variables may be suitably described by a generalized linear model. The finite population distribution of the variable of interest is viewed as if generated by a member of the exponential family, which includes Bernoulli, Poisson, gamma and inverse Gaussian distributions, among others. The resulting estimator is a generalized linear model regression estimator (GEREG). Its general form and basic statistical properties are presented and studied analytically and empirically, using Monte Carlo simulation experiments. Three applications are presented in which the GEREG estimator shows better performance than the GREG one.     

Approximation of linear constant systems

In this paper two problems are considered, the problem of modeling a given constant linear system by a constant linear system of fixed lower order, and the problem of finding a filter of fixed order to estimate a time-invariant random process from a related time-invariant random process. A quadratic criterion is used to select the optimum system in both cases. It is shown that the filtering problem reduces to the problem of modeling the corresponding Wiener filter. Necessary conditions for a solution are developed and stated in terms of standard Wiener filter theory notation. Numerical solution of the equations embodying the necessary conditions is considered and several examples are presented.     

A generalized linear integrate-and-fire neural model produces diverse spiking behaviors

For simulations of neural networks, there is a trade-off between the size of the network that can be simulated and the complexity of the model used for individual neurons. In this study, we describe a generalization of the leaky integrate-and-fire model that produces a wide variety of spiking behaviors while still being analytically solvable between firings. For different parameter values, the model produces spiking or bursting, tonic, phasic or adapting responses, depolarizing or hyperpolarizing after potentials and so forth. The model consists of a diagonalizable set of linear differential equations describing the time evolution of membrane potential, a variable threshold, and an arbitrary number of firing-induced currents. Each of these variables is modified by an update rule when the potential reaches threshold. The variables used are intuitive and have biological significance. The model's rich behavior does not come from the differential equations, which are linear, but rather from complex update rules. This single-neuron model can be implemented using algorithms similar to the standard integrate-and-fire model. It is a natural match with event-driven algorithms for which the firing times are obtained as a solution of a polynomial equation.     

A family of tests to detect misspecifications in the random-effects structure of generalized linear mixed models

Estimation in generalized linear mixed models for non-Gaussian longitudinal data is often based on maximum likelihood theory, which assumes that the underlying probability model is correctly specified. It is known that the results obtained from these models are not always robust against misspecification of the random-effects structure. Therefore, diagnostic tools for the detection of this misspecification are of the utmost importance. Three diagnostic tests, based on the eigenvalues of the variance-covariance matrices for the fixed-effects parameters estimates, are proposed in the present work. The power and type I error rate of these tests are studied via simulations. A very acceptable performance was observed in many cases, especially for those misspecifications that can have a big impact on the maximum likelihood estimators.     

On some implication type results involving generalized bounded Mocanu variations

This paper is the study of certain implication type results involving functions related to generalized bounded Mocanu variations. Basic properties involving generalized Bernardi integral transform, inclusion results and a sharp radius problem are investigated for such classes. Many interesting implications are observed as special cases of our results.     

Estimation in a linear multivariate measurement error model with a change point in the data

A linear multivariate measurement error model AX=B is considered. The errors in are row-wise finite dependent, and within each row, the errors may be correlated. Some of the columns may be observed without errors, and in addition the error covariance matrix may differ from row to row. The columns of the error matrix are united into two uncorrelated blocks, and in each block, the total covariance structure is supposed to be known up to a corresponding scalar factor. Moreover the row data are clustered into two groups, according to the behavior of the rows of true A matrix. The change point is unknown and estimated in the paper. After that, based on the method of corrected objective function, strongly consistent estimators of the scalar factors and X are constructed, as the numbers of rows in the clusters tend to infinity. Since Toeplitz/Hankel structure is allowed, the results are applicable to system identification, with a change point in the input data.     

Approximate estimation in generalized linear mixed models with applications to the Rasch model

This article discusses two different approaches to estimate the difficulty parameters (fixed effects parameters) and the variance of latent traits (variance components) in the mixed Rasch model. The first one is the generalized estimating equations (GEE2) which uses an approximation of the marginal likelihood to derive the joint moments whilst the second approach uses the maximum of the approximate likelihood. We illustrate these methods with a simulation study and with an analysis of real data from a quality of life.     

A characterization of the generalized spectral radius with Kronecker powers

Based on Turán’s power sum theory, we extend a recent result obtained by Blondel and Nesterov [Blondel, V. D., & Nesterov, Y. (2005). Computationally efficient approximations of the joint spectral radius, SIAM Journal on Matrix Analysis and Applications, 27, 256–272], by deriving a new characterization of the generalized spectral radius in terms of Kronecker powers.     

Size and power properties of some tests in the Birnbaum-Saunders regression model

The Birnbaum-Saunders distribution has been used quite effectively to model times to failure for materials subject to fatigue and for modeling lifetime data. In this paper we obtain asymptotic expansions, up to order n^−1/2 and under a sequence of Pitman alternatives, for the non-null distribution functions of the likelihood ratio, Wald, score and gradient test statistics in the Birnbaum-Saunders regression model. The asymptotic distributions of all four statistics are obtained for testing a subset of regression parameters and for testing the shape parameter. Monte Carlo simulation is presented in order to compare the finite-sample performance of these tests. We also present two empirical applications.     

基于多元线性回归模型与应用软件对世博会影响力评估研究

通过统计数据和EXCEL软件对数据的处理,在对处理结果分析的基础上,建立多元线性回归模型,通过合理的计算和总结,对定量评估2010年上海世博会的经济影响力进行了肯定的研究。     

A nonparametric circular–linear multivariate regression model with a rule-of-thumb bandwidth selector

The purpose of this paper is to propose a nonparametric circular–linear multivariate regression model using a kernel-weighted local linear method. The case of several linear regressors and one circular regressor is considered. We extend results on the asymptotic bias and variance of the linear multivariate variable to the case of circular–linear multivariate variable. The rule-of-thumb selector is used to establish the optimal bandwidths for the nonparametric model. The suitability of the model is judged from the coefficient of determination. One simulation experiment and one real problem concerning wind energy are used to study the power performance of the nonparametric model.     

Structure and linear time recognition of 3-leaf powers

A graph G is the k-leaf power of a tree T if its vertices are leaves of T such that two vertices are adjacent in G if and only if their distance in T is at most k. Then T is the k-leaf root of G. This notion was introduced and studied by Nishimura, Ragde, and Thilikos motivated by the search for underlying phylogenetic trees. Their results imply a O(n³) time recognition algorithm for 3-leaf powers. Later, Dom, Guo, Hüffner, and Niedermeier characterized 3-leaf powers as the (bull, dart, gem)-free chordal graphs. We show that a connected graph is a 3-leaf power if and only if it results from substituting cliques into the vertices of a tree. This characterization is much simpler than the previous characterizations via critical cliques and forbidden induced subgraphs and also leads to linear time recognition of these graphs.     

The sizes and powers of some stochastic dominance tests: A Monte Carlo study for correlated and heteroskedastic distributions

Testing for stochastic dominance among distributions is an important issue in the study of asset management, income inequality, and market efficiency. This paper conducts Monte Carlo simulations to examine the sizes and powers of several commonly used stochastic dominance tests when the underlying distributions are correlated or heteroskedastic. Our Monte Carlo study shows that the test developed by Davidson and Duclos [R. Davidson, J.Y. Duclos, Statistical inference for stochastic dominance and for the measurement of poverty and inequality, Econometrica 68 (6) (2000) 1435–1464] has better size and power performances than two alternative tests developed by Kaur et al. [A. Kaur, B.L.S.P. Rao, H. Singh, Testing for second order stochastic dominance of two distributions, Econ. Theory 10 (1994) 849–866] and Anderson [G. Anderson, Nonparametric tests of stochastic dominance in income distributions, Econometrica 64 (1996) 1183–1193]. In addition, we find that when the underlying distributions are heteroskedastic, both the size and power of the test developed by Davidson and Duclos [R. Davidson, J.Y. Duclos, Statistical inference for stochastic dominance and for the measurement of poverty and inequality, Econometrica 68 (6) (2000) 1435–1464] are superior to those of the two alternative tests.