Penalized single-index quantile regression

This article is made available through the Brunel Open Access Publishing Fund. Copyright for this article is retained by the author(s), with first publication rights granted to the journal. This is an open-access article distributed under the terms and conditions of the Creative Commons Attribution license (http://creativecommons.org/licenses/by/3.0/).The single-index (SI) regression and single-index quantile (SIQ) estimation methods product linear combinations of all the original predictors. However, it is possible that there are many unimportant predictors within the original predictors. Thus, the precision of parameter estimation as well as the accuracy of prediction will be effected by the existence of those unimportant predictors when the previous methods are used. In this article, an extension of the SIQ method of Wu et al. (2010) has been proposed, which considers Lasso and Adaptive Lasso for estimation and variable selection. Computational algorithms have been developed in order to calculate the penalized SIQ estimates. A simulation study and a real data application have been used to assess the performance of the methods under consideration

Forecasting Design Day Demand Using Extremal Quantile Regression

Extreme events occur rarely, making them difficult to predict. Extreme cold events strain natural gas systems to their limits. Natural gas distribution companies need to be prepared to satisfy demand on any given day that is at or warmer than an extreme cold threshold. The hypothetical day with temperature at this threshold is called the Design Day. To guarantee Design Day demand is satisfied, distribution companies need to determine the demand that is unlikely to be exceeded on the Design Day. We approach determining this demand as an extremal quantile regression problem. We review current methods for extremal quantile regression. We implement a quantile forecast to estimate the demand that has a minimal chance of being exceeded on the design day. We show extremal quantile regression to be more reliable than direct quantile estimation. We discuss the difficult task of evaluating a probabilistic forecast on rare events. Probabilistic forecasting is a quickly growing research topic in the field of energy forecasting. Our paper contributes to this field in three ways. First, we forecast quantiles during extreme cold events where data is sparse. Second, we forecast extremely high quantiles that have a very low probability of being exceeded. Finally, we provide a real world scenario on which to apply these techniques

The employment effects of innovation

The issue of technological unemployment receives perennial popular attention. Although there are previous empirical investigations that have focused on the relationship between innovation and employment, the originality of our approach lies in our choice of method. We focus on four 2-digit manufacturing industries that are known for their high patenting activity. We then use Principal Components Analysis to generate a firm-and year-specific "innovativeness" index by extracting the common variance in a firm's patenting and R&D expenditure histories. To begin with, we explore the heterogeneity of firms by using semi-parametric quantile regression. Whilst some firms may reduce employment levels after innovating, others increase employment. We then move on to a weighted least squares (WLS) analysis, which explicitly takes into account the different job-creating potential of firms of different sizes. As a result, we focus on the effect of innovation on total number of jobs, whereas previous studies have focused on the effect of innovation on firm behavior. Indeed, previous studies have typically taken the firm as the unit of analysis, implicity weighting each firm equally according to the principle of "one firm equals one observation". Our results suggest that firm-level innovative activity leads to employment creation that may have been underestimated in previous studies.Technological unemployment, innovation, firm growth, Weighted Least Squares, aggregation, quantile regression.

Uniform Bahadur Representation for Nonparametric Censored Quantile Regression: A Redistribution-of-Mass Approach

Censored quantile regressions have received a great deal of attention in the literature. In a linear setup, recent research has found that an estimator based on the idea of “redistribution-of-mass” in Efron (1967, Proceedings of the Fifth Berkeley Symposium on Mathematical Statistics and Probability, vol. 4, pp. 831–853, University of California Press) has better numerical performance than other available methods. In this paper, this idea is combined with the local polynomial kernel smoothing for nonparametric quantile regression of censored data. We derive the uniform Bahadur representation for the estimator and, more importantly, give theoretical justification for its improved efficiency over existing estimation methods. We include an example to illustrate the usefulness of such a uniform representation in the context of sufficient dimension reduction in regression analysis. Finally, simulations are used to investigate the finite sample performance of the new estimator

Using Quantile Regression in Hedonic Analysis to Reveal Submarket Competition

A root concern of hedonic property value models is that some commonly-used estimators aggregate very diverse households into a single regression, which may explain the marked differences in implicit price estimates for the same housing attributes across studies. In this paper, we extend a model that captures household heterogeneity through submarket identification and use quantile regression analysis to explore the role submarket competition plays in setting housing prices in those price ranges where different submarkets occupy homes of similar price. We find evidence of direct competition between submarkets with different preferences for at least some homes in a single neighborhood market. We cluster packages of attributes into three broad indices: dwelling structure variables, location variables, and adjacency variables. In the price ranges of competition between two submarkets, there is a clear premium paid in one of the indexed attribute by the final occupant to ‘outbid’ a member from another submarket. The attributes that realize a premium are those that are expected from prior analysis on what those submarkets prefer; and these premiums introduce variation in housing prices that would not be captured by standard hedonic approaches. By examining hedonic parameter instability at different housing price levels, we uncover not only latent diversity among homeowners but direct competition between them that calls into question policy and market conclusions drawn from standard hedonic price models, especially large sample hedonic studies.

Spillover effects among financial institutions: a state-dependent sensitivity value-at-risk approach : [Version September 2012]

In this paper, we develop a state-dependent sensitivity value-at-risk (SDSVaR) approach that enables us to quantify the direction, size, and duration of risk spillovers among financial institutions as a function of the state of financial markets (tranquil, normal, and volatile). Within a system of quantile regressions for four sets of major financial institutions (commercial banks, investment banks, hedge funds, and insurance companies) we show that while small during normal times, equivalent shocks lead to considerable spillover effects in volatile market periods. Commercial banks and, especially, hedge funds appear to play a major role in the transmission of shocks to other financial institutions. Using daily data, we can trace out the spillover effects over time in a set of impulse response functions and find that they reach their peak after 10 to 15 days