Counting by Weighing: An Alternative Sampling Scheme

Abstract

In the last decades, various methods are applied for evaluating different performance measures of change-point detection schemes. In only some cases—recent examples are Chandrasekaran et al. (Chandrasekaran, S.; English, J.R.; Disney, R.L. Modeling and analysis of EWMA control schemes with variance-adjusted control limits. IIE Transactions 1995, 277, 282–290) and Steiner (Steiner, S.H. EWMA control charts with time-varying control limits and fast initial response. Journal of Quality Technology 1999, 31 (1), 75–86)—EWMA schemes with varying control limits are considered. However, EWMA charts with just these limits are sometimes more appropriate than those with fixed limits. Here, a computational approach is presented which allows to compute the usual performance measures with high precision. The main idea is connected to earlier results of Madsen and Conn (Madsen, R.W.; Conn, P.S. Ergodic behavior for nonnegative kernels. Ann. Probab. 1973, 1, 995–1013), Woodall (Woodall, W.H. The distribution of the run length of one-sided CUSUM procedures for continuous random variables. Technometrics 1983, 25, 295–301), and Waldmann (Waldmann, K.-H. Bounds for the distribution of the run length of geometric moving average charts. J. R. Stat. Soc., Ser. C, Appl. Stat. 1986a, 35, 151–158). Additionally, quantities as the steady-state ARL and the steady-state distribution of the chart statistic can be computed very precisely.     

ANALYSIS OF THE LIKELIHOOD FUNCTION FOR MARKOV‐SWITCHING VAR(CH) MODELS

In this work, we give simple matrix formulae for maximum likelihood estimates of parameters in a broad class of vector autoregressions subject to Markovian changes in regime. This allows us to determine explicitly the asymptotic variance–covariance matrix of the estimators, giving a concrete possibility for the use of the classical testing procedures. In the context of multivariate autoregressive conditional heteroskedastic models with changes in regime, we provide formulae for the analytic derivatives of the log likelihood. Then we prove the consistency of some maximum likelihood estimators and give some formulae for the asymptotic variance of the different estimators.     

Computer Algebra Derivation of the Bias of Linear Estimators of Autoregressive Models

Abstract. A symbolic method which can be used to obtain the asymptotic bias and variance coefficients to order O(1/n) for estimators in stationary time series is discussed. Using this method, the large‐sample bias of the Burg estimator in the AR(p) for p = 1, 2, 3 is shown to be equal to that of the least squares estimators in both the known and unknown mean cases. Previous researchers have only been able to obtain simulation results for the Burg estimator's bias because this problem is too intractable without using computer algebra. The asymptotic bias coefficient to O(1/n) of Yule–Walker as well as least squares estimates is also derived in AR(3) models. Our asymptotic results show that for the AR(3), just as in the AR(2), the Yule–Walker estimates have a large bias when the parameters are near the nonstationary boundary. The least squares and Burg estimates are much better in this situation. Simulation results confirm our findings.     

Sequential model selection method for nonparametric autoregression

Abstract

In this article, the nonparametric autoregression estimation problem for quadratic risks is considered. To this end, we develop a new adaptive sequential model selection method based on the efficient sequential kernel estimators proposed by Arkoun and Pergamenshchikov (2016). Moreover, we develop a new analytical tool for general regression models to obtain the non-asymptotic sharp oracle inequalities for both usual quadratic and robust quadratic risks. Then, we show that the constructed sequential model selection procedure is optimal in the sense of oracle inequalities.     

Some Almost-Sure Convergence Properties Useful in Sequential Analysis

Abstract

Kim and Nelson propose sequential procedures for selecting the simulated system with the largest steady-state mean from a set of alternatives that yield stationary output processes. Each procedure uses a triangular continuation region so that sampling stops when the relevant test statistic first reaches the region's boundary. In applying the generalized continuous mapping theorem to prove the asymptotic validity of these procedures as the indifference-zone parameter tends to zero, we are given (i) a sequence of functions on the unit interval (which are right-continuous with left-hand limits) converging to a realization of a certain Brownian motion process with drift; and (ii) a sequence of triangular continuation regions corresponding to the functions in sequence (i) and converging to the triangular continuation region for the Brownian motion process. From each function in sequence (i) and its corresponding continuation region in sequence (ii), we obtain the associated boundary-hitting point; and we prove that the resulting sequence of such points converges almost surely to the boundary-hitting point for the Brownian motion process. We also discuss the application of this result to a statistical process-control scheme for autocorrelated data and to other selection procedures for steady-state simulation experiments.

     

Modified Three-Stage Sampling for Fixed-Width Interval Estimation of the Common Variance of Equicorrelated Normal Distributions

Abstract

In this work, we present a modified three-stage sampling procedure to construct fixed-width confidence intervals of the common variance of equicorrelated normal distributions. We derive the exact distribution of the stopping variable of this sampling scheme and also the exact distribution of the estimator of the common variance at stopping. The modified three-stage sampling substantially reduces the expected sample size compared to that of the two-stage sampling scheme of Haner and Zacks (2013 Haner , D. M. and Zacks , S. ( 2013 ). On Two-Stage Sampling for Fixed-Width Interval Estimation of the Common Variance of Equi-Correlated Normal Distributions , Sequential Analysis 32 : 1 – 13 .[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]). The coverage probabilities of the proposed interval estimators are computed exactly and are compared with the coverage probabilities obtained by two-stage sampling. We derive exact formulae for the functionals of the stopping variable and the estimator of the common variance at stopping.     

The Slippage Configuration Is Always the Least Favorable Configuration for Two Alternatives

Abstract

Performance guarantees for multinomial selection procedures are usually derived by finding the least favorable configuration (LFC)—the one for which the probability of correct selection is minimum outside the indifference zone—and then evaluating the procedure on that configuration. The slippage configuration has been proved to be the LFC for several procedures and has been conjectured to be the worst for some other procedures. The principal result of this article unifies and extends all previous results for two alternatives: the slippage configuration is the worst for all procedures that have a finite expected number of trials and always select the alternative with more successes. A generalization of the key inequality in the proof to an arbitrary number of alternatives is conjectured.     

Measurement of Both Nonvolatile and Semi-Volatile Fractions of Fine Particulate Matter in Fresno,CA

An intensive sampling campaign was performed in Fresno, CA during December 2003 measuring fine particulate matter including both the semi-volatile and nonvolatile fractions of the aerosol. Both the newly developed R&P FDMS Monitor and a PC-BOSS have been shown to measure total PM _2.5 concentrations including semi-volatile nitrate and organic material. Good agreement was observed between the PC-BOSS and the R&P FDMS Monitor in this study with linear regression analysis resulting in a zero-intercept slope of 1.00 ± 0.02 and an R ² = 0.93. Several real-time measuring systems including the R&P Differential TEOM, the Met One BAMS, and a GRIMM Monitor were also employed and comparisons of total PM _2.5 mass were made with the R&P FDMS Monitor. Agreement among these various monitors was generally good. However, differences were sometimes seen. Reasons for observed differences in the real-time mass measurement systems are explained by the composition and complexity of the measured aerosol, most importantly the composition of semi-volatile material. A newly automated ion chromatographic system developed by Dionex was also field tested and compared to both R&P 8400N Nitrate and integrated PC-BOSS inorganic species measurements. Sulfate and nitrate determined by the Dionex and PC-BOSS systems agreed. However, nitrate measured by the 8400N was low during fog events compared to the other two systems.     

Source Apportionment of One-Hour Semi-Continuous Data Using Positive Matrix Factorization with Total Mass (Nonvolatile plus Semi-Volatile) Measured by the R&P FDMS Monitor

Positive matrix factorization (PMF) was used to elucidate sources of fine particulate material (PM _2.5 ) for a study conducted during July 2003 in Rubidoux, CA. One-h averaged semi-continuous measurements were made with a suite of instruments to provide PM _2.5 mass and chemical composition data. Total PM _2.5 mass concentrations (nonvolatile plus semi-volatile) were measured with a R&P filter dynamic measurement system (FDMS) and a conventional TEOM monitor was used to measure nonvolatile mass concentrations. Semi-volatile material (SVM) was calculated as the FDMS minus the TEOM determined PM _2.5 mass. PM _2.5 chemical species monitors included a R&P 5400 carbon monitor, an Anderson Aethalometer and a R&P 8400N nitrate monitor. Gas phase data including CO, NO ₂ , NO _x , and O ₃ were also collected during the sampling period. Two distinct PMF analysis were performed. In analysis 1, the TEOM was excluded from the analysis and in analysis 2, the SVM was excluded from the analysis. PMF2 was able to identify six factors from the data set and factors corresponding to both primary and secondary sources were identified. Factors were attributed to being primarily from automobile, diesel emissions, secondary nitrate formation, a secondary photochemical associated source, organic emissions and primary emissions. Good agreement was observed between the PMF predicted mass and the FDMS measured mass for both analyses.     

Development of Solar Drying

ABSTRACT

Importance of Solar Drying is increasing worldwide, especially in areas where the use of the abundant, renewable and clean solar energy is essentially advantageous. In the developing countries and in rural areas the traditional open-air drying methods should be substituted by the more effective and more economic solar drying technologies.

R&D needs should be considered in the basic research and experimental fields; in performance measurement; in the modelling-simulation-design and testing. The international co-operation of experts should be improved and more efforts would be needed in the policy and in the public information.     

Estimation of Survival Distributions Under Right-Censoring When Sample Size is Random

Abstract

The paper deals with two classes of unbiased nonparametric estimators of survival and cumulative hazard functions in a population subject to right-censoring. Both classes of estimators are based on a sequential sampling scheme, and are similar to the well-known Kaplan–Meier and Nelson–Aalen estimators.     

Data-Efficient Quickest Change Detection with On–Off Observation Control

Abstract

In this article we extend Shiryaev's quickest change detection formulation by also accounting for the cost of observations used before the change point. The observation cost is captured through the average number of observations used in the detection process before the change occurs. The objective is to select an on–off observation control policy that decides whether or not to take a given observation, along with the stopping time at which the change is declared, to minimize the average detection delay, subject to constraints on both the probability of false alarm and the observation cost. By considering a Lagrangian relaxation of the constraint problem and using dynamic programming arguments, we obtain an a posteriori probability-based two-threshold algorithm that is a generalized version of the classical Shiryaev algorithm. We provide an asymptotic analysis of the two-threshold algorithm and show that the algorithm is asymptotically optimal—that is, the performance of the two-threshold algorithm approaches that of the Shiryaev algorithm—for a fixed observation cost, as the probability of false alarm goes to zero. We also show, using simulations, that the two-threshold algorithm has good observation cost-delay trade-off curves and provides significant reduction in observation cost compared to the naïve approach of fractional sampling, where samples are skipped randomly. Our analysis reveals that, for practical choices of constraints, the two thresholds can be set independent of each other: one based on the constraint of false alarm and another based on the observation cost constraint alone.     

Interaction of hydrogen sulfide with the pristine and B&N-doped beryllium oxide nanotube: DFT study

ABSTRACT

In this study, hydrogen sulfide interaction with pristine, B-, N-, and B&N atom-doped beryllium oxide nanotube (BeONTs) is investigated by the density functional theory (DFT) method. At the first step, we considered different configuration models for the adsorption of H₂S on the surface of nanotube and then we selected 12 stable models for this study. The structures of all selected models are optimized and the quantum properties, thermodynamic parameters, natural bond orbitals (NBO), reduced density gradient (RDG), molecular electrostatic potential (MEP), and atom in molecule (AIM) parameters are calculated at the cam–B3LYP level of theory with 6–31G (d) base set. The obtained E_ads for the exterior surface of nanotube is exothermic and is in the range –3.15 to –28.34?Kcal mol^–1, and that for the interior surface is endothermic and is in the range 19.17 to 27.17?kcal mol^–1. The gap energy for pure, B-doped, N-doped, and B&N-doped BeONTs is 10.11, 10.03 (α spin), 10.13 (α spin), and 9.35?eV, respectively. The results of thermodynamic parameters, such as ΔG and ΔH values for the adsorption of H₂S, on the surface of B-doped BeONTs are more negative than other models and favorable in thermodynamic approach. The NBO, MEP, NMR, and HOMO–LUMO results confirm that the electron charge transfer occurs from H₂S molecule toward BeONTs, as a result the bonding type of H₂S?…?BeONTs is weak ionic.     

The steady-state behavior of multivariate exponentially weighted moving average control charts

Abstract

Multivariate exponentially weighted moving average (MEWMA) charts are popular, handy, and effective procedures to detect distributional changes in a stream of multivariate data. For doing appropriate performance analysis, dealing with the steady-state behavior of the MEWMA statistic is essential. Going beyond early papers, we derive quite accurate approximations of the respective steady-state densities of the MEWMA statistic. It turns out that these densities could be rewritten as the product of two functions depending on one argument only that allows feasible calculation. For proving the related statements, the presentation of the noncentral chi-square density deploying the confluent hypergeometric limit function is applied. Using the new methods it was found that for large dimensions, the steady-state behavior becomes different from what one might expect from the univariate monitoring field. Based on the integral equation driven methods, steady-state and worst-case average run lengths are calculated with higher accuracy than before. Eventually, optimal MEWMA smoothing constants are derived for all considered measures.     

Crystal structure of tetrabutylammonium [bis(1,3-dithiole-2-thione-4,5-dithiolato)bismuthate(1-)], [NBu4][Bi(dmit)2]

The crystal structure of ionic [NBu₄][Bi(dmit)₂] (5: Q=NBu₄), obtained from BiBr₃ and [NBu₄]₂[Zn(dmit)₂], has been determined. The bismuth atoms are six coordinate, as a consequence of two inter-anion Bi–S contacts with two neighbouring anions. In addition to the four intra-anion Bi—S bonds to the two thiolato S atoms of the dmit ligands [Bi–S between 2.5872(14) and 2.8082(13) Å: the inter-anion bonds involve thione S atoms [Bi—S(10)ⁱ=3.2548(11) and Bi–S(10)ⁱⁱ 3.4628(13) Å]. Excluding consideration of any lone pair effect, the Bi atoms have very distorted octahedral geometries. The anions form centrosymmetric pairs of chains with the shortest Bi–Bi distance of 4.180 Å being between the pairs of chains; overlapping parallel dmit ligands, within the pairs of chains, are separated by a perpendicular distance of 3.477(2) Å, with the dmit centroid–dmit centroid separation of 3.529 Å, ideal for π–π interaction.     

On Residual Variance Estimation in Autoregressive Models

In this paper we consider time series models belonging to the autoregressive (AR) family and deal with the estimation of the residual variance. This is important because estimates of the variance are involved in, for example, confidence sets for the parameters of the model, estimation of the spectrum, expressions for the estimated error of prediction and sample quantities used to make inferences about the order of the model. We consider the asymptotic biases for moment and least squares estimators of the residual variance, and compare them with known results when available and with those for maximum likelihood estimators under normality. Simulation results are presented for finite samples     

Selection among Bernoulli populations in comparison with a standard

Abstract

In this article we consider the problem of comparing several Bernoulli populations in order to identify the population producing the largest success probability that is also larger than a given standard. We propose a fixed sample size procedure for which we develop the probability of a correct selection and the least favorable configuration. We also propose a curtailed version of the fixed sample size procedure and show that the curtailed procedure reaches the same probability of a correct selection as the fixed sample size procedure, while using fewer observations. We provide tables to implement the procedures and illustrate them via an example. We use simulations to estimate the savings by the curtailment procedure.     

Uranium Recovery from Seawates by Adsorption

Abstract

Results are presented of a 10 weeks field experiment producing uranium from seawater by the so-called “adsorber-loop-concept”. For the adsorption process polyamidoxin (PAO) granulate has been used with grain sizes between 0.3–1.2 mm diameter. The performance of the adsorber and the efficiency of the adsorption process—especially with regard to high volume flows of seawater—are presented.     

ESTIMATION OF AUTOCOVARIANCE MATRICES FOR INFINITE DIMENSIONAL VECTOR LINEAR PROCESS

Consider an infinite dimensional vector linear process. Under suitable assumptions on the parameter space, we provide consistent estimators of the autocovariance matrices. In particular, under causality, this includes the infinite‐dimensional vector autoregressive (IVAR) process. In that case, we obtain consistent estimators for the parameter matrices. An explicit expression for the estimators is obtained for IVAR(1), under a fairly realistic parameter space. We also show that under some mild restrictions, the consistent estimator of the marginal large dimensional variance–covariance matrix has the same convergence rate as that in case of i.i.d. samples.