A NOTE ON ARMA PARAMETERISATION*

This paper considers the relationship between ARMA parameterisations of models for y(t) and Ay(t), where A is invertible and y(t) is a vector time series (t = 0,±1,…). An ARMA model for the transformed series Ay(t) may have fewer parameters than a model for y(t). This paper shows that such a saving is illusory because the apparently saved parameters are exactly balanced by the number of new parameters appearing in A.     

Correlation between Download and Citation and Download-citation Deviation Phenomenon for Some Papers in Chinese Medical Journals

The authors collected the numbers of citations and downloads from 2005 to 2009 of papers in five Chinese general ophthalmological journals: Recent Advances in Ophthalmology, Chinese Ophthalmic Research, Ophthalmology in China, Journal of Clinical Ophthalmology and Chinese Journal of Practical Ophthalmology, published in 2005 from the Chinese Academic Journals Full-text Database and the Chinese Citation Database in Chinese National Knowledge Infrastructure (CNKI) to determine the correlation between download and citation and the peak time of download frequency (DF). The citations from 2000 to 2009 of papers published in 2000 were collected to determine the peak time of citation frequency (CF) of medical papers. There is a highly positive correlation between DF and CF (r = 4.91, P = 0.000).     

Correlation between Download and Citation and Download-citation Deviation Phenomenon for Some Papers in Chinese Medical Journals

Abstract

The authors collected the numbers of citations and downloads from 2005 to 2009 of papers in five Chinese general ophthalmological journals: Recent Advances in Ophthalmology, Chinese Ophthalmic Research, Ophthalmology in China, Journal of Clinical Ophthalmology and Chinese Journal of Practical Ophthalmology, published in 2005 from the Chinese Academic Journals Full-text Database and the Chinese Citation Database in Chinese National Knowledge Infrastructure (CNKI) to determine the correlation between download and citation and the peak time of download frequency (DF). The citations from 2000 to 2009 of papers published in 2000 were collected to determine the peak time of citation frequency (CF) of medical papers. There is a highly positive correlation between DF and CF (r = 4.91, P = 0.000).     

Construction of neighbor designs of block size 4 for all values of v ≥ 5 by using the method of addition

In this article, a general method of construction of neighbor block designs is given. The designs are constructed using variation of a simple method which we refer to as the method of addition (renamed as the method of cyclic shifts). We give complete solution of neighbor balanced designs for k = 4 for any value of v. We also give many series of generalized neighbor designs (GNDs). In the last section, we have constructed GNDs in a sequential manner (as Did John 1981) for v ≤ 50 and r is multiple of k.     

A uniform saddlepoint expansion for the null‐distribution of the wilcoxon‐mann‐whitney statistic

The authors give the exact coefficient of 1/N in a saddlepoint approximation to the Wilcoxon‐Mann‐Whitney null‐distribution. This saddlepoint approximation is obtained from an Edgeworth approximation to the exponentially tilted distribution. Moreover, the rate of convergence of the relative error is uniformly of order O (1/N) in a large deviation interval as defined in Feller (1971). The proposed method for computing the coefficient of 1/N can be used to obtain the exact coefficients of 1/Nⁱ, for any i. The exact formulas for the cumulant generating function and the cumulants, needed for these results, are those of van Dantzig (1947‐1950).     

Goodness-of-fit tests of hypothesized canonical variables

In the literature goodness-of-fit tests for canonical variables are available either in the x space or in the y space, see e.g., Bartlett (1951), Kshirsagar (1971, 1972), Radcliffe (1968), and Williams (1952). Here we present goodness-of-fit tests for canonical variables in both the x and y spaces. The results appear as extensions of the results of the above authors.     

A binomial CUSUM chart for detecting large shifts in fraction nonconforming

This article studies a unique feature of the binomial CUSUM chart in which the difference (d _t ?d ₀) is replaced by (d _t ?d ₀)² in the formulation of the cumulative sum C _t (where d _t and d ₀ are the actual and in-control numbers of nonconforming units, respectively, in a sample). Performance studies are reported and the results reveal that this new feature is able to increase the detection effectiveness when fraction nonconforming p becomes three to four times as large as the in-control value p ₀. The design of the new binomial CUSUM chart is presented along with the calculation of the in-control and out-of-control Average Run Lengths (ARL₀ and ARL₁).     

COMPUTER-AIDED CONSTRUCTION OF SMALL (M, S)-OPTIMAL INCOMPLETE BLOCK DESIGNS

A new exchange algorithm for the construction of (M, S)-optimal incomplete block designs (IBDS) is developed. This exchange algorithm is used to construct 973 (M, S)-optimal IBDs (v, k, b) for v= 4,…,12 (varieties) with arbitrary v, k (block size) and b (number of blocks). The efficiencies of the “best” (M, S)-optimal IBDs constructed by this algorithm are compared with the efficiencies of the corresponding nearly balanced incomplete block designs (NBIBDs) of Cheng(1979), Cheng & Wu (1981) and Mitchell & John(1976).     

Journal Self-citation Analysis of Some Chinese Sci-tech Periodicals

This study investigates self-citation rates of 222 Chinese journals within seven groups including 76 journals of agronomy (34.2 percent), 57 of biology (25.7 percent), 28 of environmental science and technology (12.6 percent), 15 of forestry (6.8 percent), 24 of academic journals of agricultural university (10.8 percent), 9 of aquatic sciences (4.1 percent), and 13 of animal husbandry and veterinary medicine (5.9 percent). The average self-citation rates range from 2 percent to 67 percent in 2006, 1 percent to 68 percent in 2007 and 0 percent to 67 percent in 2008. There is a significant difference in self-citation rate between most groups of journals. The self-citation rate is positively and significantly correlated with the self-citation rate in 2006 for all 222 journals (N = 222, R² = 0.194, P = 0.004) (P < 0.05). However, the self-citation rate is not significantly correlated with the journal's impact factor in 2007 (N = 222, R² = 0.114, P = 0.091) and 2008 (N = 222, R² = 0.112, P = 0.096) (P < 0.05) for the 222 journals. The relationship between self-citation rate and journal impact factor is discussed.     

Transformations for Testing the Fit of the Inverse-Gaussian Distribution

Abstract

Use of the MVUE for the inverse-Gaussian distribution has been recently proposed by Nguyen and Dinh [Nguyen, T. T., Dinh, K. T. (2003). Exact EDF goodnes-of-fit tests for inverse Gaussian distributions. Comm. Statist. (Simulation and Computation) 32(2):505–516] where a sequential application based on Rosenblatt's transformation [Rosenblatt, M. (1952). Remarks on a multivariate transformation. Ann. Math. Statist. 23:470–472] led the authors to solve the composite goodness-of-fit problem by solving the surrogate simple goodness-of-fit problem, of testing uniformity of the independent transformed variables. In this note, we observe first that the proposal is not new since it was proposed in a rather general setting in O'Reilly and Quesenberry [O'Reilly, F., Quesenberry, C. P. (1973). The conditional probability integral transformation and applications to obtain composite chi-square goodness-of-fit tests. Ann. Statist. I:74–83]. It is shown on the other hand that the results in the paper of Nguyen and Dinh (2003) are incorrect in their Sec. 4, specially the Monte Carlo figures reported. Power simulations are provided here comparing these corrected results with two previously reported goodness-of-fit tests for the inverse-Gaussian; the modified Kolmogorov–Smirnov test in Edgeman et al. [Edgeman, R. L., Scott, R. C., Pavur, R. J. (1988). A modified Kolmogorov-Smirnov test for inverse Gaussian distribution with unknown parameters. Comm. Statist. 17(B): 1203–1212] and the A ² based method in O'Reilly and Rueda [O'Reilly, F., Rueda, R. (1992). Goodness of fit for the inverse Gaussian distribution. T Can. J. Statist. 20(4):387–397]. The results show clearly that there is a large loss of power in the method explored in Nguyen and Dinh (2003) due to an implicit exogenous randomization.     

Bayesian Inference for the Jump-Diffusion Model with M Jumps

In this article, we propose a new class of models—jump-diffusion models with M jumps (JD(M)J). These structures generalize the discretized arithmetic Brownian motion (for logarithmic rates of return) and the Bernoulli jump-diffusion model. The aim of this article is to present Bayesian tools for estimation and comparison of JD(M)J models. Presented methodology is illustrated with two empirical studies, employing both simulated and real-world data (the S&P100 Index).     

On the consistency of the maximum spacing method

The main result of this paper is a consistency theorem for the maximum spacing method, a general method of estimating parameters in continuous univariate distributions, introduced by Cheng and Amin (J. Roy. Statist. Soc. Ser. A 45 (1983) 394–403) and independently by Ranneby (Scand. J. Statist. 11 (1984) 93–112). This main result generalizes a theorem of Ranneby (Scand. J. Statist. 11 (1984) 93–112). Also, some examples are given, which shows that this estimation method works also in cases where the maximum likelihood method breaks down.     

ESTIMATING THE ROOT OF A NONPARAMETRIC REGRESSION FUNCTION IN A ROBUST FASHION

For a nonparametric regression model y = m(x)+e with n independent observations, we analyze a robust method of finding the root of m(x) based on an M-estimation first discussed by Härdle & Gasser (1984). It is shown here that the robustness properties (minimaxity and breakdown function) of such an estimate are quite analogous to those of an M -estimator in the simple location model, but the rate of convergence is somewhat limited due to the nonparametric nature of the problem.     

Aggregate statistical data: models for their representation

The paper gives a review of a number of data models for aggregate statistical data which have appeared in the computer science literature in the last ten years.After a brief introduction to the data model in general, the fundamental concepts of statistical data are introduced. These are called statistical objects because they are complex data structures (vectors, matrices, relations, time series, etc) which may have different possible representations (e.g. tables, relations, vectors, pie-charts, bar-charts, graphs, and so on). For this reason a statistical object is defined by two different types of attribute (a summary attribute, with its own summary type and with its own instances, called summary data, and the set of category attributes, which describe the summary attribute). Some conceptual models of statistical data (CSM, SDM4S), some semantic models of statistical data (SCM, SAM*, OSAM*), and some graphical models of statistical data (SUBJECT, GRASS, STORM) are also discussed.     

Simultaneous marginal survival estimators when doubly censored data is present

A doubly censoring scheme occurs when the lifetimes T being measured, from a well-known time origin, are exactly observed within a window [L, R] of observational time and are otherwise censored either from above (right-censored observations) or below (left-censored observations). Sample data consists on the pairs (U, δ) where U = min{R, max{T, L}} and δ indicates whether T is exactly observed (δ = 0), right-censored (δ = 1) or left-censored (δ = −1). We are interested in the estimation of the marginal behaviour of the three random variables T, L and R based on the observed pairs (U, δ). We propose new nonparametric simultaneous marginal estimators [^(S)]_T, [^(S)]_L{\hat S_{T}, \hat S_{L}} and [^(S)]_R{\hat S_{R}} for the survival functions of T, L and R, respectively, by means of an inverse-probability-of-censoring approach. The proposed estimators [^(S)]_T, [^(S)]_L{\hat S_{T}, \hat S_{L}} and [^(S)]_R{\hat S_{R}} are not computationally intensive, generalize the empirical survival estimator and reduce to the Kaplan-Meier estimator in the absence of left-censored data. Furthermore, [^(S)]_T{\hat S_{T}} is equivalent to a self-consistent estimator, is uniformly strongly consistent and asymptotically normal. The method is illustrated with data from a cohort of drug users recruited in a detoxification program in Badalona (Spain). For these data we estimate the survival function for the elapsed time from starting IV-drugs to AIDS diagnosis, as well as the potential follow-up time. A simulation study is discussed to assess the performance of the three survival estimators for moderate sample sizes and different censoring levels.     

On the asymptotic normality of the L1- and L2-errors in histogram density estimation

The L₁ and L₂-errors of the histogram estimate of a density f from a sample X₁,X₂,…,Xn using a cubic partition are shown to be asymptotically normal without any unnecessary conditions imposed on the density f. The asymptotic variances are shown to depend on f only through the corresponding norm of f. From this follows the asymptotic null distribution of a goodness-of-fit test based on the total variation distance, introduced by Györfi and van der Meulen (1991). This note uses the idea of partial inversion for obtaining characteristic functions of conditional distributions, which goes back at least to Bartlett (1938).     

CONSTRUCTION OF BALANCED TERNARY DESIGNS

In this paper variance balanced ternary designs are constructed in unequal block sizes for situations when suitable BIB designs do not exist for a given number of treatments because of the constraints bk=vr,and λ(v - 1) =r(k- 1).     

Maximum term of a particular autoregressivesequence with discrete margins

In this paper we consider a stationary sequence of discrete random variables with marginal distribution H(x), obtained by a simple transformation from the max-AR(1) sequence considered by Alpuim (1989). Because discrete distributions impose severe restrictions on the convergence of the normalized maxima to an extreme value distribution, it is seen that in this particular case, whenever H(x) belongs to the domain of attraction of any max-stable distribution, the sequence possesses an extremal index 0 = 0. Nevertheless, it, is possible to obtain a nondegenerate limiting distribution for the linearized maxima by choosing other sets of normalizing constants. Whenever H(x) does not belong to the domain of attraction of any max-stable distribution, but, satisfies adequate conditions, the maxima nearly possess an asymptotic stability with the presence of an extremal index 0 <θ<1.

Motivated by the behaviour of these sequences we obtained a more general result extending the results of Anderson (1970) and Me (Jon nick and Park (1992) over the mixing conditionsD ^(k)(u_n), defined by Chermck et al (1991).

Several examples, obtained after simulation, are presented in order to illustrate the different situations that may occur.     

A Markov Chain Copula Model for Credit Default Swaps with Bilateral Counterparty Risk

Reduced-form credit risk models are widely used in pricing and hedging credit derivatives. Generating default dependency is the key element in any such model. In this article, we use Markov copulae approach to model the dependence structure of defaults between the three obligors, one is the reference entity, another is the protection seller, the other is the protection buyer(the investor), so we can consider the bilateral counterparty risk of credit default swaps(CDS). In this Markov chain copula model, we obtain the explicit formulas of the CDS premium rates C ₁(T) (with unilateral counterparty risk) and C ₂(T) (with bilateral counterparty risk). And then we perform some numerical experiments to analyze the difference of the fair spreads between the unilateral case and the bilateral case.     

New estimators of distribution functions

ABSTRACT

This article considers the estimation of a distribution function F_X(x) based on a random sample X₁, X₂, …, X_n when the sample is suspected to come from a close-by distribution F₀(x). The new estimators, namely the preliminary test (PTE) and Stein-type estimator (SE) are defined and compared with the “empirical distribution function” (edf) under local departure. In this case, we show that Stein-type estimators are superior to edf and PTE is superior to edf when it is close to F₀(x). As a by-product similar estimators are proposed for population quantiles.