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We introduce a family of tests for regression coefficients based on signs of quantile regression residuals. In our approach, we first fit a quantile regression for the model where an independent variable of interest is not included in the set of model predictors (the null model). Then signs of residuals of this null model are tested for association with the predictor of interest. This conditionally exact testing procedure is applicable for randomized studies. Further, we extend this testing procedure to observational data when co-linearity between the variable of interest and other model predictors is possible. In the presence of possible co-linearity, tests for conditional association controlling for other model predictors are used. Monte Carlo simulation studies show superior performance of the introduced tests over several other widely available testing procedures. These simulations explore situations when normality of regression coefficients is not met. An illustrative example shows the use of the proposed tests for investigating associations of hypertension with quantiles of hemoglobin A1C change.

The purpose of the article is developing methods of calculating quantitative characteristics of public satisfaction with the activities of the local self-government, as well as with quality of public services provided at the municipality. We suppose that initial data are provided by a sociological survey of the population of the municipal district. Data processing is performed using the determinacy analysis and based on the calculation of variety of conditional frequencies of some properties in the context of other properties. Determinacy analysis provides an extension of regular technique. Along with calculation of the level of satisfaction with a service in a particular group of respondents (intensity), it uses a percentage of satisfaction which is explained by contribution of the particular group (capacity). The joint usage of intensity and capacity enrich and make more complete the interpretation of a survey data. In addition, we propose a technique for evaluation and usage of significance of individual answers. As a result we can adjust the intensity and capacity for extraction of useful information and for the better description of regularities observed in the survey data. DOI: 10.5901/mjss.2015.v6n6s2p444

A sign-based (SB) approach suggests an alternative criterion for quantile regression fit. The SB criterion is a piecewise constant function, which often leads to a non-unique solution. We compare the mid-point of this SB solution with the least absolute deviations (LAD) method and describe asymptotic properties of SB estimators under a weaker set of assumptions as compared with the assumptions often used with the generalized method of moments. Asymptotic properties of LAD and SB estimators are equivalent; however, there are finite sample differences as we show in simulation studies. At small to moderate sample sizes, the SB procedure for modelling quantiles at longer tails demonstrates a substantially lower bias, variance, and mean-squared error when compared with the LAD. In the illustrative example, we model a 0.8-level quantile of hospital charges and highlight finite sample advantage of the SB versus LAD.

The problem of statistical estimation of a linear functional of an unknown distribution with prior guess about the value of this functional is considered. A combined estimator of the functional is proposed to be used. The estimator is a linear combination of prior guess and nonparametric estimator. The optimal (in terms of minimal mean square error) weighting factor is subject of estimation itself, that can be done by using of prior guess recursively k times. According to this, k–adaptive combined estimators of the functional are proposed, their limiting distributions are presented. Examples of combined estimators and numerical results are provided.