Communication in Statistics- Theory and Methods

Conto López, Romario A.; Correa Espinal, Alexander A.; Úsuga Manco, Olga C.

doi: 10.1080/03610926.2023.2185472pmid: N/A

Abstract Run orders in factorial designs have been a topic of interest in recent decades because the basic principle of randomization does not necessarily eliminate the bias caused by unknown factors and also generates many level changes, making experimentation more expensive. Therefore, the literature in this area has addressed the construction of preestablished run orders to eliminate the bias produced by unknown factors and/or minimize the cost of the experiment. This paper presents the results of a systematic literature review (SLR) and a taxonomical classification of studies about run orders for factorial designs published between 1952 and 2021. The objective here is to describe the findings and main and future research directions in this field. The main components considered in each study and the methodologies they used to obtain run sequences are also highlighted, allowing professionals to select an appropriate ordering for their problem. This review shows that obtaining orderings with good properties for an experimental design with any number of factors and levels is still an unresolved issue.

Kim, Hyoung-Moon; Jang, Yu-Hyeong; Arnold, Barry C.; Zhao, Jun

doi: 10.1080/03610926.2023.2179880pmid: N/A

Abstract For some distributions, there is no available closed-form maximum likelihood estimator (MLE). This could be a problem when estimating the parameters of state-space models or of real-time processing models, because of time consuming iterations required to obtain an MLE. A simple method of obtaining a closed-form and efficient estimators for the univariate Weibull distribution is presented. Furthermore, an alternative efficient estimator for bivariate Weibull distribution parameters other than the MLE is also suggested. For the bivariate Weibull distribution, one estimator is not in closed-form, but the others are all in closed-form. In general, if we have a closed-form n -consistent estimator for each parameter, then we have a closed-form solution set which is efficient and has asymptotic normality. This is quite striking since we can obtain such a closed-form and efficient estimator using a very simple strategy. Roughly speaking, our suggested estimator is approximately 11 times as fast as the MLE for univariate case and 85 times for bivariate case. A simulation study is done for univariate and bivariate Weibull distributions to find some small sample properties. A real data illustration is also provided.

Bouzebda, Salim; Nezzal, Amel

doi: 10.1080/03610926.2023.2179887pmid: N/A

Abstract Stute (1991) introduced a class of so-called conditional U-statistics, which may be viewed as a generalization of the Nadaraya-Watson estimates of a regression function. Stute proved their strong pointwise consistency to: r ( k ) ( φ , t ) : = E [ φ ( Y 1 , … , Y k ) | ( X 1 , … , X k ) = t ] ,     for     t ∈ R d k . This article deals with a quite general non parametric statistical curve estimation setting including the Stute estimator as a particular case. The class of “delta sequence estimators” is defined and treated here. This class includes also the orthogonal series and histogram methods. The theoretical results concerning the exponential inequalities and the asymptotic normality, established in this article, are (or will be) key tools for many further developments in functional estimation. As a by-product of our proofs, we state consistency results for the delta sequences conditional U-statistics estimator, under the random censoring. Potential applications include discrimination problems, metric learning and multipartite ranking, Kendall rank correlation coefficient, generalized U-statistics, and set indexed conditional U-statistics.

R., Shenbagam; Y., Sarada

doi: 10.1080/03610926.2023.2185473pmid: N/A

Abstract To build highly reliable software products, software testing is required. The software engineer has a problem determining whether to complete the testing process and when to release the software system to the market. As the focus on high software increases, project managers must consider the cost of testing, testing availability time, and release time strategy. This research article utilizes a phase type non-homogeneous Poisson process to investigate the cost analysis and operational availability of a software reliability model. The software failure inter-arrival time is considered to follow a phase type distribution. The phase type software reliability model is valuable in reducing the time and effort required to select the appropriate models for software reliability evaluation. An explicit expression for the expected, bi-criterion cost analysis and operational availability is derived using standard results of the renewal reward theorem. The optimal software release policy T* is obtained analytically. Numerical illustrations and sensitivity analysis have been presented to illustrate the cost and availability analysis’s efficiency and demonstrate conformity with the study’s observations.

Kharrati-Kopaei, Mahmood; Shenavari, Zahra

doi: 10.1080/03610926.2023.2185752pmid: N/A

Abstract There are several objective tests for analyzing unreplicated two-level factorial designs. However, there is no single test that can detect all patterns of possible active effects. Tests are sensitive to the number and/or the magnitude of active effects. Therefore, it is reasonable to combine recommended tests into a single test to provide researchers with a testing approach that leverages many existing methods to detect different patterns of active effects. The problem is how to combine multiple dependent tests into a single test. In this article, we review four methods for combining dependent tests and present four combined tests. In addition, we review four recommended object tests for detecting active effects. We also propose a new test procedure that can detect active effects when the number of active effects is large. We finally evaluate these nine tests (five original tests and four combined tests) in terms of controlling the type I error rate and the power performance via a simulation study. Simulation results show that the combined test that is based on the Jacobi polynomial expansion can be recommended as a test procedure to detect active effects.

Vinaykumar, L. N.; Varghese, Cini; Harun, Mohd; Karmakar, Sayantani

doi: 10.1080/03610926.2023.2185753pmid: N/A

Abstract For situations in multi-site varietal trials where the experimenters demand incomplete blocks with unequal sizes, minimum number of replications, or both, new series of incomplete block designs have been presented. The proposed designs are higher associate partially balanced incomplete block designs in two replications having flexible block sizes. These designs are affine resolvable and are optimal in the competing class of resolvable incomplete block designs. The underlying association schemes of these designs are defined. Further, they can be advantageously used for obtaining designs for various stages of breeding trials. An R-package developed for generating these designs has also been demonstrated.

Tzavelas, George; Politis, Konstadinos

doi: 10.1080/03610926.2023.2186729pmid: N/A

Abstract We study the behavior of the failure rate associated with the distribution of a random variable of the form X = Y + U , where Y, U are independent and U has bounded support. First, we obtain monotonicity results and bounds for the failure rate of X in the case where U has a uniform distribution and, in particular we show that, asymptotically, the failure rates of X and Y tend to the same limit. Some of the results are generalized for the case where the distribution of U is not uniform, but has bounded support. Further, we show that if the failure rate of a non negative variable X is constant in some interval ( L , ∞ ) , then X can be written as the sum of two independent random variables, one of which is exponential and the other (which is not necessarily uniform) has support [ 0 , L ] .

Möttönen, Jyrki; Lähderanta, Tero; Salonen, Janne; Sillanpää, Mikko J.

doi: 10.1080/03610926.2023.2189059pmid: N/A

Abstract Zero-inflated explanatory variables, as opposed to outcome variables, are common, for example, in environmental sciences. In this article, we address the problem of having excess of zero values in some continuous explanatory variables, which are subject to multi-outcome lasso-regularized variable selection. In short, the problem results from the failure of the lasso-type of shrinkage methods to recognize any difference between zero value occurring either in the regression coefficient or in the corresponding value of the explanatory variable. This kind of confounding will obviously increase the number of false positives – all non-zero regression coefficients do not necessarily represent true outcome effects. We present here the adaptive LAD-lasso for multiple outcomes, which extends the earlier work of multi-outcome LAD-lasso with adaptive penalization. In addition to well-known property of having less biased regression coefficients, we show that the adaptivity also improves method’s ability to recover from influences of excess of zero values measured in continuous covariates.

Shi, Jianan; Yu, Zhenhong; Miao, Yu

doi: 10.1080/03610926.2023.2189498pmid: N/A

Abstract Let { X , X n , n ≥ 1 } be a sequence of pairwise NQD identically distributed random variables and { b n , n ≥ 1 } be a sequence of positive constants. In this article, we study the strong laws of large numbers for the sequence { X , X n , n ≥ 1 } , under the general moment condition ∑ n = 1 ∞ P ( | X | > b n /   log   n ) < ∞ , which improve some known results.

Aswin, I. C.; Sankaran, P. G.; Sunoj, S. M.

doi: 10.1080/03610926.2023.2189499pmid: N/A

Abstract In some experiments such as stress testing and industrial quality control experiments, only values which are larger or smaller than all previous ones are observed. Study of such extremes are of great importance. An extensive research on record values using distribution function are available in literature; however, a quantile-based study on the same have not been considered so far. Motivated with these, in this article, we introduce a quantile function approach of record values, which is an equivalent and alternative to the traditional distribution function approach. We study various properties of quantile-based measures of record values. We also obtain some stochastic comparison and ageing properties of quantile-based record values. The L-moment estimation method of hazard quantile function of record values is explained using a real-data example.