Weak Invariance Principles for Regression Rank Statistics

Abstract

Weak invariance principles are proved for regression rank statistics. As a consequence limit theorems for max- and L _p -functionals of partial sums of vectors of simple linear rank statistics are obtained. The results are useful in change point analysis, particularly in justification of application of permutation arguments, see Antoch and Hu?ková [Antoch, J.; Hu?ková, M. Detection of Structural Changes in Regression. Tatra Mountains Publications, 2003, 26, 1–15] and Hu?ková and Picek [Hu?ková, M.; Picek, J. M-tests for detection of structural changes in regression. In Statistical Data Analysis Based on the L ₁-Norm and Related Methods; Dodge, Y., Ed.; Birhäuser: Basel, 2002; 213–229]. The results of Hu?ková [Hu?ková, M. Limit theorems for rank statistics. Statist. Probab. Letters 1997, 32, 45–55] are generalized.     

Sequentially Updated Residuals and Detection of Stationary Errors in Polynomial Regression Models

Abstract

The question whether a time series behaves as a random walk or as a stationary process is an important and delicate problem, particularly arising in financial statistics, econometrics, and engineering. This article studies the problem to detect sequentially that the error terms in a polynomial regression model no longer behave as a random walk but as a stationary process. We provide the asymptotic distribution theory for a Monitoring procedure given by a control chart; i.e., a stopping time, which is related to a well-known unit root test statistic calculated from sequentially updated residuals. We provide a functional central limit theorem for the corresponding stochastic process that implies a central limit theorem for the control chart. The finite sample properties are investigated by a simulation study.     

CUSUM of Squares‐Based Tests for a Change in Persistence

Abstract. Using standardized cumulative sums of squared sub‐sample residuals, we propose a new ratio‐based test of the null hypothesis that a time series exhibits no change in its persistence structure [specifically that it displays constant I(1) behaviour] against the alternative of a change in persistence from trend stationarity to difference stationarity, or vice versa. Neither the direction nor location of any possible change under the alternative hypothesis need be assumed known. A key feature of our proposed test which distinguishes it from extant tests for persistence change [certain of which test the null hypothesis of constant I(0) behaviour while others, like our proposed test, test the null hypothesis of constant I(1) behaviour] is that it displays no tendency to spuriously over‐reject when applied to series which, although not constant I(1) series, do not display a change in persistence [specifically are constant I(0) processes]. Moreover, where our ratio test correctly rejects the null of no persistence change, the tail in which the rejection occurs can also be used to identify the direction of change since, even in relatively small samples, the test almost never rejects in the right [left] tail when there is a change from I(0) to I(1) [I(1) to I(0)]. Again this useful property is not shared by existing tests. As a by‐product of our analysis, we also propose breakpoint estimators which are consistent where the timing of the change in persistence is unknown.     

Identification of Components of Male-Produced Pheromone of Coffee White Stemborer, Xylotrechus quadripes

The coffee white stem borer, Xylotrechus quadripes Chevrolat (Coleoptera: Cerambycidae), is the foremost pest of arabica coffee in India, Sri Lanka, China, Vietnam, and Thailand. Previous work showed that female beetles were attracted to traps baited with male beetles. Analyses of volatiles from male X. quadripes of Indian origin by gas chromatography (GC) linked to electroantennographic (EAG) recording from a female beetle antenna showed three male-specific components comprising more than 90% of the volatiles, two of which elicited EAG responses. The major EAG-active component was produced at up to 2 μg hr⁻¹ insect⁻¹ and was identified as (S)-2-hydroxy-3-decanone (I) by comparison of GC data, and mass (MS), infrared, and nuclear magnetic resonance (NMR) spectra with those of synthetic standards. The second component was identified as 3-hydroxy-2-decanone (II) produced in part by isomerization of I under the conditions of the GC analysis, although the NMR spectrum suggested it is naturally produced at up to 7% of I. The minor component that elicited an EAG response, present at 7% of the amount of I, was identified as (S,S)-2,3-dihydroxyoctane (III) from GC and MS data. 2-Hydroxy-3-octanone (0.2–0.5% of I), 2,3-decanedione (2% of I), 2-phenylethanol (3% of I), and octanoic acid (4% of I) were also identified in volatiles from male beetles. A general, stereospecific synthetic route to the enantiomers of 2-hydroxy-3-alkanones from the enantiomers of ethyl lactate was developed. The enantiomers of III were synthesized from (E)-2-octene by Sharpless asymmetric dihydroxylation. (S)-(I) was attractive to male X. quadripes in laboratory bioassays, but addition of (S,RS)-(III) at 10% of I reduced attractiveness. In field trials carried out in India with sticky, cross-vane traps, (S)- and (RS)-(I) attracted male X. quadripes and addition of (S,S)-(III) at 10% of I reduced attractiveness. Significant numbers of female Demonax balyi Pascoe (Coleoptera: Cerambycidae) were sometimes caught in traps baited with (S)-(I) alone.     

Bootstrap procedures for detecting multiple persistence shifts in heteroskedastic time series

This article proposes new bootstrap procedures for detecting multiple persistence shifts in a time series driven by non-stationary volatility. The assumed volatility process can accommodate discrete breaks, smooth transition variation as well as trending volatility. We develop wild bootstrap sup-Wald tests of the null hypothesis that the process is either stationary [I(0)] or has a unit root [I(1)] throughout the sample. We also propose a sequential procedure to estimate the number of persistence breaks based on ordering the regime-specific bootstrap p-values. The asymptotic validity of the advocated procedures is established both under the null of stability and a variety of persistence change alternatives. A comparison with existing tests that assume homoskedasticity illustrates the finite sample improvements offered by our methods. An application to OECD inflation rates highlights the empirical relevance of the proposed approach and weakens the case for persistence change relative to existing procedures.     

NON-PARAMETRIC ESTIMATION WITH STRONGLY DEPENDENT MULTIVARIATE TIME SERIES

Smooth non-parametric kernel density and regression estimators are studied when the data are strongly dependent. In particular, we derive central (and non-central) limit theorems for the kernel density estimator of a multivariate Gaussian process and an infinite-order moving average of an independent identically distributed process, as well as the estimator's consistency for other types of data, such as non-linear functions of a Gaussian process. We find that the kernel density estimator at two different points, under certain conditions, is not only perfectly correlated but may converge to the same random variable. Also, central (and non-central) limit theorems of the non-parametric kernel regression estimator are studied. One important and surprising characteristic found is that its asymptotic variance does not depend on the point at which the regression function is estimated and also that its asymptotic properties are the same whether or not regressors are strongly dependent. Finally, a Monte Carlo experiment is reported to assess the behaviour of the estimators in finite samples.     

Testing for parameter stability in nonlinear autoregressive models

In this article we develop testing procedures for the detection of structural changes in nonlinear autoregressive processes. For the detection procedure, we model the regression function by a single layer feedforward neural network. We show that CUSUM‐type tests based on cumulative sums of estimated residuals, that have been intensively studied for linear regression, can be extended to this case. The limit distribution under the null hypothesis is obtained, which is needed to construct asymptotic tests. For a large class of alternatives, it is shown that the tests have asymptotic power one. In this case, we obtain a consistent change‐point estimator which is related to the test statistics. Power and size are further investigated in a small simulation study with a particular emphasis on situations where the model is misspecified, i.e. the data is not generated by a neural network but some other regression function. As illustration, an application on the Nile data set as well as S&P log‐returns is given.     

Uniform limit theorems for the integrated periodogram of weakly dependent time series and their applications to Whittle's estimate

Abstract. We prove uniform convergence results for the integrated periodogram of a weakly dependent time series, namely a strong law of large numbers and a central limit theorem. These results are applied to Whittle's parametric estimation. Under general weak‐dependence assumptions, the strong consistency and asymptotic normality of Whittle's estimate are established for a large class of models. For instance, the causal θ‐weak dependence property allows a new and unified proof of those results for autoregressive conditionally heteroscedastic (ARCH)(∞) and bilinear processes. Non‐causal η‐weak dependence yields the same limit theorems for two‐sided linear (with dependent inputs) or Volterra processes.     

Living tandem free radical polymerization of a liquid crystalline monomer

Treatment of 1-β-(4′-acetylphenyl)vinyl-3-vinyl-1,1,3,3-tetramethyldisiloxane (I) (an AB₂ monomer) with dihydridocarbonyltris(triphenylphosphine)ruthenium (Ru) leads to a hyperbranched material, poly[1-β-(4′-acetylphenyl)vinyl-3-vinyl-1,1,3,3-tetramethyldisiloxane] (II). I has been prepared by a Pd catalyzed Heck reaction between 4-bromo-acetophenone and 1,3-divinyl-1,1,3,3-tetramethyldisiloxane. The structure of the soluble hyperbranched material (II) has been determined by ¹H, ¹³C and ²⁹Si NMR, as well as by IR and UV spectroscopy. It has also been characterized by GPC, TGA, DSC and elemental analysis. Polymerization occurs by Ru catalyzed addition of the aromatic C−H bonds which are ortho to the activating acetyl group of I across the C−C double bond of the terminal Si-vinyl group in an anti-Markovnikov manner. Received: 8 September 1997/Revised version: 19 October 1997/Accepted: 20 November 1997     

A New Method for Evaluating the Effectiveness of Separation Processes

Abstract

A new method for evaluating the ability of a sorting process to attain a specific set of goals is presented. This ability is characterized by an inefficiency number, I, which ranges between zero and unity. Processes which fractionate objects without committing sorting errors are characterized by an I of zero. Separation processes which merely subdivide a collection of objects without regard to their type are characterized by an I of unity. The inefficiency number of a sorting process is calculated from observations of the number and type of errors it makes while sorting a representative collection of objects. The cost of these sorting errors is then assessed by determining how much these errors detract from the goals of the sorting procedure. This cost is then divided by the cost of randomly sorting the same collection of objects to yield the inefficiency number of the process being evaluated.     

Synthesis, characterization, and platinum-catalyzed hydrosilation cross-linking of copoly(methylsilylene/1,4-phenylene/methylvinylsilylene): Properties of aromatic carbosilane thermosets

Low molecular weight copoly(methylsilylene/1,4-phenylene/methylvinylsilylene) (I) has been prepared by the reaction of a mixture of methyldichlorosilane and methylvinyldichlorosilane with the di-Grignard reagent prepared fromp-dibromobenzene.I has been characterized by¹H,¹³C, and²⁹Si NMR as well as FT-IR spectroscopy. Its molecular weight distribution has been determined by gel permeation chromatography (GPC), its thermal stability in nitrogen evaluated by thermogravimetric analysis (TGA), and its glass transition temperature (T _g) measured by differential scanning calorimetry (DSC). Platinum-catalyzed hydrosilation cross-linking ofI yields a thermoset material. The bending modulus (logE), tan·, andT _g of these cross-linked materials have been measured by dynamic mechanical thermal analysis (DMTA). Carbon fabric treated with catalytic amounts of platinum has been coated withI. Multilayers of coated carbon fabric have been consolidated (cured) to yield aromatic carbosilane/carbon composite materials. The interlaminar shear strength of these materials has been determined by short beam shear. Flexure strength and modulus of elasticity of these composite samples have been measured. The ultimate compressive strength and compression modulus as well as the tensile strength and elastic modulus of these have been determined.Presented at the XXVIth Silicon Symposium, Indiana University-Purdue University of Indianapolis, March 26–27, 1993.     

Degradation Measurements of Linen Fabrics

Abstract

Different artificial aging techniques, e.g., thermal, chemical, and photodegradation were applied to raw linen fabrics to produce artificial model samples that mimic the archeological ones for in conservation and consolidation experiments of ancient textile fabrics. The artificially aged samples were evaluated via several instrumental methods, i.e., mechanically, spectrophotometrically, x-ray diffraction, and viscosity measurements. The results indicated that degradation reactions including oxidation, took place at glycosidic bonds as well as at hydroxyl groups of cellulose to cause scission of the molecular chains where molecular weight decreases. These aging techniques are responsible for the changes in whiteness (W_I ) and yellowness (Y_I ) indices and also of color differences (ΔE ).     

The Slow Convergence of Ordinary Least Squares Estimators of α, β and Portfolio Weights under Long‐Memory Stochastic Volatility

We consider inference for the market model coefficients based on simple linear regression under a long memory stochastic volatility generating mechanism for the returns. We obtain limit theorems for the ordinary least squares (OLS) estimators of α and β in this framework. These theorems imply that the convergence rate of the OLS estimators is typically slower than if both the regressor and the predictor have long memory in volatility, where T is the sample size. The traditional standard errors of the OLS‐estimated intercept () and slope (), which disregard long memory in volatility, are typically too optimistic, and therefore the traditional t‐statistic for testing, say, α = 0 or β = 1, will diverge under the null hypothesis. We also obtain limit theorems (which imply slow convergence) for the estimated weights of the minimum variance portfolio and the optimal portfolio in the same framework. In addition, we propose and study the performance of a subsampling‐based approach to hypothesis testing for α and β. We conclude by noting that analogous results hold under more general conditions on long‐memory volatility models and state these general conditions which cover certain fractionally integrated exponential generalized autoregressive conditional heteroskedasticity (EGARCH) models.     

Synthesis of LiNiO2 cathode by the combustion method

To determine optimum conditions for the synthesis of LiNiO₂ by the combustion method, syntheses were carried out in air and under oxygen at various calcination temperatures and for different times. The electrochemical properties of the prepared samples were then investigated. The optimum conditions are preheating at 400 °C for 30 min in air in the mole ratio of urea to nitrate 3.6 and calcination at 750 °C for 36 h under O₂. The LiNiO₂ synthesized under these conditions had a first discharge capacity of 189 mAh g⁻¹ at 0.1 C-rate and relatively good cycling performance. This sample has a larger value of I ₀₀₃/I ₁₀₄ (smaller cation mixing) and a smaller R-factor (larger hexagonal ordering). Cycling performance was investigated in various voltage ranges. The first discharge capacity increased as the upper limit of the voltage range rose. The first discharge capacity was small but cycling performance was good when the sample was cycled in the voltage range with the lowest upper limit.     

Kinetic Aspects of Copper‐LIX ® Extraction from Nitrate/Nitric Acid Aqueous Solutions

Abstract

A comparative kinetic study of the extraction of copper from nitrate/nitric acid aqueous solutions by different classes of LIX ^® reagents (LIX 984N, LIX 860N‐I, LIX 84‐I, LIX 65N) was performed. Using a Rotating Diffusion Cell, the rate constants of the chemical reactions (forward and reverse) were estimated and compared. In the case of the mixed extractant LIX 984N, a synergistic effect was observed. The values of the forward reaction constants of all the extractants were found to be an order of magnitude higher than those of the reverse reaction. The relatively low E _a ‐values prove the substantial influence of the diffusion on the extraction kinetics under the experimental conditions studied.     

Association-Dissociation Phenomena in Biopolymers

Abstract

Association between biological macromolecules by non-covalent interactions is not only a wide-spread phenomenon in nature but also is of invaluable importance for life processes. In most cases the association is practically irreversible under experimentally accessible conditions, but a few examples are known where a reversible association-dissociation equilibrium can be studied. Such studies are of basic importance for the understanding of the association mechanisms and thus for the questions concerning the self-organization of living material. In addition, association-dissociation equilibria also must be assumed to play an important part in the regulative systems of the organisms. Very little data is available for the parameters of the micro-environment of the biological macromolecules in the different cell compartments, so that in vitro studies of regulative processes under a wide variety of solvent conditions are not only of academic interest. In the present review some examples of association-dissociation equilibria involving, e.g., chymotrypsin, chymotrypsinogen, glutamate dehydrogenase, hemerythrin, hemocyanins, phosphofructokinase, phosphorylase, tobacco mosaic virus protein, are compiled which are among the most thoroughly studied and which are considered to be typical representatives of the different aspects of this phenomenon. Both regulative and probably non-regulative associations are discussed. Closed equilibria serving as models for self-assembly of concrete structures, as well as open equilibria showing possibilities of looser but wide-ranging organizations are presented. Association between identical subunits is compared to that between different components, especially between proteins and nucleic acids, e.g., tRNA and aminoacyl tRNA synthetase, represser and DNA. The physico-chemical data which are known up to now are presented and the physiological aspects are discussed.     

Robust Wilcoxon‐Type Estimation of Change‐Point Location Under Short‐Range Dependence

We introduce a robust estimator of the location parameter for the change‐point in the mean based on Wilcoxon statistic and establish its consistency for L₁ near‐epoch dependent processes. It is shown that the consistency rate depends on the magnitude of the change. A simulation study is performed to evaluate the finite sample properties of the Wilcoxon‐type estimator under Gaussianity as well as under heavy‐tailed distributions and disturbances by outliers, and to compare it with a CUSUM‐type estimator. It shows that the Wilcoxon‐type estimator is equivalent to the CUSUM‐type estimator under Gaussianity but outperforms it in the presence of heavy tails or outliers in the data.     

Film formation from polystyrene–poly(butyl acrylate‐co‐methyl methacrylate) latex blends

We have employed steady sate fluorescence (SSF) and UV‐visible (UVV) techniques to determine the film formation behavior of latex blends. Blend films were prepared from mixtures of a high‐T_g pyrene (P) labeled polystyrene (PS) latex and a low‐T_g copolymer of poly(butyl acrylate‐co‐methyl methacrylate) (BuA/MMA4). Eleven different blend films were prepared in various hard/soft latex compositions at room temperature and annealed at elevated temperatures above glass‐transition (T_g) temperature of polystyerene for 10 min. Fluorescence intensity (I_P) from P was measured after each annealing step to monitor the stages of film formation. The evolution of transparency of latex films was monitored using photon transmission intensity, I_tr. Film morphologies were examined by atomic force microscopy (AFM). A significant change occurs in both I_P and I_tr intensities at a certain critical weight fraction of hard latex (R_c = 0.3). Above R_c, two distinct film formation stages, which are named as void closure and interdiffusion processes, were seen in fluorescence data. Transparency of the films was decreased with decreasing PS content, indicating that a phase separation process occurs between PS and BuA/MMA4 phases by thermal treatment, which results in turbid films. However, below R_c, no change was observed in I_P and I_tr upon annealing, whereas transparency increased overall with increasing BuA/MMA4 ratio. We explained this result as the phase separation process between PS and BuA/MMA4 blends. These results were also confirmed by AFM pictures. Film formation stages above R_c were modeled and related activation energies were calculated. POLYM. COMPOS., 27:431–442, 2006. © 2006 Society of Plastics Engineers     

Onset of marangoni convection in an initially quiescent spherical droplet subjected to the transient heat conduction

The onset of Marangoni convection in an initially quiescent spherical droplet subjected to the impulsive change in boundary temperature is analyzed under the linear theory. For this system in which instabilities are driven by interface-tension gradients, a stability analysis on regular cell modes is conducted on the basis of the propagation theory we have developed. The present stability analysis predicts that τ _c decreases with increasing Ma. For the limiting case of τ→0, the present study approaches the planar limit as expected.