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ALGORITHMICA 2001年第3期31卷 442-457页

作者： Smythe, RT Wellner, J Oregon State Univ Dept Stat Corvallis OR 97331 USA Univ Washington Dept Stat Seattle WA 98195 USA

We analyze the Shell Sort algorithm under the usual random permutation model. Using empirical distribution functions, we recover Louchard's result that the running time of the 1-stage of (2, 1)-Shell Sort has a limiting distribution given by the area under the absolute Brownian bridge. The analysis extends to (h, 1)Shell Sort where we find a limiting distribution given by the sum of areas under correlated absolute Brownian bridges. A variation of (h, 1)-Shell Sort which is slightly more efficient is presented and its asymptotic behavior analyzed.

关键词： empirical distribution functions Brownian bridge sorting algorithm random permutation model asymptotic distribution

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Goodness-of-fit-based outlier detection for Phase I monitoring

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COMMUNICATIONS IN STATISTICS-SIMULATION AND COMPUTATION 2018年第10期47卷 2979-2991页

作者： Yang, Xiaona Wang, Zhaojun Zi, Xuemin Nankai Univ Inst Stat Tianjin 300071 Peoples R China Nankai Univ LPMC Tianjin 300071 Peoples R China Tianjin Univ Technol & Educ Sch Sci Tianjin Peoples R China

Nonparametric charts are useful in statistical process control when there is a lack of or limited knowledge about the underlying process distribution. Most existing approaches in the literature of Phase I monitoring assume that outliers have the same distributions as the in-control sample but only differ in location or scale parameters, they may not be effective with distributional changes. This article develops a new procedure based on the integration of the classical Anderson-Darling goodness-of-fit test and the stepwise isolation method. Our proposed procedure is efficient in detecting potential shifts in location, scale, or shape, and thus it offers robust protection against variation in various underlying distributions. The finite sample performance of our method is evaluated through simulations and is compared with that of available outlier detection methods for Phase I monitoring.

关键词： Anderson-Darling test distributional change empirical distribution functions Nonparametric Stepwise procedure

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Analysis of a Statistical Relationship Between Dose and Error Tallies in Semiconductor Digital Integrated Circuits for Application to Radiation Monitoring Over a Wireless Sensor Network

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IEEE TRANSACTIONS ON NUCLEAR SCIENCE 2017年第5期64卷 1151-1158页

作者： Colins, Karen Li, Liqian Liu, Yu Canadian Nucl Labs Chalk River ON K0J 1J0 Canada

Mass production of widely used semiconductor digital integrated circuits (ICs) has lowered unit costs to the level of ordinary daily consumables of a few dollars. It is therefore reasonable to contemplate the idea of an engineered system that consumes unshielded low-cost ICs for the purpose of measuring gamma radiation dose. Underlying the idea is the premise of a measurable correlation between an observable property of ICs and radiation dose. Accumulation of radiation-damage-induced state changes or error events is such a property. If correct, the premise could make possible low-cost wide-area radiation dose measurement systems, instantiated as wireless sensor networks (WSNs) with unshielded consumable ICs as nodes, communicating error events to a remote base station. The premise has been investigated quantitatively for the first time in laboratory experiments and related analyses performed at the Canadian Nuclear Laboratories. State changes or error events were recorded in real time during irradiation of samples of ICs of different types in a Co-60 gamma cell. From the error-event sequences, empirical distribution functions of dose were generated. The distribution functions were inverted and probabilities scaled by total error events, to yield plots of the relationship between dose and error tallies. Positive correlation was observed, and discrete functional dependence of dose quantiles on error tallies was measured, demonstrating the correctness of the premise. The idea of an engineered system that consumes unshielded low-cost ICs in a WSN, for the purpose of measuring gamma radiation dose over wide areas, is therefore tenable.

关键词： empirical distribution functions ionizing radiation sensors radiation dose measurement radiation monitoring wireless sensor networks (WSNs)

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P-boxes for cost uncertainty analysis

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MECHANICAL SYSTEMS AND SIGNAL PROCESSING 2013年第1-2期37卷 253-263页

作者： Mehl, Christopher H. OMNITEC Solut Inc Bethesda MD 20817 USA

After years of developing point estimates analysts knew were uncertain, the estimating and acquisition community has embraced the concept of viewing a cost estimate as a potential distribution of cost represented by a Cumulative distribution Function (CDF), commonly called the S-curve. Unfortunately, the very thing S-curves were intended to counter, i.e. the implication of preciseness that was inherent in point estimates for the cost, has become a preciseness about percentile values. Decision makers use the S-curve to make funding decisions. Decision makers, for example, have come to view the 50th percentile as an absolute and wonder why the number budgeted at 50% is shown as 30% when the estimate is updated. While there are many reasons for changes in the numbers, part of the error is inherent in the way the S-curve is developed. Ideally all input distributions in a cost estimate would be derived from reliable data and would have known shape and parameter values. In reality many inputs to an estimate are based on expert opinion and data of unknown relevance, making the distributions for these inputs uncertain. We can treat the S-curve, which is the CDF output of a cost analysis model, as an estimate of a "true" CDF, analogous to an empirical distribution Function (EDF), to help quantify the epistemic uncertainty inherent in the cost analysis process. Utilizing Kolmogorov-Smirnov and non-parametric quantile bounds, a p-box? is developed from which an analyst can now define a range of costs associated with specified levels of probability, or ranges in probability associated with specific costs. (C) 2012 Elsevier Ltd. All rights reserved.

关键词： Cost uncertainty estimation Cumulative distribution function empirical distribution functions Kolmogorov-Smirnov bounds Nonparametric bounds P-boxes

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A statistical method for the determination of the appropriate order in a general class of time series models

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COMMUNICATIONS IN STATISTICS-THEORY AND METHODS 2003年第4期32卷 875-891页

作者： Contreras-Cristán, A González-Barrios, JM Univ Nacl Autonoma Mexico IIMAS Dept Probabil & Stat Mexico City 01000 DF Mexico

We propose a method to determine the order q of a model in a general class of time series models. For the subset of linear moving average models (MA(q)), our method is compared with that of the sample autocorrelations. Since the sample autocorrelation is meant to detect a linear structure of dependence between random variables, it turns out to be more suitable for the linear case. However, our method presents a competitive option in that case, and for nonlinear models (NLMA(q)) it is shown to work better. The main advantages of our approach are that it does not make assumptions on the existence of moments and on the distribution of the noise involved in the moving average models. We also include an example with real data corresponding to the daily returns of the exchange rate process of mexican pesos and american dollars.

关键词： nonlinear moving average models measures of stochastic dependence sample autocorrelation empirical distribution functions moving average models

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Parameter estimation for pair-copula constructions

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BERNOULLI 2013年第2期19卷 462-491页

作者： Haff, Ingrid Hobaek Norwegian Comp Ctr NO-0373 Oslo Norway

We explore various estimators for the parameters of a pair-copula construction (PCC), among those the stepwise semiparametric (SSP) estimator, designed for this dependence structure. We present its asymptotic properties, as well as the estimation algorithm for the two most common types of PCCs. Compared to the considered alternatives, that is, maximum likelihood, inference functions for margins and semiparametric estimation, SSP is in general asymptotically less efficient. As we show in a few examples, this loss of efficiency may however be rather low. Furthermore, SSP is semiparametrically efficient for the Gaussian copula. More importantly, it is computationally tractable even in high dimensions, as opposed to its competitors. In any case, SSP may provide start values, required by the other estimators. It is also well suited for selecting the pair-copulae of a PCC for a given data set.

关键词： copulae efficiency empirical distribution functions hierarchical construction stepwise estimation vines

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Comparison of estimators for pair-copula constructions

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JOURNAL OF MULTIVARIATE ANALYSIS 2012年 110卷 91-105页

作者： Haff, Ingrid Hobaek Norwegian Comp Ctr NO-0373 Oslo Norway

We compare two of the most used estimators for the parameters of a pair-copula construction (FCC), namely the semiparametric (SP) and the stepwise semiparametric (SSP) estimators. By construction, the computational speed of the SSP estimator is considerably higher, at the expense of its asymptotic efficiency. Based on an extensive simulation study, we find that the performance of the SSP estimator is overall satisfactory compared to its contender. SSP loses some efficiency with respect to SP with increasing dependence, especially in the top levels of the FCC. On the other hand, the SSP estimator may suffer less under reduced sample sizes and misspecification of the model. Finally, it is the only real alternative for large-dimensional problems. Though it struggles with the top level parameters, the lower order dependences of the resulting estimated FCC mimic the true distribution well. All in all, this study supports the use of SSP in most applications. (C) 2011 Elsevier Inc. All rights reserved.

关键词： Semiparametric estimation Copulae Hierarchical structures empirical distribution functions Simulation study

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ORDER-STATISTICS FOR NONSTATIONARY TIME-SERIES

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ANNALS OF THE INSTITUTE OF STATISTICAL MATHEMATICS 1993年第4期45卷 665-686页

作者： TRAN, LT WU, B NATL CHENGCHI UNIV TAIPEI TAIWAN

Order statistics has an important role in statistical inference. The main purpose of this paper is to investigate order statistics, and also explore its applications in the analysis of nonstationary time series. Our results show that linear functions of order statistics for a large class of time series are asymptotically normal. The methods of proof involve approximations of serially dependent random variables by independent ones. The problems of testing for the existence of a linear trend and the problem of testing randomness versus serial dependence are considered as applications.

关键词： NONSTATIONARY AUTOREGRESSIVE PROCESSES ABSOLUTE REGULARITY empirical distribution functions ORDER STATISTICS

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Interactive effects between nest microclimate and nest vegetation structure confirm microclimate thresholds for Lesser Prairie-Chicken nest survival

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CONDOR 2016年第4期118卷 728-746页

作者： Grisham, Blake A. Godar, Alixandra J. Boal, Clint W. Haukos, David A. Texas Tech Univ Dept Nat Resources Management Lubbock TX 79409 USA Texas Tech Univ US Geol Survey Texas Cooperat Fish & Wildlife Res Unit Lubbock TX 79409 USA Kansas State Univ US Geol Survey Kansas Cooperat Fish & Wildlife Res Unit Manhattan KS 66506 USA

The range of Lesser Prairie-Chickens (Tympanuchus pallidicinctus) spans 4 unique ecoregions along 2 distinct environmental gradients. The Sand Shinnery Oak Prairie ecoregion of the Southern High Plains of New Mexico and Texas is environmentally isolated, warmer, and more arid than the Short-Grass, Sand Sagebrush, and Mixed-Grass Prairie ecoregions in Colorado, Kansas, Oklahoma, and the northeast panhandle of Texas. Weather is known to influence Lesser Prairie-Chicken nest survival in the Sand Shinnery Oak Prairie ecoregion;regional variation may also influence nest microclimate and, ultimately, survival during incubation. To address this question, we placed data loggers adjacent to nests during incubation to quantify temperature and humidity distribution functions in 3 ecoregions. We developed a suite of a priori nest survival models that incorporated derived microclimate parameters and visual obstruction as covariates in Program MARK. We monitored 49 nests in Mixed-Grass, 22 nests in Sand Shinnery Oak, and 30 nests in Short-Grass ecoregions from 2010 to 2014. Our findings indicated that (1) the Sand Shinnery Oak Prairie ecoregion was hotter and drier during incubation than the Mixed-and Short-Grass ecoregions;(2) nest microclimate varied among years within ecoregions;(3) visual obstruction was positively associated with nest survival;but (4) daily nest survival probability decreased by 10% every half-hour when temperature was greater than 34 degrees C and vapor pressure deficit was less than -23 mmHg during the day (about 0600-2100 hours). Our major finding confirmed microclimate thresholds for nest survival under natural conditions across the species' distribution, although Lesser Prairie-Chickens are more likely to experience microclimate conditions that result in nest failures in the Sand Shinnery Oak Prairie ecoregion. The species would benefit from identification of thermal landscapes and management actions that promote cooler, more humid nest microclimates.

关键词： empirical distribution functions humidity Kansas Lesser Prairie-Chicken microclimate nest survival New Mexico temperature Texas Tympanuchus pallidicinctus

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Two-sample Dvoretzky-Kiefer-Wolfowitz inequalities

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STATISTICS & PROBABILITY LETTERS 2012年第3期82卷 636-644页

作者： Wei, Fan Dudley, Richard M. MIT Cambridge MA 02139 USA

The Dvoretzky-Kiefer-Wolfowitz (DKW) inequality says that if F-n is an empirical distribution function for variables lid. with a distribution function F, and K-n is the Kolmogorov statistic root n sup(x) vertical bar(F-n - F)(x)vertical bar, then there is a constant C such that for any M > 0, Pr(K-n > M) <= C exp (-2M(2)). Massart proved that one can take C = 2 (DKWM inequality), which is sharp for F continuous. We consider the analogous Kolmogorov-Smirnov statistic for the two-sample case and show that for m = n, the DKW inequality holds for n >= n(0) for some C depending on n(0), with C = 2 if and only if no >= 458. The DKWM inequality fails for the three pairs (m, n) with 1 <= m < n <= 3. We found by computer search that the inequality always holds for n >= 4 if 1 >= m < n <= 200, and further for n = 2m if 101 <= m <= 300. We conjecture that the DKWM inequality holds for all pairs in <= n with the 457 + 3 = 460 exceptions mentioned. (C) 2011 Elsevier B.V. All rights reserved.

关键词： Kolmogorov-Smirnov test empirical distribution functions

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