Weight smoothing for nonprobability surveys

Adjustment techniques to mitigate selection bias in nonprobability samples often involve modelling the propensity to participate in the nonprobability sample along with inverse propensity weighting. It is well known that procedures for estimating weights are effective if the covariates selected in the propensity model are related to both the variable of interest and the participation indicator. In most surveys, there are many variables of interest, making weight adjustments difficult to determine as a suitable weight for one variable may be unsuitable for other variables. The standard compromise is to include a large number of covariates in the propensity model but this may increase the variability of the estimates, especially when some covariates are weakly related to the variables of interest. Weight smoothing, developed for probability surveys, could be helpful in these situations. It aims to remove the variability caused by overfit propensity models by replacing the inverse propensity weights with predicted weights obtained using a smoothing model. In this article, we study weight smoothing in the nonprobability survey context, both theoretically and empirically, to understand its effectiveness at improving the efficiency of estimates.

Tractable circula densities from Fourier series

This article proposes an approach, based on infinite Fourier series, to constructing tractable densities for the bivariate circular analogues of copulas recently coined ‘circulas’. As examples of the general approach, we consider circula densities generated by various patterns of nonzero Fourier coefficients. The shape and sparsity of such arrangements are found to play a key role in determining the properties of the resultant models. The special cases of the circula densities we consider all have simple closed-form expressions involving no computationally demanding normalizing constants and display wide-ranging distributional shapes. A highly successful model identification tool and methods for parameter estimation and goodness-of-fit testing are provided for the circula densities themselves and the bivariate circular densities obtained from them using a marginal specification construction. The modelling capabilities of such bivariate circular densities are compared with those of five existing models in a numerical experiment, and their application illustrated in an analysis of wind directions.

Stochastic monotonicity of dependent variables given their sum

Given a finite set of independent random variables, assume one can observe their sum, and denote with s its value. Efron in 1965, and Lehmann in 1966, described conditions on the involved variables such that each of them stochastically increases in the value s, i.e., such that the expected value of any non-decreasing function of the variable increases as s increases. In this paper, we investigate conditions such that this stochastic monotonicity property is satisfied when the assumption of independence is removed. Comparisons in the stronger likelihood ratio order are considered as well.