Tests of ordered hypotheses in linkage in heredity

The asymptotic null distribution of the likelihood ratio test for two cases of ordered hypotheses in a particular genetic model is considered. A simple iterative process is proposed in order to get the restricted estimates. It is shown that both tests have asymptotically a chi-bar squared distribution and the same size. A simulation study is also conducted in order to compare the usual unrestricted test with the corresponding one of ordered hypotheses. Finally, the results are extended to some special cases.     

Active set algorithms for isotonic regression; A unifying framework

In this and subsequent papers we will show that several algorithms for the isotonic regression problem may be viewed as active set methods. The active set approach provides a unifying framework for studying algorithms for isotonic regression, simplifies the exposition of existing algorithms and leads to several new efficient algorithms. We also investigate the computational complexity of several algorithms.In this paper we consider the isotonic regression problem with respect to a complete order where eachw _i is strictly positive and eachy _i is an arbitrary real number. We show that the Pool Adjacent Violators algorithm (due to Ayer et al., 1955; Miles, 1959; Kruskal, 1964), is a dual feasible active set method and that the Minimum Lower Set algorithm (due to Brunk et al., 1957) is a primal feasible active set method of computational complexity O(n ²). We present a new O(n) primal feasible active set algorithm. Finally we discuss Van Eeden's method and show that it is of worst-case exponential time complexity.This work was supported by the National Science and Engineering Research Council of Canada under Research Grant A8189 and an Ontario Graduate Scholarship.     

Validation of a screening method for the simultaneous identification of fat-soluble and water-soluble vitamins (A,E, B<Subscript>1</Subscript>, B<Subscript>2</Subscript> and B<Subscript>6</Subscript>) in an aqueous micellar medium of hexadecyltrimethylammonium chloride

Simultaneous determination of the fat-soluble vitamins A and E and the water-soluble vitamins B₁, B₂ and B₆ has been carried using a screening method from fluorescence contour graphs. These graphs show different colour zones in relation to the fluorescence intensity measured for the pair of excitation/emission wavelengths. The identification of the corresponding excitation/emission wavelength zones allows the detection of different vitamins in an aqueous medium regardless of the fat or water solubility of each vitamin, owing to the presence of a surfactant which forms micelles in water at the used concentration (over the critical micelle concentration). The micelles dissolve very water insoluble compounds, such as fat-soluble vitamins, inside the aggregates. This approach avoids the use of organic solvents in determining these vitamins and offers the possibility of analysing fat- and water-soluble vitamins simultaneously. The method has been validated in terms of detection limit, cut-off limit, sensitivity, number of false positives, number of false negatives and uncertainty range. The detection limit is about g L^–1. The screening method was applied to different samples such as pharmaceuticals, juices and isotonic drinks.     

The Projection onto a Direct Product of Convex Cones

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Extending the Iterative Convex Minorant Algorithm to the Cox Model for Interval-Censored Data

Abstract

The iterative convex minorant (ICM) algorithm proposed by Groeneboom and Wellner is fast in computing the NPMLE of the distribution function for interval censored data without covariates. We reformulate the ICM as a generalized gradient projection method (GGP), which leads to a natural extension to the Cox model. It is also easily extended to support Tibshirani's Lasso method. Some simulation results are also shown. For illustration we reanalyze two real datasets.     

Isotonic Regression under Lipschitz Constraint

The pool adjacent violators (PAV) algorithm is an efficient technique for the class of isotonic regression problems with complete ordering. The algorithm yields a stepwise isotonic estimate which approximates the function and assigns maximum likelihood to the data. However, if one has reasons to believe that the data were generated by a continuous function, a smoother estimate may provide a better approximation to that function. In this paper, we consider the formulation which assumes that the data were generated by a continuous monotonic function obeying the Lipschitz condition. We propose a new algorithm, the Lipschitz pool adjacent violators (LPAV) algorithm, which approximates that function; we prove the convergence of the algorithm and examine its complexity. The authors were supported by the Intramural Research Program of NIH, National Library of Medicine.     

对数正态分布场合下恒定应力加速寿命试验的保序估计

讨论了对数正态分布场合下恒定应力和加速寿命试验的最优线性无偏估计及保序估计,获得了保序估计的表达式,并给出了一个数值例子。     

Quantization of quadratic Liénard-type equations by preserving Noether symmetries

The classical quantization of a family of a quadratic Liénard-type equation (Liénard II equation) is achieved by a quantization scheme (Nucci 2011) [28] that preserves the Noether point symmetries of the underlying Lagrangian in order to construct the Schrödinger equation. This method straightforwardly yields the Schrödinger equation as given in Choudhury and Guha (2013) [6].     

凸规划下的保序回归

本文从约束最优化的观点来研究保序回归的解的问题 ,利用MATLAB给出了保序回归问题的求解方法 ,使得求解速度大大加快。本文的方法对进一步讲座其他保序回归问题具有一般性。     

On periodically isotonic climate change

In a view of the past two millennia, is the recent 160-year global warmth an anomaly or a continuation of past climate pattern? In this work, we present two non-parametric χ² tests based on the U-test for the isotonic change-point problem proposed in an unpublished work by G. Shen and H. Xu (henceforth abbreviated as SX (unpublished)) and apply them to the global warming data. Our tests do not require any structure assumption on the underlying the deterministic mean process {μ_t} under the periodically isotonic alternative, but accommodate a large class of the models for the random error process. Being more attractive, the two tests obviate estimation of {μ_t} and possess explicit asymptotic distributions for short-range dependence data, and have asymptotic power 1 even under the local alternative.