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We consider component-wise estimation of order-restricted location/scale parameters of a general bivariate location/scale probability distribution under the Generalized Pitman Nearness (GPN) criterion, with a general loss function. In contrast to earlier studies on the same theme, that were mainly focused to specific probability distributions having independent components (marginals), we consider a general bivariate location/scale model and unify various studies made in the literature by developing some general results. These results are useful in finding improvements over arbitrary location/scale equivariant estimators, satisfying certain conditions, under the GPN criterion. In particular, under certain conditions, our results provide improvements over unrestricted Pitman nearest location/scale equivariant estimators and restricted maximum likelihood estimators. We illustrate the usefulness of these results through their applications to specific probability models. Additionally, we conduct a simulation study to compare the performances of different estimators under the GPN criterion with a specific loss function. Furthermore, we provide a real-life data analysis to demonstrate implementation of proposed estimators. [ABSTRACT FROM AUTHOR]

In this paper, the cumulative hazard function is used to solve estimation and prediction problems for generalized ordered statistics (defined in a general setup) based on any continuous distribution. The suggested method makes use of Rényi representation. The method can be used with type Ⅱ right-censored data as well as complete data. Extensive simulation experiments are implemented to assess the efficiency of the proposed procedures. Some comparisons with the maximum likelihood (ML) and ordinary weighted least squares (WLS) methods are performed. The comparisons are based on both the root mean squared error (RMSE) and Pitman's measure of closeness (PMC). Finally, two real data sets are considered to investigate the applicability of the presented methods.

In this paper, the cumulative hazard function is used to solve estimation and prediction problems for generalized ordered statistics (defined in a general setup) based on any continuous distribution. The suggested method makes use of R'enyi representation. The method can be used with type II right-censored data as well as complete data. Extensive simulation experiments are implemented to assess the effciency of the proposed procedures. Some comparisons with the maximum likelihood (ML) and ordinary weighted least squares (WLS) methods are performed. The comparisons are based on both the root mean squared error (RMSE) and Pitman's measure of closeness (PMC). Finally, two real data sets are considered to investigate the applicability of the presented methods. [ABSTRACT FROM AUTHOR]

Two modified ranked set sampling schemes are used to estimate the upper and lower quantiles of an underlying distribution. The performance of these sampling schemes is compared with that of ordinary ranked set sampling in view of Pitman's measure of closeness criterion. Actually, a way of choosing estimators is proposed in the paper based on Pitman closeness which demonstrates that the mentioned modifications on ranked set sampling are useful in the problem of quantile estimation. The results are applied to the location-scale family of distributions and the Pitman closeness probabilities are obtained numerically for the cases of exponential and uniform distributions. It is shown that the proposed sampling schemes would improve the performance of the point estimators of the population quantiles specially for extreme quantiles. The proposed procedure is used to estimate the quantiles of a real data set. [ABSTRACT FROM AUTHOR]

A single outlier sequence in which the distribution of the first observation differs from the others is considered and the properties of record statistics extracted from such sequence are studied. The problem of estimating the model parameters is discussed in the proportional hazard rate model. The maximum likelihood estimator and the uniformly minimum variance unbiased estimator are obtained for the special case of exponential distribution. The best linear unbiased (invariant) estimator is also derived for the location-scale family of distributions and their efficiencies are calculated. The problems of predicting the future records and reconstructing the past records are investigated. Various predictors and reconstructors are presented and some of their properties are stated. The precision of the obtained predictors are compared based on both the mean squared prediction error and Pitman's measure of closeness criteria. Finally, an example with real data is given to illustrate the results. [ABSTRACT FROM AUTHOR]

In this article, the performances of different point predictors of future record data based on some informative records from the two-parameter exponential distribution are studied in the sense of Pitman's measure of closeness. On the basis of one-sample and two-sample prediction problems, we apply the Pitman's measure of closeness to comparing the best unbiased, best invariant, maximum likelihood, conditional median predictors of the future records. Finally, all these predictors are compared with respect to the median unbiased predictor in the sense of Pitman closeness. Numerical computations for Pitman's closeness of all predictors are performed, presented and discussed to examine how these predictors are compared among themselves. On the whole, it is shown from our results that the best unbiased and conditional median predictors are very competitive predictors in terms of Pitman closeness when compared to all other predictors for both prediction problems. [ABSTRACT FROM AUTHOR]

Due to the high importance of the American economy, in the past, announcements of US macroeconomic data were shown to have a significant impact on financial markets in general, and on European stock markets in particular. However, as this effect may vary in time, this paper examines the changes in the impact of US macroeconomic news on the WIG20, the main index of the Warsaw Stock Exchange. Based on intraday data from 2004- 2019 we study the changes in significance and in the strength of the reaction of WIG20 to announcements of unexpected values of 13 indicators describing the American economy. On the basis of the event study analysis, we describe the reaction of the WIG20 index in the first few minutes after these kinds of announcements. [ABSTRACT FROM AUTHOR]

A study that would otherwise be eligible is commonly excluded from a meta-analysis when the standard error of its treatment-effect estimator, or the estimate of the variance of the outcomes, is not reported and cannot be recovered from the available information. This is wasteful when the estimate of the treatment effect is reported. We assess the loss of information caused by this practice and explore methods of imputation for the missing variance. The methods are illustrated on two sets of examples, one constructed specifically for illustration and another based on a published systematic review. [ABSTRACT FROM AUTHOR]

The proper choice of strata boundaries is an important factor determining the efficiency of the estimator of the considered characteristics of a population. In this article, the Cum 3√Di(x,z) Rule (i=3,4) for obtaining approximately optimum strata boundaries has been applied, taking into account a single-study variable along with two concomitant variables serving as the basis of the stratification variables. The relative efficiency of the proposed methods has been demonstrated theoretically and empirically by comparing them to a selection of already-existing methods in a simulation study with the use of the proportional allocation method. [ABSTRACT FROM AUTHOR]

In this article, a new proper and favorite stress-strength parameter has been introduced. The maximum likelihood and uniformly minimum variance unbiased estimators of the purposed parameter have been derived for the Exponential distribution. Moreover, the nonparametric estimator of this parameter has also been obtained as well as some important properties of this estimator. A simulation study and the analysis of a real data set have been done for illustrative purposes. [ABSTRACT FROM AUTHOR]

We perform a Bayesian analysis of the upper truncated Zeghdoudi distribution based on type II censored data. Using various loss functions including the generalized quadratic, entropy and Linex functions, we obtain Bayes estimators and the corresponding posterior risks. As tractable analytical forms of these estimators are out of reach, we propose Markov chain Monte-Carlo (MCMC) based simulation approach to study their performance. Moreover, given initial values for the parameters of the model, we obtain maximum likelihood estimators. Furthermore, we compare their performance with those of the Bayesian estimators using Pitman’s closeness criterion and integrated mean square error. Finally, we illustrate our approach through an example with real data. [ABSTRACT FROM AUTHOR]

Inferences about estimation and prediction of the two-parameter exponential distribution are based on generalized order statistics. Point and interval estimates are used for scale and location parameters. Unbiased point predictors and reconstructors are based upon pivotal quantities. The mean square error and Pitman's measure help assess the closeness of estimators and predictors. Point estimators of scale and location parameters and point predictors of future observations are computed in the application of durations until remission of 20 leukemia patients and in the application until failure of air-conditioning systems. [ABSTRACT FROM AUTHOR]

The inverse Gaussian distribution is one of the important continuous distributions and it has wide applications in many fields, which attracted the attention of many researchers to search for a good estimator for the parameters of this distribution. Therefore, in this study we examined the adoption of the Pitman method to find an estimator for the scale parameter of inverse Gaussian distribution along with other estimation methods such as the maximum likelihood method and Bayes method based on the gamma prior distribution. Simulation experiments were used to check the performance of the estimators based on the mean square error as a comparison criterion. The results showed that the Pitman estimator performed well in estimating the scale parameter in the inverse Gaussian distribution compared to other estimators in most of the simulated cases. [ABSTRACT FROM AUTHOR]

In this paper we consider the capital asset pricing model under the multivariate normal distribution for modeling asset returns. We develop and implement local influence diagnostic techniques not based on likelihood displacement. The main interest is to consider the test of mean-variance efficiency of a given portfolio as objective function. Sensitivity of maximum likelihood estimators of slopes is also considered. For this purpose, first and second-order local influence measures are calculated under a case weights perturbation scheme. In particular, for our objective functions, which have nonzero first derivative at the critical point, the proposed second-order measures are scale invariant, unlike the normal curvature. The performance of the proposed measures is illustrated by using two real data sets as well as a simulation study and a simulated data set. Empirical results seem to indicate that the Wald test statistic is less sensitive to atypical returns than maximum likelihood estimators of the slopes. By the other hand, there is some evidence about the convenience of jointly using first and second-order influence measures, to detect months/days with outlying returns, principally in Wald test statistic. [ABSTRACT FROM AUTHOR]

Assume that a linear regression model is written as a partitioned form. In such a case, it is quite convenient to determine the role of each subset of regressors, and to derive estimators of unknown partial parameters in the partitioned model. In this paper, we consider the relationships between the well-known ordinary least-squares estimators (OLSEs) and the best linear unbiased estimators (BLUEs) of the whole and partial mean parameter vectors in a general partitioned linear model with parameter restrictions. We first review some known results on the OLSEs and the BLUEs and their properties under general linear models. We then present a variety of necessary and sufficient conditions for OLSEs to be BLUEs under a general partitioned linear model with parameter restrictions. [ABSTRACT FROM AUTHOR]

In this paper, two new classes of estimators called the restricted almost unbiased ridge-type principal components estimator and the restricted almost unbiased Liu-type principal components estimator are introduced. For the two cases when the restrictions are true and not true, necessary and sufficient conditions for the superiority of the proposed estimators are derived and compared, respectively. Finally, A Monte Carlo simulation study is given to illustrate the performance of the proposed estimators. [ABSTRACT FROM AUTHOR]

Pitman's measure of closeness and mean square error of prediction are two well-known criteria for comparison between estimators and also between predictors. In a stationary first order multiplicative spatial autoregressive model, interpolation and extrapolation are compared based on these two criteria. A wide class of different innovation types are also studied containing Gaussian, exponential, asymmetric Laplace and extended skew t distributions. [ABSTRACT FROM AUTHOR]

By applying the empirical likelihood method, we construct a new weighted estimator of the conditional mean function for a left-truncated and right-censored model. Assuming that the observations form a stationary α-mixing sequence, we derive weak convergence with a certain rate and prove asymptotic normality of the weighted estimator. The asymptotic normality shows that the weighted estimator preserves the bias, variance, and, more importantly, automatic good boundary behavior of a local linear estimator of the conditional mean function. Also, a Berry-Esseen type bound for the weighted estimator is established. A simulation study is conducted to study the finite sample behavior of the new estimator and a real data application is provided. [ABSTRACT FROM AUTHOR]

Identifying the most influential nodes is one of the most promising domains in understanding and controlling propagation processes in complex network. According to the percolation theory, there is a epidemic threshold difference between the residual network and the original network after removing a node. We think that the threshold difference can represent the node’s global influence, which the absence of the node can promote or suppress the epidemic outbreak. By considering threshold differences and the local property (degree centrality), we propose a comprehensive influence method (CI) to identify the influential nodes. Comparing with the susceptible-infected-recovered model, the experimental results for nine empirical networks show that the CI method which can be applied to most networks with the different structures is more accurate than the K -shell, degree, closeness, and eigenvector centralities. [ABSTRACT FROM AUTHOR]

Two-sample scale problem is a well-known problem in the area of nonparametric inference. In this paper, a class of tests based on two-sample U-statistic, whose kernel is a function of sub-sample medians is proposed. An alternative expression in terms of ordered ranks is presented. Its large sample properties in terms of Pitman asymptotic relative efficiency (ARE) and small sample properties in terms of empirical power are discussed. [ABSTRACT FROM AUTHOR]

A single-outlier data set containing some independent random variables is considered such that all of observations expect one have the same distribution. To describe the model of interested, a location-scale family of distributions is used and the estimation problem of the parameters is studied when the data are collected under Type-II censoring scheme. Moreover, three different predictors are presented to predict the censored order statistics. They are also compared regarding both of mean squared prediction error and Pitman's measure of closeness criteria. The role of outlier parameter as well as censorship rate is studied on performance of proposed estimator and predictors. The results of the paper are illustrated via a real data set. Finally, some conclusions are stated. [ABSTRACT FROM AUTHOR]

The efficiency concepts of Bahadur and Pitman are used to compare the Wilcoxon tests in paired and independent survey samples. A comparison through the length of corresponding confidence intervals is also done. Simple conditions characterizing the dominance of a procedure are derived. Statistical tests for checking these conditions are suggested and discussed. [ABSTRACT FROM AUTHOR]

Fault diagnosis of systems is an important area of study in the design and maintenance of multiprocessor systems. In 2012, Peng et al. proposed a new measure for the fault diagnosis of systems, namely g -good-neighbor conditional diagnosability, which requires that any fault-free vertex has at least g fault-free neighbors in the system. The g -good-neighbor conditional diagnosabilities of a graph G under the PMC model and the MM* model are denoted by t g PMC ( G ) and t g MM * ( G ) , respectively. In this paper, we first determine that t g PMC ( G ) = t g MM * ( G ) if g  ≥ 2. Second, we establish a general result on the 1, 2-good-neighbor conditional diagnosabilities of some regular graphs. As applications, the 1, 2-good-neighbor conditional diagnosabilities of BC graphs, folded hypercubes and four classes of Cayley graphs, namely unicyclic-transposition graphs, wheel-transposition graphs, complete-transposition graphs and tree-transposition graphs, are determined under the PMC model and the MM* model. In addition, we determine the R 2 -connectivities of BC graphs and folded hypercubes. [ABSTRACT FROM AUTHOR]

One of the most sensitive characteristics of network vulnerability is residual closeness. Calculating the closeness and the residual closeness of larger graphs is a time consuming and operations heavy process. In this article, we try to mitigate the process for thorn graphs - we present the thorn graphs residual closeness as a function of the closeness and the residual closeness of the original graphs. [ABSTRACT FROM AUTHOR]

Leaderless consensus for the fractional-order nonlinear multi-agent systems is investigated in this paper. At the first part, a control protocol is proposed to achieve leaderless consensus for the nonlinear single-integrator multi-agent systems. At the second part, based on sliding mode estimator, a control protocol is given to solve leaderless consensus for the the nonlinear single-integrator multi-agent systems. It shows that the control protocol can improve the systems’ convergence speed. At the third part, a control protocol is designed to accomplish leaderless consensus for the nonlinear double-integrator multi-agent systems. To judge the systems’ stability in this paper, two classic continuous Lyapunov candidate functions are chosen. Finally, several worked out examples under directed interaction topology are given to prove above results. [ABSTRACT FROM AUTHOR]

Word sense disambiguation (WSD) refers to the task of finding the intended meaning of a word in a given sentence. WordNet® (lexical database based on psychological principals) based on WSD methods have been discussed extensively. WordNet® relates words through various relations and all the WSD approaches available in the literature till date rely on the notion of assigning equal importance to each relation. But actually in real-world situations, these relations do not exhibit equal importance, so they should not be given equal weight. The paper presents a novel method for exploiting the idea of WordNet® relations weight based on its importance and thus assigns the weights to the edges of the WordNet® graph, µ ∊  (0, 1]. This helps in fuzzifying the WordNet® graph, where nodes represent the words and weighted edges represent the relation of the words with strength∈ (0,1]. The values for edge weight assignment are obtained using test cases based on a simulated annealing method. The proposed method utilizes various Fuzzy graph connectivity measures to determine the significance of each node in the Fuzzy graph, resulting in identification of the intended meaning of the word. This method is tested on the SemCor dataset and observed that it gives better results when compared to state-of-the-art approaches. [ABSTRACT FROM AUTHOR]

In this paper, we developed an empirical evaluation of four estimation procedures for the dependence parameter of the Gumbel-Barnett copula obtained from a Gumbel type I distribution. We used the maximum likelihood, moments and Bayesian methods and studied the performance of the estimates, assuming three dependence levels and 20 different sample sizes. For each method and scenario, a simulation study was conducted with 1000 runs and the quality of the estimator was evaluated using four different criteria. A Bayesian estimator assuming a Beta(a,b) as prior distribution, showed the best performance regardless the sample size and the dependence structure. [ABSTRACT FROM AUTHOR]

This paper introduces a new four-parameter lifetime model called the odd log-logistic Dagum distribution. The new model has the advantage of being capable of modeling various shapes of aging and failure criteria. We derive some structural properties of the model odd log-logistic Dagum such as order statistics and incomplete moments. The maximum likelihood method is used to estimate the model parameters. Simulation results to assess the performance of the maximum likelihood estimation are discussed. We prove empirically the importance and flexibility of the new model in modeling real data. [ABSTRACT FROM AUTHOR]

The paper considers the problem of hypothesis testing and confidence intervals in high dimensional proportional hazards models. Motivated by a geometric projection principle, we propose a unified likelihood ratio inferential framework, including score, Wald and partial likelihood ratio statistics for hypothesis testing. Without assuming model selection consistency, we derive the asymptotic distributions of these test statistics, establish their semiparametric optimality and conduct power analysis under Pitman alternatives. We also develop new procedures to construct pointwise confidence intervals for the baseline hazard function and conditional hazard function. Simulation studies show that all tests proposed perform well in controlling type I errors. Moreover, the partial likelihood ratio test is empirically more powerful than the other tests. The methods proposed are illustrated by an example of a gene expression data set. [ABSTRACT FROM AUTHOR]

The g -good-neighbor conditional diagnosability is a new measure for fault diagnosis of systems. Xu et al. (2017) [27] determined the g -good-neighbor conditional diagnosability of ( n , k ) -star networks S n , k (i.e., t g ( S n , k ) ) with 1 ≤ k ≤ n − 1 for 1 ≤ g ≤ n − k under the PMC model and the MM ⁎ model. In this paper, we determine t g ( S n , k ) for all the remaining cases with 1 ≤ k ≤ n − 1 for 1 ≤ g ≤ n − 1 under the two models, from which we can obtain the g -good-neighbor conditional diagnosability of the star graph obtained by Li et al. (2017) [16] for 1 ≤ g ≤ n − 2 . [ABSTRACT FROM AUTHOR]

Diagnosability of a multiprocessor system is an important study topic. S. L. Peng, C. K. Lin, J. J. M. Tan, and L. H. Hsu [Appl. Math. Comput., 2012, 218(21): 10406-10412] proposed a new measure for fault diagnosis of the system, which is called the g-good-neighbor conditional diagnosability that restrains every fault-free node containing at least g fault-free neighbors. As a famous topological structure of interconnection networks, the n-dimensional star graph S has many good properties. In this paper, we establish the g-good-neighbor conditional diagnosability of S under the PMC model and MM* model. [ABSTRACT FROM AUTHOR]

Estimation of two normal means with an order restriction is considered when a covariance matrix is known. It is shown that restricted maximum likelihood estimator (MLE) stochastically dominates both estimators proposed by Hwang and Peddada [Confidence interval estimation subject to order restrictions. Ann Statist. 1994;22(1):67–93] and Peddada et al. [Estimation of order-restricted means from correlated data. Biometrika. 2005;92:703–715]. The estimators are also compared under the Pitman nearness criterion and it isshownthat the MLE is closer to ordered means than the other two estimators. Estimation of linear functions of ordered means is also considered and a necessary and sufficient condition on the coefficients is given for the MLE to dominate the other estimators in terms of mean squared error. [ABSTRACT FROM PUBLISHER]

Three linear prediction methods of a single missing value for a stationary first order multiplicative spatial autoregressive model are proposed based on the quarter observations, observations in the first neighborhood, and observations in the nearest neighborhood. Three different types of innovations including Gaussian (symmetric and thin tailed), exponential (skew to right), and asymmetric Laplace (skew and heavy tailed) are considered. In each case, the proposed predictors are compared based on the two well-known criteria: mean square prediction and Pitman's measure of closeness. Parameter estimation is performed by maximum likelihood, least square errors, and Markov chain Monte Carlo (MCMC). [ABSTRACT FROM AUTHOR]

This paper demonstrates the feasibility of implementing real-time state estimators for active distribution networks in field-programmable gate arrays (FPGAs) by presenting an operational prototype. The prototype is based on a linear state estimator that uses synchrophasor measurements from phasor measurement units. The underlying algorithm is the sequential discrete Kalman filter (SDKF), an equivalent formulation of the DKF for the case of uncorrelated measurement noise. In this regard, this paper formally proves the equivalence of SDKF and the DKF, and highlights the suitability of the SDKF for an FPGA implementation by means of a computational complexity analysis. The developed prototype is validated using a case study adapted from the IEEE 34-node distribution test feeder. [ABSTRACT FROM PUBLISHER]

We studied the large deviation expansion for maximum-likelihood estimator of α −Brownian bridge by using change of measure and time-varying change of probability. The full expansion provided a useful tool to approximate the tail probability of maximum-likelihood estimator. [ABSTRACT FROM AUTHOR]

We investigate properties of estimators obtained by minimization of U -processes with the Lasso penalty in the high-dimensional setting. Our attention is focused on the ranking problem that is popular in machine learning. It is related to guessing the ordering between objects on the basis of their observed predictors. We prove the oracle inequality for the excess risk of the considered estimator as well as the bound for the l 1 distance | θ ^ − θ * | 1 between the estimator and the oracle. Besides, we study properties of estimators on simulated data sets. [ABSTRACT FROM AUTHOR]

This article purposes the estimation of population proportion of a sensitive attribute through randomized response technique. An efficient estimator is suggested using six decks of cards to randomise the response. Many existing models can now be viewed as the special case of the proposed model. The superiority of the proposed procedure is established through numerical calculation of percentage relative efficiency with prominent competitors. The proposed procedure is also studied under stratified random sampling protocol. In addition, it is shown that, the proposed stratified estimator, performs better in term of efficiency than its only existing two deck stratified competitor. [ABSTRACT FROM AUTHOR]

R-squared (R2) and adjusted R-squared (R2Adj) are sometimes viewed as statistics detached from any target parameter, and sometimes as estimators for the population multiple correlation. The latter interpretation is meaningful only if the explanatory variables are random. This article proposes an alternative perspective for the case where thex’s are fixed. A new parameter is defined, in a similar fashion to the construction ofR2, but relying on the true parameters rather than their estimates. (The parameter definition includes also the fixedxvalues.) This parameter is referred to as the “parametric” coefficient of determination, and denoted by ρ2*. The proposed ρ2*remains stable when irrelevant variables are removed (or added), unlike the unadjustedR2, which always goes up when variables, either relevant or not, are added to the model (and goes down when they are removed). The value of the traditionalR2Adjmay go up or down with added (or removed) variables, either relevant or not. It is shown that the unadjustedR2overestimates ρ2*, while the traditionalR2Adjunderestimates it. It is also shown that for simple linear regression the magnitude of the bias ofR2Adjcan be as high as the bias of the unadjustedR2(while their signs are opposite). Asymptotic convergence in probability ofR2Adjto ρ2*is demonstrated. The effects of model parameters on the bias ofR2andR2Adjare characterized analytically and numerically. An alternative bi-adjusted estimator is presented and evaluated. [ABSTRACT FROM PUBLISHER]

We consider estimation of a missing value for a stationary autoregressive process of order one with exponential innovations and compare two methods of estimation of the missing value, with respect to Pitman's measure of closeness (PMC). [ABSTRACT FROM PUBLISHER]

In this article, based on generalized order statistics from a family of proportional hazard rate model, we use a statistical test to generate a class of preliminary test estimators and shrinkage preliminary test estimators for the proportionality parameter. These estimators are compared under Pitman measure of closeness (PMC) as well as MSE criteria. Although the PMC suffers from non transitivity, in the first class of estimators, it has the transitivity property and we obtain the Pitman-closest estimator. Analytical and graphical methods are used to show the range of parameter in which preliminary test and shrinkage preliminary test estimators perform better than their competitor estimators. Results reveal that when the prior information is not too far from its real value, the proposed estimators are superior based on both mentioned criteria. [ABSTRACT FROM PUBLISHER]

This article introduces a class of first-order stationary time-varying Pitman-Yor processes. Subsuming our construction of time-varying Dirichlet processes presented in (Caron et al., 2007), these models can be used for time-dynamic density estimation and clustering. Our intuitive and simple construction relies on a generalized Pólya urn scheme. Significantly, this construction yields marginal distributions at each time point that can be explicitly characterized and easily controlled. Inference is performed using Markov chain Monte Carlo and sequential Monte Carlo methods. We demonstrate our models and algorithms on epidemiological and video tracking data. [ABSTRACT FROM AUTHOR]

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Diagnosability is an important metric for measuring the reliability of multiprocessor systems. In 2012, Penget al.proposed a new measure for fault tolerance of the system, which is calledg-good-neighbour diagnosability that restrains every fault-free node containing at leastgfault-free neighbours. As a favourable topology structure of interconnection networks, the Cayley graphgenerated by the transposition treehas many good properties. In this paper, we give that the 1-good-neighbour diagnosability ofunder the PMC model and MMmodel isexcept the bubble-sort graphunder MMmodel, where, and the 1-good-neighbour diagnosability ofunder the MMmodel is 4. [ABSTRACT FROM AUTHOR]

On a spherical Earth, the mean elevation (approximately-22440 m) would be everywhere at a mean Earth radius from the center. This directly links an elevation at the surface to physical dimensions of Earth, including surface area and volume, which are at most very slowly evolving components of the Earth system. Earth's mean elevation thus provides a framework within which to consider changes in height of Earth's solid surface as a function of time. In this article, the focus will be on long-term, nonglacially controlled sea level. Long-term sea level has long been argued to be largely controlled by changes in ocean basin volume related to changes in the area-age distribution of oceanic lithosphere. As generally modeled by Walter Pitman and subsequent workers, the age-depth relationship of oceanic lithosphere, including both the ridge depth and the coefficients describing the age-depth relationship, are assumed constant. This article examines the consequences of adhering to these assumptions when placed within the larger framework of maintaining a constant mean radius of Earth. Self-consistent estimates of long-term sea level height and changes in the mean depth of the oceanic crust are derived from the assumption that the mean elevation and corresponding mean radius are unchanging aspects of Earth's shorter-term evolution. Within this context, changes in the mean depth of the oceanic crust, corresponding with changes in the mean age of oceanic lithosphere, acting over the area of the oceanic crust represent a volume change that is required to be balanced by a compensating equal but opposite volume change under the area of the continental crust. Models of cumulative paleohypsometry derived from a starting glacial isostatic adjustment (GIA)Ccorrected ice-free hypsometry that conserve mean elevation provide a basis for understanding how these compensating changes impact global hypsometry and particularly estimates of global mean shoreline height. Paleoshoreline height and areal extent of flooding can be defined as the height and corresponding cumulative area of the solid surface of Earth at which the integral of area as a function of elevation, from the maximum depth upward, equals the volume of ocean water filling it with respect to cumulative paleohypsometry. The present height of the paleoshoreline is the height on the GIA-corrected cumulative hypsometry at an area equal to the areal extent of flooding. Paleogeographic estimates of the global extent of ocean flooding from the Middle Jurassic to end Eocene, when combined with conservation of mean elevation and ocean water volume, allow an explicit estimate of the paleoheight and the present height of the paleoshoreline. The best-fitting estimate of the present height of the paleoshoreline, equivalent to a long-term "eustatic" sea level curve, implies very modest (25±22 m) changes in long-term sea level above the ice-free sea level height of approximately 140 m. These, in turn, imply quite limited changes in the mean depth of the oceanic crust (15±11 m) and in the mean age of the oceanic lithosphere (~62.1±2.4 My) since the Middle Jurassic. [ABSTRACT FROM AUTHOR]

In regression analysis, to deal with the problem of multicollinearity, the restricted principal components regression estimator is proposed. In this paper, we compared the restricted principal components regression estimator, the principal components regression estimator, and the ordinary least-squares estimator with each other under the Pitman's closeness criterion. We showed that the restricted principal components regression estimator is always superior to the principal components regression estimator, under certain conditions the restricted principal components regression estimator is superior to the ordinary least-squares estimator under the Pitman's closeness criterion and under certain conditions the principal components regression estimator is superior to the ordinary least-squares estimator under the Pitman's closeness criterion. [ABSTRACT FROM PUBLISHER]

Many large-scale multiprocessor or multi-computer systems take interconnection networks as underlying topologies. Fault diagnosis is especially important to identify fault tolerability of such systems. The g-good-neighbor ( conditional ) diagnosability such that every fault-free node has at least g fault-free neighbors is a novel measure of diagnosability. In this paper, we show that the g -good-neighbor diagnosability of the ( n , k ) -star graph S n , k under the PMC model ( 2 ≤ k ≤ n − 1 and 1 ≤ g ≤ n − k ) and the comparison model ( 2 ≤ k ≤ n − 1 and 2 ≤ g ≤ n − k ) is n + g ( k − 1 ) − 1 , respectively. In addition, we derive that 1-good-neighbor diagnosability of S n , k under the comparison model is n + k − 2 for 3 ≤ k ≤ n − 1 and n ≥ 4 . As a supplement, we also derive that the g -good-neighbor diagnosability of the ( n , 1 ) -star graph S n , 1 ( 1 ≤ g ≤ ⌊ n / 2 ⌋ − 1 and n ≥ 4 ) under the PMC model and the comparison model is ⌈ n / 2 ⌉ − 1 , respectively. [ABSTRACT FROM AUTHOR]

The conditional diagnosability of many well-known networks has been explored. In this paper, we analyze the conditional diagnosability of a family of networks, called the round matching composition networks, which are a class of networks composed of r ( r ≥ 4 ) components of the same order linked by r perfect matchings. Applying the result, we determine the conditional diagnosability of the k -ary n -cubes and the recursive circulant graphs under the PMC model and the MM model, respectively. [ABSTRACT FROM AUTHOR]