J. Santos Domínguez-Menchero

An L 2 point of view in testing monotone regression

In this paper, we propose a new approach to test isotonic regression based on the L 2-distance from a regression estimator to the set of all nondecreasing functions. This distance represents a natural measure of nondecrease and it provides a completely nonparametric test. The procedure is analyzed in fixed design models allowing more than one observation per design point. Up to now, only χ¯2-tests could be applied in this context, and these classical tests require normality of conditional distributions, as well as important restrictions on the variances and complex calculations when being carried out. In contrast, the nonparametric technique that we present does not require any restriction on the conditional variances and it is very simple to implement. In addition, its power under normality assumptions is similar to that of the classical χ¯2-tests.

A method to derive strong laws of large numbers for random upper semicontinuous functions

In this paper, we suggest a new method which is useful to study convergences of certain random upper semicontinuous elements by taking advantages of some well-known results concerning random cadlag functions. The suggested method is applied in the paper to developed strong laws of large numbers.

A Methodology to Collect Information on Future Hotel Prices Using Internet Distribution Systems

Specialised Internet Distribution Systems (IDS) offer an opportunity to design a sound methodological framework to monitor, collect and process data on hotel prices. IDS publish real-time prices enabling automatized information gathering. Thus, representative market snapshots can be taken in a reliable, robust and cost-efficient way. A modelling hotel dynamic pricing system based on data collected from IDS is developed. It provides information about current and future hotel prices. As an application example, an isotonic model is used to show the day of the booking plays a significant role in price and availability when booking a hotel room within 15 days in advance.

The Spiking Problem in the Context of the Isotonic Regression

The usual estimators of the regression under isotonicity are known to present the so-called spiking problem, that is, they are very sensitive at the tails. Three design-based strategies in order to alleviate this effect are discussed. The proposed strategies will provide uniform consistency on the (closed and bounded) working interval. Firstly, the usual isotonic regression with a suitable number of observations at the edges of the interval is considered. Secondly, a reallocation of part of the edge observations at some artificial adjacent points is suggested. Finally, a strategy based on constraining the isotonic regression to take values within some horizontal bands is investigated. Simulation studies illustrate the performance of the proposed estimators in practice.

Modelling Dynamic Hotel Pricing with Isotonic Functions

Hotel room rates and available rooms via online channels vary from day to day. From the customer’s point of view, when should a tourist book a room? In order to detect the optimal time to purchase a hotel room, modelling dynamic hotel pricing behaviour patterns must be considered. Nonparametric techniques using isotonic functions are shown to be useful to estimate a reliable model that analyses the evolution of room rates. Online hotel prices were observed for eight months, collecting more than 133,000 valid records. The results of this study show that a generally recommended strategy is to make the booking at least 15 days prior to the arrival date. Other booking strategy patterns are also detailed.

Testing constancy in monotone response models

A model in which the response is monotonically related to a given exposure or predictor is considered. This is motivated by dose-response analysis, however it also applies to survival distributions depending on a series of ordered multinomial parameters or, in a more general context, to change-point problems. In these contexts, although the monotonicity of the response may be a priori known, it is often crucial to determine whether the relationship is effective in a given interval, in the sense of not being constant. An efficient nonparametric test for the constancy of the regression when it is known to be monotone is developed for both independent and dependent data. The asymptotic null distribution of a test statistic based on the integrated regression function is obtained. The power against local alternatives is investigated, and the improvements with respect to the previous studies in the topic are shown. Some bootstrap procedures for the case of independent and dependent data are developed and employed in several applications.

On the local behaviour of the Yang regression estimate

Here we study the finite dimensional distribution of a process based on the Yang regression estimate. In getting information about the local behaviour of this estimate, our result allows solving the handicap of its asymptotical independence at finitely many points.