Estimating cumulative incidence functions when the life distributions are constrained

In competing risks studies, the Kaplan-Meier estimators of the distribution functions (DFs) of lifetimes and the corresponding estimators of cumulative incidence functions (CIFs) are used widely when no prior information is available for these distributions. In some cases better estimators of the DFs of lifetimes are available when they obey some inequality constraints, e.g., if two lifetimes are stochastically or uniformly stochastically ordered, or some functional of a DF obeys an inequality in an empirical likelihood estimation procedure. If the restricted estimator of a lifetime differs from the unrestricted one, then the usual estimators of the CIFs will not add up to the lifetime estimator. In this paper we show how to estimate the CIFs in this case. These estimators are shown to be strongly uniformly consistent. In all cases we consider, when the inequality constraints are strict the asymptotic properties of the restricted and the unrestricted estimators are the same, thus providing the asymptotic properties of the restricted estimators essentially “free of charge”. We give an example to illustrate our procedure.     

On a model selection problem from high-dimensional sample covariance matrices

Modern random matrix theory indicates that when the population size p is not negligible with respect to the sample size n, the sample covariance matrices demonstrate significant deviations from the population covariance matrices. In order to recover the characteristics of the population covariance matrices from the observed sample covariance matrices, several recent solutions are proposed when the order of the underlying population spectral distribution is known. In this paper, we deal with the underlying order selection problem and propose a solution based on the cross-validation principle. We prove the consistency of the proposed procedure.     

An exact branch-and-price algorithm for scheduling rescue units during disaster response

In disaster operations management, a challenging task for rescue organizations occurs when they have to assign and schedule their rescue units to emerging incidents under time pressure in order to reduce the overall resulting harm. Of particular importance in practical scenarios is the need to consider collaboration of rescue units. This task has hardly been addressed in the literature. We contribute to both modeling and solving this problem by (1) conceptualizing the situation as a type of scheduling problem, (2) modeling it as a binary linear minimization problem, (3) suggesting a branch-and-price algorithm, which can serve as both an exact and heuristic solution procedure, and (4) conducting computational experiments – including a sensitivity analysis of the effects of exogenous model parameters on execution times and objective value improvements over a heuristic suggested in the literature – for different practical disaster scenarios. The results of our computational experiments show that most problem instances of practically feasible size can be solved to optimality within ten minutes. Furthermore, even when our algorithm is terminated once the first feasible solution has been found, this solution is in almost all cases competitive to the optimal solution and substantially better than the solution obtained by the best known algorithm from the literature. This performance of our branch-and-price algorithm enables rescue organizations to apply our procedure in practice, even when the time for decision making is limited to a few minutes. By addressing a very general type of scheduling problem, our approach applies to various scheduling situations.     

Conditional information criteria for selecting variables in linear mixed models

In this paper, we consider the problem of selecting the variables of the fixed effects in the linear mixed models where the random effects are present and the observation vectors have been obtained from many clusters. As the variable selection procedure, here we use the Akaike Information Criterion, AIC. In the context of the mixed linear models, two kinds of AIC have been proposed: marginal AIC and conditional AIC. In this paper, we derive three versions of conditional AIC depending upon different estimators of the regression coefficients and the random effects. Through the simulation studies, it is shown that the proposed conditional AIC’s are superior to the marginal and conditional AIC’s proposed in the literature in the sense of selecting the true model. Finally, the results are extended to the case when the random effects in all the clusters are of the same dimension but have a common unknown covariance matrix.     

Recursive state and parameter estimation with applications in water resources

Hydrologic models, as well as measurements of hydrologic processes, are corrupted by noise. The Kalman filter is a convenient tool to estimate the true but unknown state of a hydrologic system. It is, however, difficult to specify the necessary error covariances. A procedure is proposed to estimate the error covariances recursively in a combined state and parameter filter. Applications of the procedure yield meaningful results for two hydrologic data series of very different character. A major benefit of the proposed algorithm seems to be its robustness against instability.     

Dimensionality in Manova Tested by a Closed Testing Procedure

The decision on dimensionality of the space spanned by general linear functions of the parameter matrix of a MANOVA model is considered. This problem is related to the investigation, whether graphically or analytically, of significant empirical departures from the overall null hypothesis on these functions. A closed testing procedure for a sequence of relevant hypotheses is proposed. Unlike the classical procedures based on asymptotic distributions of the likelihood ratio statistics, the proposed method ensures that the Type I familywise error rate does not exceed the nominalα-level. Also, it is consistent with testing the overall null hypothesis, while relying on tests of subsequent linear hypotheses implied by the former. Examples are given to compare the proposed procedure with a classical one.     

Bias-corrected empirical likelihood in a multi-link semiparametric model

In this paper, we investigate the empirical likelihood for constructing a confidence region of the parameter of interest in a multi-link semiparametric model when an infinite-dimensional nuisance parameter exists. The new model covers the commonly used varying coefficient, generalized linear, single-index, multi-index, hazard regression models and their generalizations, as its special cases. Because of the existence of the infinite-dimensional nuisance parameter, the classical empirical likelihood with plug-in estimation cannot be asymptotically distribution-free, and the existing bias correction is not extendable to handle such a general model. We then propose a link-based correction approach to solve this problem. This approach gives a general rule of bias correction via an inner link, and consists of two parts. For the model whose estimating equation contains the score functions that are easy to estimate, we use a centering for the scores to correct the bias; for the model of which the score functions are of complex structure, a bias-correction procedure using simpler functions instead of the scores is given without loss of asymptotic efficiency. The resulting empirical likelihood shares the desired features: it has a chi-square limit and, under-smoothing technique, high order kernel and parameter estimation are not needed. Simulation studies are carried out to examine the performance of the new method.     

二维Helmholtz方程不适定问题的一种算子软化正则法

本文研究带有混合边界的二维Helmholtz方程不适定问题.为了获得稳定的数值解，利用基于de la ValléePoussin算子的软化正则方法，得到了正则近似解，给出正则近似解与精确解之间在先验参数选取规则之下的误差估计，并通过数值实验检验了数据有噪声扰动时方法的有效性和稳定性.     

Nonparametric tests for conditional independence in two-way contingency tables

Testing for the independence between two categorical variables R and S forming a contingency table is a well-known problem: the classical chi-square and likelihood ratio tests are used. Suppose now that for each individual a set of p characteristics is also observed. Those explanatory variables, likely to be associated with R and S, can play a major role in their possible association, and it can therefore be interesting to test the independence between R and S conditionally on them. In this paper, we propose two nonparametric tests which generalise the chi-square and the likelihood ratio ideas to this case. The procedure is based on a kernel estimator of the conditional probabilities. The asymptotic law of the proposed test statistics under the conditional independence hypothesis is derived; the finite sample behaviour of the procedure is analysed through some Monte Carlo experiments and the approach is illustrated with a real data example.     

Thek-in-a-row procedure in selection theory

Summary Ak-in-a-row procedure is proposed to select the most demanded element in a set ofn elements. We show that the least favorable configuration of the proposed procedure which always selects the element when the same element has been demanded (or observed)k times in a row has a simple form similar to those of classical selection procedures. Moreover, numerical evidences are provided to illustrate the fact thatk-in-a-row procedure is better than the usual inverse sampling procedure and fixed sample size procedure when the distance between the most demanded element and the other elements is large and when the number of elements is small.     

On sparse estimation for semiparametric linear transformation models

Semiparametric linear transformation models have received much attention due to their high flexibility in modeling survival data. A useful estimating equation procedure was recently proposed by Chen et al. (2002) [21] for linear transformation models to jointly estimate parametric and nonparametric terms. They showed that this procedure can yield a consistent and robust estimator. However, the problem of variable selection for linear transformation models has been less studied, partially because a convenient loss function is not readily available under this context. In this paper, we propose a simple yet powerful approach to achieve both sparse and consistent estimation for linear transformation models. The main idea is to derive a profiled score from the estimating equation of Chen et al. [21], construct a loss function based on the profile scored and its variance, and then minimize the loss subject to some shrinkage penalty. Under regularity conditions, we have shown that the resulting estimator is consistent for both model estimation and variable selection. Furthermore, the estimated parametric terms are asymptotically normal and can achieve a higher efficiency than that yielded from the estimation equations. For computation, we suggest a one-step approximation algorithm which can take advantage of the LARS and build the entire solution path efficiently. Performance of the new procedure is illustrated through numerous simulations and real examples including one microarray data.     

Restricted colored permutations and Chebyshev polynomials

Several authors have examined connections between restricted permutations and Chebyshev polynomials of the second kind. In this paper we prove analogues of these results for colored permutations. First we define a distinguished set of length two and length three patterns, which contains only 312 when just one color is used. Then we give a recursive procedure for computing the generating function for the colored permutations which avoid this distinguished set and any set of additional patterns, which we use to find a new set of signed permutations counted by the Catalan numbers and a new set of signed permutations counted by the large Schröder numbers. We go on to use this result to compute the generating functions for colored permutations which avoid our distinguished set and any layered permutation with three or fewer layers. We express these generating functions in terms of Chebyshev polynomials of the second kind and we show that they are special cases of generating functions for involutions which avoid 3412 and a layered permutation.     

Robust discrimination under a hierarchy on the scatter matrices

Under normality, Flury and Schmid [Quadratic discriminant functions with constraints on the covariances matrices: some asymptotic results, J. Multivariate Anal. 40 (1992) 244-261] investigated the asymptotic properties of the quadratic discrimination procedure under hierarchical models for the scatter matrices, that is: (i) arbitrary scatter matrices, (ii) common principal components, (iii) proportional scatter matrices and (iv) identical matrices. In this paper, we study the properties of robust quadratic discrimination rules based on robust estimates of the involved parameters. Our analysis is based on the partial influence functions of the functionals related to these parameters and allows to derive the asymptotic variances of the estimated coefficients under models (i)-(iv). From them, we conclude that the asymptotic variances verify the same order relations as those obtained by Flury and Schmid [Quadratic discriminant functions with constraints on the covariances matrices: some asymptotic results, J. Multivariate Anal. 40 (1992) 244-261] for the classical estimators. We also perform a Monte Carlo study for different sample sizes and different hierarchies which shows the advantage of using robust procedures over classical ones, when anomalous data are present. It also confirms that better rates of misclassification can be achieved if a more parsimonious model among all the correct ones is used instead of the standard quadratic discrimination.     

无限阶段网络博弈中合作解的策略稳定性

合作博弈的经典合作解不满足时间一致性, 并缺乏策略稳定性. 本文研究无限阶段网络博弈合作解的策略稳定性理论. 首先建立时间一致的分配补偿程序实现合作解的动态分配, 然后建立针对联盟的惩罚策略, 给出合作解能够被强Nash均衡策略支撑的充分性条件, 最后证明了博弈中的惩罚策略局势是强Nash均衡, 从而保证了合作解的策略稳定性. 作为应用, 考察了重复囚徒困境网络博弈中Shapley值的策略稳定性.     

Equivariant quantizations for AHS-structures

We construct an explicit scheme to associate to any potential symbol an operator acting between sections of natural bundles (associated to irreducible representations) for a so-called AHS-structure. Outside of a finite set of critical (or resonant) weights, this procedure gives rise to a quantization, which is intrinsic to this geometric structure. In particular, this provides projectively and conformally equivariant quantizations for arbitrary symbols on general (curved) projective and conformal structures.     

An efficient method for calculating smoothing splines using orthogonal transformations

Summary A procedure for calculating the mean squared residual and the trace of the influence matrix associated with a polynomial smoothing spline of degree 2m–1 using an orthogonal factorization is presented. The procedure substantially overcomes the problem of ill-conditioning encountered by a recently developed method which employs a Cholesky factorization, but still requires only orderm ² n operations and ordermn storage.     

On the use of Hadamard expansions in hyperasymptotic evaluation of Laplace-type integrals—III: Clusters of saddle points

It is shown how the recently developed Hadamard expansion procedure can be applied to the hyperasymptotic evaluation of Laplace-type integrals containing a large variable when the phase function has a cluster of close-lying saddle points. The modification to this procedure that is required when the saddles in the cluster coalesce to form a single higher-order saddle is discussed. An example is also considered in which there is both a coalescence of saddles and a Stokes phenomenon as the phase of the large variable is allowed to vary. Numerical examples are given to illustrate the accuracy that can be obtained with this new procedure.     

Forecasting demand variation when there are stockouts

This paper addresses the common problem of forecasting demand when there are a large number of stockouts. The well-known single period stochastic inventory (or ‘newsboy’) problem provides the optimum, single period, stocking level for a product subject to stochastic demand. There are many situations where repetitive ‘newsboy’ solutions are implemented to guide stocking of repeat, but related, products, such as newspapers, magazines, or perishable groceries. Implementation of the ‘newsboy’ solution requires forecasts of the distribution of demand, although there are many plausible cost parameters that lead to optimum stocking policies where there is a high probability of a stockout. The company is, therefore, faced with the problem of attempting to forecast demand when a high percentage of the available sales data reflects the stock available for sale, rather than the true demand.A procedure has been developed¹ to improve estimates of the mean and variance of the distribution of demand when there are stockouts, but this procedure fails when the percentage of stockouts increases above 50%. A modified stockout adjustment procedure is presented in this paper, and it is shown that use of this new procedure can lead to greatly improved estimates of demand parameters, and greatly improved profitability, when there are a high percentage of stockouts.     

On the steepest descent approximation method for the zeros of generalized accretive operators

In this paper we present certain characteristic conditions for the convergence of the generalized steepest descent approximation process to a zero of a generalized strongly accretive operator, defined on a uniformly smooth Banach space. Our study is based on an important result of Reich [S. Reich, An iterative procedure for constructing zeros of accretive sets in Banach spaces, Nonlinear Anal. 2 (1978) 85–92] and given results extend and improve some of the earlier results which include the steepest descent approximation method.