Nonparametric Estimation with Aggregated Data

We introduce a kernel-based estimator of the density function and regression function for data that have been grouped into family totals. We allow for a common intra-family component but require that observations from different families be in dependent. We establish consistency and asymptotic normality for our procedures. As usual, the rates of convergence can be very slow depending on the behaviour of the characteristic function at infinity. We investigate the practical performance of our method in a simple Monte Carlo experimentAggregated data, deconvolution, grouped data, kernel, nonparametric regression

Asymptotic theory for nonparametric regression with spatial data

Nonparametric regression with spatial, or spatio-temporal, data is considered. The conditional mean of a dependent variable, given explanatory ones, is a nonparametric function, while the conditional covariance reflects spatial correlation. Conditional heteroscedasticity is also allowed, as well as non-identically distributed observations. Instead of mixing conditions, a (possibly non-stationary) linear process is assumed for disturbances, allowing for long range, as well as short-range, dependence, while decay in dependence in explanatory variables is described using a measure based on the departure of the joint density from the product of marginal densities. A basic triangular array setting is employed, with the aim of covering various patterns of spatial observation. Sufficient conditions are established for consistency and asymptotic normality of kernel regression estimates. When the cross-sectional dependence is sufficiently mild, the asymptotic variance in the central limit theorem is the same as when observations are independent; otherwise, the rate of convergence is slower. We discuss application of our conditions to spatial autoregressive models, and models defined on a regular lattice.

On Setting Apartment Rental Rates: A Regression-Based Approach

This study presents a regression-based analysis of apartment rents for a cross-section of properties located in an "edge city" submarket. It attempts to provide a solution for owners and managers of apartments to the thorny problem of setting a property's rental rate. The approach used in this analysis differs from previous studies in at least three important respects: (1) vacancy is treated as part of the dependent variable, (2) the property-specific rental rate generated by the regression analysis is compared to the property's actual effective rent, and (3) each property in the submarket is ranked by the difference between its actual effective rent and its characteristic-adjusted effective rent. This is then followed by several observations concerning the advantages and disadvantages of such an analysis in a practical setting.

A Censored Random Coefficients Model for Pooled Survey Data with Application to the Estimation of Power Outage Costs

In many surveys multiple observations on the dependent variable are collected from a given respondent. The resulting pooled data set is likely to be censored and to exhibit cross-sectional heterogeneity. We propose a model that addresses both issues by allowing regression coefficients to vary randomly across respondents and by using the Geweke-Hajivassiliou-Keane simulator and Halton sequences to estimate high-order probabilities. We show how this framework can be usefully applied to the estimation of power outage costs to firms using data from a recent survey conducted by a U.S. utility. Our results strongly reject the hypotheses of parameter constancy and cross-sectional homogeneity.