# Elsevier

# Statistics & Probability Letters

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### September 2008, Volume 78, Issue 13

**1878-1884 Optimality of the Holm procedure among general step-down multiple testing procedures***by*Gordon, Alexander Y. & Salzman, Peter**1885-1893 A variance component test for mixed hidden Markov models***by*Altman, Rachel MacKay**1894-1902 Confidence intervals for long memory regressions***by*Ko, Kyungduk & Lee, Jaechoul & Lund, Robert**1903-1913 Central limit theorems for the integrated squared error of derivative estimators***by*Birke, Melanie**1914-1921 Optimal minimax designs over a prespecified interval in a heteroscedastic polynomial model***by*Chen, Ray-Bing & Wong, Weng Kee & Li, Kun-Yu**1922-1928 Conditional independence between two variables given any conditioning subset implies block diagonal covariance matrix for multivariate Gaussian distributions***by*Marrelec, Guillaume & Benali, Habib**1929-1932 Collision probability for an occupancy problem***by*Nakata, Toshio**1933-1942 Lee discrepancy and its applications in experimental designs***by*Zhou, Yong-Dao & Ning, Jian-Hui & Song, Xie-Bing**1943-1947 Unit root testing based on BLUS residuals***by*Vougas, Dimitrios V.**1948-1954 A saddlepoint approximation to the probability of ruin in the compound Poisson process with diffusion***by*Gatto, Riccardo**1955-1963 Prediction intervals for future records***by*Raqab, Mohammad Z. & Balakrishnan, N.**1964-1970 A note on the almost sure central limit theorem for negatively associated fields***by*Wang, Jiang-Feng & Liang, Han-Ying**1971-1980 Likelihood ratio tests for triply multivariate data with structured correlation on spatial repeated measurements***by*Roy, Anuradha & Leiva, Ricardo**1981-1989 A new class of excited random walks on trees***by*Del Greco M., Fabiola & Di Marzio, Marco & Panzera, Agnese**1990-1998 Test for parameter change in ARMA models with GARCH innovations***by*Lee, Sangyeol & Song, Junmo

### September 2008, Volume 78, Issue 12

**1349-1354 Characterizations using the bivariate failure rate function***by*Navarro, Jorge**1355-1361 A class of autoregressive processes***by*Krishnarani, S.D. & Jayakumar, K.**1362-1368 Modified Simes' critical values under independence***by*Cai, Gengqian & Sarkar, Sanat K.**1369-1374 A generalization and extension of an autoregressive model***by*Satheesh, S. & Sandhya, E. & Rajasekharan, K.E.**1375-1383 Parameter estimation using partial information with applications to queueing and related models***by*Basawa, I.V. & Bhat, U.N. & Zhou, J.**1384-1387 On the central limit theorem and the law of the iterated logarithm***by*Fukuyama, Katusi & Ueno, Yôhei**1388-1396 Equidistant and D-optimal designs for parameters of Ornstein-Uhlenbeck process***by*Kiselák, Jozef & Stehlík, Milan**1397-1403 A method to compute the transition function of a piecewise deterministic Markov process with application to reliability***by*Chiquet, Julien & Limnios, Nikolaos**1404-1411 Seasonal fractional ARIMA with stable innovations***by*Diongue, Abdou Kâ & Diop, Aliou & Ndongo, Mor**1412-1421 A higher order multifractal formalism***by*Ben Mabrouk, Anouar**1422-1429 An assumption for the development of bootstrap variants of the Akaike information criterion in mixed models***by*Shang, Junfeng & Cavanaugh, Joseph E.**1430-1433 The asymptotic and exact Fisher information matrices of a vector ARMA process***by*Klein, André & Mélard, Guy & Saidi, Abdessamad**1434-1439 Extended Glivenko-Cantelli Theorem in ARCH(p)-time series***by*Cheng, Fuxia**1440-1444 On the max-domain of attraction of distributions with log-concave densities***by*Müller, Samuel & Rufibach, Kaspar**1445-1451 Empirical likelihood for linear models in the presence of nuisance parameters***by*Kim, Mi-Ok & Zhou, Mai**1452-1458 On computation of NPMLE for middle-censored data***by*Mangalam, Vasudevan & Nair, Gopalan M. & Zhao, Yun**1459-1465 On Pólya mixtures of multivariate Gaussian distributions***by*Grigelionis, Bronius**1466-1472 Complete convergence of weighted sums for [rho]* -mixing sequence of random variables***by*Jun, An & Demei, Yuan**1473-1479 A note on the closed-form identification of regression models with a mismeasured binary regressor***by*Chen, Xiaohong & Hu, Yingyao & Lewbel, Arthur**1480-1489 The autocorrelation structure of the Markov-switching asymmetric power GARCH process***by*Haas, Markus**1490-1497 Clustering gene expression profile data by selective shrinkage***by*Ishwaran, Hemant & Sunil Rao, J.**1498-1504 A note on auxiliary particle filters***by*Johansen, Adam M. & Doucet, Arnaud**1505-1513 Distribution of runs in a sequence of exchangeable multi-state trials***by*EryIlmaz, Serkan**1514-1516 A problem on extreme magnitudes of characteristic functions: The general case***by*He, Xin**1517-1525 On exit times of Lévy-driven Ornstein-Uhlenbeck processes***by*Borovkov, Konstantin & Novikov, Alexander**1526-1533 A generalized Gittins index for a Markov chain and its recursive calculation***by*Sonin, Isaac M.**1534-1540 Growth rates for pure birth Markov chains***by*Athreya, K.B.**1541-1547 A self-normalized central limit theorem for [rho] -mixing stationary sequences***by*Jiang, Xinxin & Hahn, Marjorie**1548-1556 Spiking problem in monotone regression: Penalized residual sum of squares***by*Pal, Jayanta Kumar**1557-1559 Two refinements of the Chernoff bound for the sum of nonidentical Bernoulli random variables***by*Xia, Ye**1560-1569 Zero finite-order serial correlation test in a semi-parametric varying-coefficient partially linear errors-in-variables model***by*Hu, Xuemei & Wang, Zhizhong & Liu, Feng**1570-1576 How to construct asymptotically stable iterated function systems***by*Jaroszewska, Joanna**1577-1582 Extreme variances of order statistics in dependent samples***by*Rychlik, Tomasz**1583-1592 Edgeworth expansions in operator form***by*Szewczak, Zbigniew S.**1593-1600 On the matching noise of some nonparametric imputation procedures***by*Marella, Daniela & Scanu, Mauro & Luigi Conti, Pier**1601-1611 Spectral density estimation for linear processes with dependent innovations***by*Bensaïd, Nadia & Yazourh-Benrabah, Ouafae**1612-1618 Hausdorff moment problem: Reconstruction of distributions***by*Mnatsakanov, Robert M.**1619-1623 Some moment relationships for multivariate skew-symmetric distributions***by*Umbach, Dale**1624-1633 Moment estimation in a semiparametric generalized linear model***by*Wang, Xueqin & Peng, Hanxiang**1634-1638 A note on extreme values and kernel estimators of sample boundaries***by*Girard, Stéphane & Jacob, Pierre**1639-1648 A lower bound for the reliability function of multiple failure mode systems***by*Milienos, F.S. & Koutras, M.V.**1649-1655 A regeneration proof of the central limit theorem for uniformly ergodic Markov chains***by*Jasra, Ajay & Yang, Chao**1656-1661 Limiting distribution of the G statistics***by*Zhang, Tonglin**1662-1670 kth records from geometric distribution***by*Dembinska, Anna**1671-1672 R-squared for general regression models in the presence of sampling weights***by*Freels, S. & Sinha, K.**1673-1682 Asymptotic behavior of the variance of the EWMA statistic for autoregressive processes***by*Vermaat, M.B. & van der Meulen, F.H. & Does, R.J.M.M.

### August 2008, Volume 78, Issue 11

**1251-1254 On fake Brownian motions***by*Oleszkiewicz, Krzysztof**1255-1258 H(n)-factors in random graphs***by*Yan, Yun-Zhi & Wang, Han-Xing & Wang, Jun & Yin, Xiang-Feng**1259-1265 BSDE driven by a simple Lévy process with continuous coefficient***by*El Otmani, Mohamed**1266-1273 A new three-parameter extension of the inverse Gaussian distribution***by*Leiva, Víctor & Sanhueza, Antonio & Silva, Andrés & Galea, Manuel**1274-1282 Log-normal, log-gamma and log-negative inverted gamma scenarios in multifractal products of stochastic processes***by*Anh, V.V. & Leonenko, N.N.**1283-1289 A note on the complete convergence for arrays of rowwise independent random elements***by*Sung, Soo Hak**1290-1300 Codispersion coefficients for spatial and temporal series***by*Rukhin, Andrew L. & Vallejos, Ronny**1301-1304 How to compute the extremal index of stationary random fields***by*Ferreira, H. & Pereira, L.**1305-1313 Algebraic polynomials with random non-symmetric coefficients***by*Farahmand, K. & Stretch, C.T.**1314-1316 The Karcher mean of a class of symmetric distributions on the circle***by*Kaziska, David & Srivastava, Anuj**1317-1327 Asymptotic properties for Cauchy's principal values of Brownian and random walk local time***by*Wen, Jiwei & Lin, Zhengyan**1328-1338 Multiple comparisons of several heteroscedastic multivariate populations***by*Kakizawa, Yoshihide**1339-1348 Prolate spheroidal spectral estimates***by*Lii, K.S. & Rosenblatt, M.

### August 2008, Volume 78, Issue 10

**1161-1164 A note on a transformation under censoring with application to partial least squares regression***by*Basu, Sanjib & Ebrahimi, Nader**1165-1167 A generalization of the Balakrishnan skew-normal distribution***by*Yadegari, Iraj & Gerami, Abbas & Khaledi, Majid Jafari**1168-1173 A note on checking the Clayton model assumption based on left-truncated bivariate data***by*Wang, Antai**1174-1180 On asymptotic failure rates in bivariate frailty competing risks models***by*Finkelstein, Maxim & Esaulova, Veronica**1181-1188 On comonotonicity of Pareto optimal risk sharing***by*Ludkovski, Michael & Rüschendorf, Ludger**1189-1193 A k-nearest neighbor approach for functional regression***by*Laloë, Thomas**1194-1199 Modelling marked point patterns by intensity-marked Cox processes***by*Ho, Lai Ping & Stoyan, D.**1200-1205 Noncanonical representation with an infinite-dimensional orthogonal complement***by*Ouknine, Youssef & Erraoui, Mohamed**1206-1214 Precise large deviation results for the total claim amount under subexponential claim sizes***by*Baltrunas, Aleksandras & Leipus, Remigijus & Siaulys, Jonas**1215-1221 On moments of the maximum of normed partial sums of [rho] -mixing random variables***by*Chen, Pingyan & Gan, Shixin**1222-1225 When do cylinder [sigma]-algebras equal Borel [sigma]-algebras in Polish spaces?***by*Yan, Yi**1226-1229 On monotonicity of regression quantile functions***by*Neocleous, Tereza & Portnoy, Stephen**1230-1235 On first and last ruin times of Gaussian processes***by*Hüsler, Jürg & Zhang, Yueming**1236-1245 Nonparametric confidence intervals for quantile intervals and quantile differences based on record statistics***by*Ahmadi, J. & Balakrishnan, N.**1246-1249 On the Gaussian representation of intrinsic volumes***by*Vitale, R.A.

### July 2008, Volume 78, Issue 9

**1051-1055 Precise asymptotics in the law of the iterated logarithm and the complete convergence for uniform empirical process***by*Zhang, Yong & Yang, Xiao-Yun**1056-1061 Reproducibility probability estimation for testing statistical hypotheses***by*De Martini, Daniele**1062-1071 Existence and uniqueness of solutions to stochastic Volterra equations with singular kernels and non-Lipschitz coefficients***by*Wang, Zhidong**1072-1075 On the maximal correlation coefficient***by*Yu, Yaming**1076-1087 Estimating the parameter of the population selected from discrete exponential family***by*Vellaisamy, P. & Jain, Sushmita**1088-1093 On the link between dependence and independence in extreme value theory for dynamical systems***by*Freitas, Ana Cristina Moreira & Freitas, Jorge Milhazes**1094-1100 Confidence intervals for the normal mean utilizing prior information***by*Farchione, David & Kabaila, Paul**1101-1109 Modelling heterogeneity for bivariate survival data by the log-normal distribution***by*Hanagal, David D.**1110-1118 A general SLLN for the one-dimensional class cover problem***by*Wierman, John C. & Xiang, Pengfei**1119-1127 Proper Bayesian estimating equation based on Hilbert space method***by*Lin, Lu & Tan, Lin**1128-1137 Strong pointwise consistency of the kT -occupation time density estimator***by*Labrador, Boris**1138-1147 Sampling based succinct matrix approximation***by*Liu, Rong & Shi, Yong**1148-1157 p-variation of an integral functional driven by fractional Brownian motion***by*Yan, Litan & Yang, Xiangfeng & Lu, Yunsheng

### June 2008, Volume 78, Issue 8

**945-952 On the residual lifelengths of the remaining components in an n-k+1 out of n system***by*Bairamov, Ismihan & Arnold, Barry C.**953-962 Large deviations in testing fractional Ornstein-Uhlenbeck models***by*Bishwal, Jaya P.N.**963-969 A new generalized p-value for ANOVA under heteroscedasticity***by*Xu, Li-Wen & Wang, Song-Gui**970-974 Stratified two-stage sampling in domains: Sample allocation between domains, strata, and sampling stages***by*Kozak, Marcin & Zielinski, Andrzej & Singh, Sarjinder**975-984 On the minimization of concave information functionals for unsupervised classification via decision trees***by*Karakos, Damianos & Khudanpur, Sanjeev & Marchette, David J. & Papamarcou, Adrian & Priebe, Carey E.**985-991 Distribution functions of linear combinations of lattice polynomials from the uniform distribution***by*Marichal, Jean-Luc & Kojadinovic, Ivan**992-996 Note on integer-valued bilinear time series models***by*Drost, Feike C. & van den Akker, Ramon & Werker, Bas J.M.**997-1005 Diagnostic checking of multivariate nonlinear time series models with martingale difference errors***by*Chabot-Hallé, Dominique & Duchesne, Pierre**1006-1016 A new weighted integral goodness-of-fit statistic for exponentiality***by*Baringhaus, L. & Henze, N.**1017-1023 Some strong limit theorems for -mixing sequences of random variables***by*Wu, Qunying & Jiang, Yuanying**1024-1033 A limit theorem for solutions to BSDEs in the space of processes***by*Fan, Sheng-Jun & Hu, Jian-Hua**1034-1042 An approximation for the power function of a non-parametric test of fit***by*Boukili Makhoukhi, Mohammed**1043-1049 Consistency of the regression estimator with functional data under long memory conditions***by*Benhenni, K. & Hedli-Griche, S. & Rachdi, M. & Vieu, P.

### May 2008, Volume 78, Issue 7

**839-846 Complete moment convergence of moving average processes under dependence assumptions***by*Kim, Tae-Sung & Ko, Mi-Hwa**847-853 A functional ergodic theorem for the occupation time process of a branching system***by*Talarczyk, Anna**854-860 An almost sure invariance principle for additive functionals of Markov chains***by*Rassoul-Agha, F. & Seppäläinen, T.**861-868 Talagrand's inductive method and isoperimetric inequalities involving random sets***by*Zanger, Daniel Z.**869-879 Large deviation principle for an estimator of the diffusion coefficient in a jump-diffusion process***by*Mancini, Cecilia**880-884 A note on the Lasso for Gaussian graphical model selection***by*Meinshausen, Nicolai**885-889 A note on the Hájek-Rényi inequality for associated random variables***by*Sung, Soo Hak**890-895 A strong law of large numbers for pairwise independent identically distributed random variables with infinite means***by*Kruglov, Victor M.**896-903 Optimal foldover plans for regular s-level fractional factorial designs***by*Ai, Mingyao & Hickernell, Fred J. & Lin, Dennis K.J.**904-914 On a software reliability model by Koch and Spreij***by*Ledoux, James**915-923 Convergence in distribution for the sup-norm of a kernel density estimator for GARCH innovations***by*Mimoto, Nao**924-926 The Baum-Katz theorem for bounded subsequences***by*Stoica, George**927-937 A conditional Koziol-Green model under dependent censoring***by*Braekers, Roel & Veraverbeke, Noël**938-943 On the optimal allocation of components within coherent systems***by*Bhattacharya, Debasis & Samaniego, Francisco J.

### April 2008, Volume 78, Issue 6

**577-581 Small deviations for stable processes via compactness properties of the parameter set***by*Aurzada, Frank**582-593 Random coefficient volatility models***by*Thavaneswaran, A. & Peiris, S. & Appadoo, S.**594-598 Large deviations for the empirical mean of associated random variables***by*Henriques, Carla & Eduardo Oliveira, Paulo**599-607 Empirical likelihood for non-degenerate U-statistics***by*Jing, Bing-Yi & Yuan, Junqing & Zhou, Wang**608-615 Minimax designs for optimum mixtures***by*Pal, Manisha & Mandal, Nripes Kumar**616-621 Revisiting Sen's inequalities on order statistics***by*Balakrishnan, N. & Balasubramanian, K.**622-628 Behaviour of Dickey-Fuller tests when there is a break under the unit root null hypothesis***by*Sen, Amit**629-636 Testing parametric models in the presence of instrumental variables***by*Holzmann, Hajo**637-642 Characterizations of multiparameter Cox and Poisson processes by the renewal property***by*Merzbach, Ely & Shaki, Yair Y.**643-653 Asymptotic comparison of the mixed moment and classical extreme value index estimators***by*Gomes, M. Ivette & Neves, Cláudia**654-660 Infinite divisibility of skew Gaussian and Laplace laws***by*Kozubowski, Tomasz J. & Nolan, John P.**661-668 A spatial rank test and corresponding estimators for several samples***by*Nevalainen, Jaakko & Möttönen, Jyrki & Oja, Hannu**669-674 On bounded Gaussian processes***by*Le, H.**675-681 On the maxiset comparison between hard and block thresholding methods***by*Chesneau, Christophe**682-686 A continuous non-Brownian motion martingale with Brownian motion marginal distributions***by*Albin, J.M.P.**687-697 Moment inequalities for spatial processes***by*Gao, Jiti & Lu, Zudi & Tjøstheim, Dag**698-706 Unbounded mappings and weak convergence of measures***by*Zapala, August Michal**707-715 Ruin probabilities for discrete time risk models with stochastic rates of interest***by*Wei, Xiao & Hu, Yijun**716-719 A note on the weak convergence of probability measures in the D[0,1] space***by*Pakshirajan, R.P.**720-727 Statistical properties of exact confidence intervals from discrete data using studentized test statistics***by*Kabaila, Paul**728-735 A note on the autocorrelation properties of temporally aggregated Markov switching Gaussian models***by*Chan, Wai-Sum & Chan, Yin-Ting**736-738 Convergence in distribution of random compact sets in Polish spaces***by*Elalaoui-Talibi, Hussain & Peterson, Lisa D.**739-742 A note on the identifiability of the conditional expectation for the mixtures of neural networks***by*Stockis, Jean-Pierre & Tadjuidje-Kamgaing, Joseph & Franke, Jürgen**743-748 The size performance of a nonparametric unit root test under a variance shift***by*Maki, Daiki**749-758 The general principle for precise large deviations of heavy-tailed random sums***by*Lin, Jianxi**759-765 Runs in continuous-valued sequences***by*Eryilmaz, Serkan & Fu, James C.**766-770 How badly are the Burkholder-Davis-Gundy inequalities affected by arbitrary random times?***by*Nikeghbali, Ashkan**771-779 Probabilistic approach in weighted Markov branching processes***by*Chen, Anyue & Li, Junping & Ramesh, N.I.**780-784 Some results on subordination, selfdecomposability and operator semi-stability***by*Suk Choi, Gyeong**785-793 Asymptotic expansions for the moments of a semi-Markovian random walk with exponential distributed interference of chance***by*Khaniyev, T. & Kesemen, T. & Aliyev, R. & Kokangul, A.**794-803 A general method to the strong law of large numbers and its applications***by*Yang, Shanchao & Su, Chun & Yu, Keming**804-809 Central limit theorem of random quadratics forms involving random matrices***by*Pan, Guangming & Miao, Baiqi & Jin, Baisuo**810-814 Markovian extensions of a stochastic process***by*Petrovic, Ljiljana**815-823 Systems with weighted components***by*Samaniego, Francisco J. & Shaked, Moshe**824-829 A note on distortions induced by truncation with applications to linear regression systems***by*Marchetti, Giovanni M. & Stanghellini, Elena**830-838 Uniform convergence of autocovariances***by*Kavalieris, Laimonis

### April 2008, Volume 78, Issue 5

**463-470 Order statistics and renormalization***by*Pakes, Anthony G.**471-480 Finding a needle in a haystack: Conditions for reliable detection in the presence of clutter***by*Jedynak, Bruno & Karakos, Damianos**481-487 A note on the CIR process and the existence of equivalent martingale measures***by*Guo, Zhi Jun**488-489 A note on confidence intervals for the power of t-test***by*Gilliland, Dennis & Li, Mingfei**490-498 Exponential stability of non-autonomous stochastic partial differential equations with finite memory***by*Wan, Li & Duan, Jinqiao**499-507 Some improvements on a boundary corrected kernel density estimator***by*Karunamuni, R.J. & Zhang, S.**508-517 A note on constrained estimation in the simple linear measurement error model***by*Davidov, Ori & Griskin, Vladimir**518-527 Schur- and E-optimal two-level factorial designs***by*Butler, Neil A.**528-536 A generalized existence theorem of reflected BSDEs with double obstacles***by*Zheng, Shiqiu & Zhou, Shengwu**537-547 How rich is the class of processes which are infinitely divisible with respect to time?***by*Es-sebaiy, Khalifa & Ouknine, Youssef**548-556 Empirical likelihood for the two-sample mean problem***by*Liu, Yukun & Zou, Changliang & Zhang, Runchu**557-563 The mean resultant length of the spherically projected normal distribution***by*Presnell, Brett & Rumcheva, Pavlina**564-575 The theta-dependence coefficient and an Almost Sure Limit Theorem for random iterative models***by*Giuliano-Antonini, R. & Weber, M.

### March 2008, Volume 78, Issue 4

**327-335 On estimation of the exponent of regular variation using a sample with missing observations***by*Mladenovic, Pavle & Piterbarg, Vladimir**336-346 Asymptotic distributions of non-degenerate U-statistics on trimmed samples***by*Borovskikh, Yuri V. & Weber, N.C.**347-357 The almost sure central limit theorems in the joint version for the maxima and sums of certain stationary Gaussian sequences***by*Dudzinski, Marcin**358-366 On approximations for two classes of Poisson mixtures***by*Vinogradov, Vladimir**367-375 An almost sure central limit theorem for products of sums under association***by*Li, Yun-Xia & Wang, Jian-Feng**376-383 Generalized multivariate rank type test statistics via spatial U-quantiles***by*Zhou, Weihua & Serfling, Robert**384-389 An approximate method for nonlinear mixed-effects models with nonignorably missing covariates***by*Wu, Lang**390-395 The Borel-Cantelli lemma under dependence conditions***by*Chandra, Tapas Kumar**396-401 Empirical saddlepoint approximations of the Studentized mean under stratified random sampling***by*Hu, Zhishui & Ma, Chunsheng & Robinson, John**402-404 Generalized least squares transformation and estimation with autoregressive error***by*Vougas, Dimitrios V.**405-411 The equality of REML and ANOVA estimators of variance components in unbalanced normal classification models***by*Wulff, Shaun S.**412-419 Convergence of Archimedean copulas***by*Charpentier, Arthur & Segers, Johan**420-425 Inference on mean sub-vectors of two multivariate normal populations with unequal covariance matrices***by*Gamage, Jinadasa & Mathew, Thomas**426-434 FBSDE approach to utility portfolio selection in a market with random parameters***by*Ferland, René & Watier, François**435-444 Equivalence of Volterra processes: Degenerate case***by*Ouknine, Youssef & Erraoui, Mohamed**445-455 Strong convergence of a class of non-homogeneous Markov arrival processes to a Poisson process***by*Ledoux, James**456-462 On the statistical properties of a stationary process sampled by a stationary point process***by*Charlot, F. & Rachdi, M.

### February 2008, Volume 78, Issue 3

**207-213 An explicit representation of the limit of the LRT for interval mapping of quantitative trait loci***by*Zhang, Hong & Chen, Hanfeng & Li, Zhaohai**214-224 Independence after adaptive allocation***by*Bélisle, Claude & Melfi, Vince**225-230 Limiting behavior of a generalized branching process with immigration***by*Rahimov, I. & Al-Sabah, W.S.**231-237 A class of backward stochastic differential equations with discontinuous coefficients***by*Jia, Guangyan**238-248 Large deviations probabilities for a symmetry test statistic based on delta-sequence density estimation***by*Berrahou, Noureddine