scholarly journals Asymptotic Size of Covering Arrays: An Application of Entropy Compression

2017 ◽  
Vol 25 (6) ◽  
pp. 243-257 ◽  
Author(s):  
Nevena Francetić ◽  
Brett Stevens
Keyword(s):  
Covering Arrays ◽  
Asymptotic Size ◽  
Entropy Compression

Analysis of Communication-to-Computation Based on Asymptotic Size for Iterative Methods

2014 ◽  
Vol 36 (4) ◽  
pp. 782-789
Author(s):  
Xiao-Wen XU ◽  
Ze-Yao MO ◽  
Lin-Ping WU
Keyword(s):  
Iterative Methods ◽  
Asymptotic Size

Factorials Experiments, Covering Arrays, and Combinatorial Testing

2021 ◽  
Author(s):  
Raghu N. Kacker ◽  
D. Richard Kuhn ◽  
Yu Lei ◽  
Dimitris E. Simos
Keyword(s):  
Combinatorial Testing ◽  
Covering Arrays

Testing for long memory in the presence of a general trend

2001 ◽  
Vol 38 (04) ◽  
pp. 1033-1054 ◽  
Author(s):  
Liudas Giraitis ◽  
Piotr Kokoszka ◽  
Remigijus Leipus
Keyword(s):  
Long Memory ◽  
Change Point ◽  
General Trend ◽  
Quantitative Description ◽  
Stationary Sequence ◽  
Change Points ◽  
Asymptotic Size ◽  
Short Memory ◽  
The Impact ◽  
Do So

The paper studies the impact of a broadly understood trend, which includes a change point in mean and monotonic trends studied by Bhattacharyaet al.(1983), on the asymptotic behaviour of a class of tests designed to detect long memory in a stationary sequence. Our results pertain to a family of tests which are similar to Lo's (1991) modifiedR/Stest. We show that both long memory and nonstationarity (presence of trend or change points) can lead to rejection of the null hypothesis of short memory, so that further testing is needed to discriminate between long memory and some forms of nonstationarity. We provide quantitative description of trends which do or do not fool theR/S-type long memory tests. We show, in particular, that a shift in mean of a magnitude larger thanN-½, whereNis the sample size, affects the asymptotic size of the tests, whereas smaller shifts do not do so.

New optimal covering arrays using an orderly algorithm

2018 ◽  
Vol 10 (01) ◽  
pp. 1850011 ◽  
Author(s):  
Idelfonso Izquierdo-Marquez ◽  
Jose Torres-Jimenez
Keyword(s):  
Small Subset ◽  
Computational Results ◽  
Covering Array ◽  
Covering Arrays ◽  
Computational Search ◽  
Minimum Number ◽  
Orderly Algorithm

A covering array [Formula: see text] is an [Formula: see text] array such that every [Formula: see text] subarray covers at least once each [Formula: see text]-tuple from [Formula: see text] symbols. For given [Formula: see text], [Formula: see text], and [Formula: see text], the minimum number of rows for which exists a CA is denoted by [Formula: see text] (CAN stands for Covering Array Number) and the corresponding CA is optimal. Optimal covering arrays have been determined algebraically for a small subset of cases; but another alternative to find CANs is the use of computational search. The present work introduces a new orderly algorithm to construct non-isomorphic covering arrays; this algorithm is an improvement of a previously reported algorithm for the same purpose. The construction of non-isomorphic covering arrays is used to prove the nonexistence of certain covering arrays whose nonexistence implies the optimality of other covering arrays. From the computational results obtained, the following CANs were established: [Formula: see text] for [Formula: see text], [Formula: see text], and [Formula: see text]. In addition, the new result [Formula: see text], and the already known existence of [Formula: see text], imply [Formula: see text].

scholarly journals Refining the In-Parameter-Order Strategy for Constructing Covering Arrays

2008 ◽  
Vol 113 (5) ◽  
pp. 287 ◽  
Author(s):  
Michael Forbes ◽  
Jim Lawrence ◽  
Yu Lei ◽  
Raghu N. Kacker ◽  
D. Richard Kuhn
Keyword(s):  
Covering Arrays

Research Notes: Binary Test-Suites Using Covering Arrays

2018 ◽  
Vol 28 (09) ◽  
pp. 1321-1337 ◽  
Author(s):  
Jose Torres-Jimenez ◽  
Himer Avila-George ◽  
Ezra Federico Parra-González
Keyword(s):  
Software Testing ◽  
Test Generation ◽  
Software Systems ◽  
Combinatorial Testing ◽  
Covering Array ◽  
Covering Arrays ◽  
Almost All ◽  
Generation Problem ◽  
Test Suites

Software testing is an essential activity to ensure the quality of software systems. Combinatorial testing is a method that facilitates the software testing process; it is based on an empirical evidence where almost all faults in a software component are due to the interaction of very few parameters. The test generation problem for combinatorial testing can be represented as the construction of a matrix that has certain properties; typically this matrix is a covering array. Covering arrays have a small number of tests, in comparison with an exhaustive approach, and provide a level of interaction coverage among the parameters involved. This paper presents a repository that contains binary covering arrays involving many levels of interaction. Also, it discusses the importance of covering array repositories in the construction of better covering arrays. In most of the cases, the size of the covering arrays included in the repository reported here are the best upper bounds known, moreover, the files containing the matrices of these covering arrays are available to be downloaded. The final purpose of our Binary Covering Arrays Repository (BCAR) is to provide software testing practitioners the best-known binary test-suites.

A density-based greedy algorithm for higher strength covering arrays

2009 ◽  
Vol 19 (1) ◽  
pp. 37-53 ◽  
Author(s):  
Renée C. Bryce ◽  
Charles J. Colbourn
Keyword(s):  
Greedy Algorithm ◽  
Covering Arrays

Covering arrays from m-sequences and character sums

2016 ◽  
Vol 85 (3) ◽  
pp. 437-456 ◽  
Author(s):  
Georgios Tzanakis ◽  
Lucia Moura ◽  
Daniel Panario ◽  
Brett Stevens
Keyword(s):  
Character Sums ◽  
Covering Arrays ◽  
M Sequences

scholarly journals ASYMPTOTIC SIZE OF KLEIBERGEN’S LM AND CONDITIONAL LR TESTS FOR MOMENT CONDITION MODELS

2016 ◽  
Vol 33 (5) ◽  
pp. 1046-1080 ◽  
Author(s):  
Donald W.K. Andrews ◽  
Patrik Guggenberger
Keyword(s):  
Moment Condition ◽  
Rank Statistic ◽  
Confidence Sets ◽  
Null Distributions ◽  
Asymptotic Size ◽  
Instrumental Variable Regression ◽  
Lm Test ◽  
Endogenous Variables ◽  
Influential Paper ◽  
Special Case

An influential paper by Kleibergen (2005, Econometrica 73, 1103–1123) introduces Lagrange multiplier (LM) and conditional likelihood ratio-like (CLR) tests for nonlinear moment condition models. These procedures aim to have good size performance even when the parameters are unidentified or poorly identified. However, the asymptotic size and similarity (in a uniform sense) of these procedures have not been determined in the literature. This paper does so.This paper shows that the LM test has correct asymptotic size and is asymptotically similar for a suitably chosen parameter space of null distributions. It shows that the CLR tests also have these properties when the dimension p of the unknown parameter θ equals 1. When p ≥ 2, however, the asymptotic size properties are found to depend on how the conditioning statistic, upon which the CLR tests depend, is weighted. Two weighting methods have been suggested in the literature. The paper shows that the CLR tests are guaranteed to have correct asymptotic size when p ≥ 2 when the weighting is based on an estimator of the variance of the sample moments, i.e., moment-variance weighting, combined with the Robin and Smith (2000, Econometric Theory 16, 151–175) rank statistic. The paper also determines a formula for the asymptotic size of the CLR test when the weighting is based on an estimator of the variance of the sample Jacobian. However, the results of the paper do not guarantee correct asymptotic size when p ≥ 2 with the Jacobian-variance weighting, combined with the Robin and Smith (2000, Econometric Theory 16, 151–175) rank statistic, because two key sample quantities are not necessarily asymptotically independent under some identification scenarios.Analogous results for confidence sets are provided. Even for the special case of a linear instrumental variable regression model with two or more right-hand side endogenous variables, the results of the paper are new to the literature.

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