On tests of symmetry,marginal homogeneity and quasi-symmetry in two-way contingency tables based on minimum φ-divergence estimator with constraints

The restricted minimum φ-divergence estimator, [Pardo, J.A., Pardo, L. and Zografos, K., 2002, Minimum φ-divergence estimators with constraints in multinomial populations. Journal of Statistical Planning and Inference, 104, 221–237], is employed to obtain estimates of the cell frequencies of an I×I contingency table under hypotheses of symmetry, marginal homogeneity or quasi-symmetry. The associated φ-divergence statistics are distributed asymptotically as chi-squared distributions under the null hypothesis. The new estimators and test statistics contain, as particular cases, the classical estimators and test statistics previously presented in the literature for the cited problems. A simulation study is presented, for the symmetry problem, to choose the best function φ₂ for estimation and the best function φ₁ for testing.     

Consumers’ credit card repayment decisions: The role of higher anchors and future repayment concern

We investigated two aspects of credit card repayment decisions: the extent to which the anchoring effect of minimum repayment information may be mitigated by information on alternative anchors, specifically repayments that would repay the balance in two years (Study 1) or nine months (Study 2); and the role of future repayment concern. In two experiments, three realistic credit card statements were presented with different outstanding balances. Participants, who were randomly allocated to one of four information conditions depending on supplementary information provided on the statements, stated how much they would repay that month. They were then asked about concerns they would have about repayment difficulties if they had a fixed consumer loan over three years. In Study 1 the alternative two-year repayment anchor had a negative effect on percent repayment, whereas in Study 2 the nine-month repayment anchor had a significant positive effect, especially for those with higher future repayment concern. Also, in both studies, future repayment concern had a direct inverse effect on repayment decisions which partially mediated the effect of disposable income. It is concluded that the addition to credit card statements of a table of cost and duration information for a range of repayment amounts may usefully support repayment decisions.     

Probability Generating Function Based Jeffrey's Divergence for Statistical Inference

Statistical inference procedures based on transforms such as characteristic function and probability generating function have been examined by many researchers because they are much simpler than probability density functions. Here, a probability generating function based Jeffrey's divergence measure is proposed for parameter estimation and goodness-of-fit test. Being a member of the M-estimators, the proposed estimator is consistent. Also, the proposed goodness-of-fit test has good statistical power. The proposed divergence measure shows improved performance over existing probability generating function based measures. Real data examples are given to illustrate the proposed parameter estimation method and goodness-of-fit test.     

Lower bound of average centered L2-discrepancy for U-type designs

Uniform designs are widely used in various scientific investigations and industrial applications. By considering all possible level permutation of the factors, a connection between average centered L₂-discrepancy and generalized wordlength pattern for asymmetrical fractional factorial designs is derived. Moreover, we present new lower bounds to the average centered L₂-discrepancy for symmetrical and asymmetrical U-type designs. For illustration of the theoretical results, the lower bounds for symmetrical and asymmetrical U-type designs are tabulated, and numerical results indicate that our lower bounds behave well and can be recommended for use in practice.     

Estimating a sensitive proportion through randomized response procedures based on auxiliary information

Randomized response techniques are widely employed in surveys dealing with sensitive questions to ensure interviewee anonymity and reduce nonrespondents rates and biased responses. Since Warner’s (J Am Stat Assoc 60:63–69, 1965) pioneering work, many ingenious devices have been suggested to increase respondent’s privacy protection and to better estimate the proportion of people, π _A , bearing a sensitive attribute. In spite of the massive use of auxiliary information in the estimation of non-sensitive parameters, very few attempts have been made to improve randomization strategy performance when auxiliary variables are available. Moving from Zaizai’s (Model Assist Stat Appl 1:125–130, 2006) recent work, in this paper we provide a class of estimators for π _A , for a generic randomization scheme, when the mean of a supplementary non-sensitive variable is known. The minimum attainable variance bound of the class is obtained and the best estimator is also identified. We prove that the best estimator acts as a regression-type estimator which is at least as efficient as the corresponding estimator evaluated without allowing for the auxiliary variable. The general results are then applied to Warner and Simmons’ model.     

Two-step estimation for inhomogeneous spatial point processes

Summary.  The paper is concerned with parameter estimation for inhomogeneous spatial point processes with a regression model for the intensity function and tractable second-order properties ( K -function). Regression parameters are estimated by using a Poisson likelihood score estimating function and in the second step minimum contrast estimation is applied for the residual clustering parameters. Asymptotic normality of parameter estimates is established under certain mixing conditions and we exemplify how the results may be applied in ecological studies of rainforests.     

Can the minimum living standard guarantee scheme enable the poor to escape the poverty trap in rural China?

The rural Minimum Living Standard Guarantee (Dibao) Scheme is the most important social assistance programme in rural China. However, how the rural Dibao programme affects household expenditures and whether it can enable the poor to escape the poverty trap are questions that remain largely unexplored. This study used data from the 2012 Rural Household Survey in China to investigate the impact of the rural Dibao programme on household expenditures. We found that the programme significantly improved the well‐being of low‐income households. Particularly, the programme significantly increased household expenditures on housing, education and health; furthermore, the impact was greater for households with educated household heads. However, the programme did not significantly affect household expenditures on food, transportation or farming inputs. The results imply that participation in the rural Dibao programme induces household investment in human capital, which could help to break the inter‐generational transmission of poverty and raise long‐run welfare.     

Generalized minimum aberration mixed-level orthogonal arrays: A general approach based on sequential integer quadratically constrained quadratic programming

Orthogonal fractional factorial designs and in particular orthogonal arrays (OAs) are frequently used in many fields of application, including medicine, engineering, and agriculture. In this article, we present a methodology and an algorithm to find an OA, of given size and strength, which satisfies the generalized minimum aberration criterion. The methodology is based on the joint use of polynomial counting functions, complex coding of levels, and algorithms for quadratic optimization and puts no restriction on the number of levels of each factor.     

Optimal split‐plot orthogonal arrays

It is well known that many industrial experiments have split‐plot structures. Compared to completely randomised experiments, split‐plot designs are more economical and thus have received much attention among researchers. Much work has been done for two‐level split‐plot designs. In this article, we consider split‐plot designs with factors of three, more than three, or mixed levels and with both qualitative and quantitative factors. We show that if two designs with both qualitative and quantitative factors are geometrically isomorphic, then their generalised wordlength patterns are identical. Three design scenarios are considered for optimal designs. The corresponding wordlength patterns are defined and the minimum aberration mixed‐level split‐plot designs having 18 and 36 runs are tabulated.