Small-area estimation with spatial similarity

A class of composite estimators of small area quantities that exploit spatial (distancerelated)similarity is derived. It is based on a distribution-free model for the areas, but theestimators are aimed to have optimal design-based properties. Composition is applied alsoto estimate some of the global parameters on which the small area estimators depend.It is shown that the commonly adopted assumption of random effects is not necessaryfor exploiting the similarity of the districts (borrowing strength across the districts). Themethods are applied in the estimation of the mean household sizes and the proportions ofsingle-member households in the counties (comarcas) of Catalonia. The simplest version ofthe estimators is more efficient than the established alternatives, even though the extentof spatial similarity is quite modest.

A simple randomized algorithm for consistent sequential prediction of ergodic time series

We present a simple randomized procedure for the prediction of a binary sequence. The algorithm uses ideas from recent developments of the theory of the prediction of individual sequences. We show that if thesequence is a realization of a stationary and ergodic random process then the average number of mistakes converges, almost surely, to that of the optimum, given by the Bayes predictor.

Fighting against Malaria: Prevent wars while waiting for the "miraculous" vaccine

The World Health Organization estimates that 300 million clinical cases of malaria occur annually and observed that during the 80's and part of the 90's its incidence increased. In this paper we explore the influence of refugees from civil wars on the incidence of malaria in the refugee-receiving countries. Using civil wars as an instrumental variable we show that for each 1,000 refugees there are between 2,000 and 2,700 cases of malaria in the refugee receiving country. On average 13% of the cases of malaria reported by the WHO are caused by forced migration as a consequence of civil wars.

Worst-case bounds for the logarithmic loss of predictors

We investigate on-line prediction of individual sequences. Given a class of predictors, the goal is to predict as well as the best predictor in the class, where the loss is measured by the self information (logarithmic) loss function. The excess loss (regret) is closely related to the redundancy of the associated lossless universal code. Using Shtarkov's theorem and tools from empirical process theory, we prove a general upper bound on the best possible (minimax) regret. The bound depends on certain metric properties of the class of predictors. We apply the bound to both parametric and nonparametric classes ofpredictors. Finally, we point out a suboptimal behavior of the popular Bayesian weighted average algorithm.

Estimating parliamentary composition through electoral polls

Any electoral system has an electoral formula that converts voteproportions into parliamentary seats. Pre-electoral polls usually focuson estimating vote proportions and then applying the electoral formulato give a forecast of the parliament's composition. We here describe theproblems arising from this approach: there is always a bias in theforecast. We study the origin of the bias and some methods to evaluateand to reduce it. We propose some rules to compute the sample sizerequired for a given forecast accuracy. We show by Monte Carlo simulationthe performance of the proposed methods using data from Spanish electionsin last years. We also propose graphical methods to visualize how electoralformulae and parliamentary forecasts work (or fail).

University admission marks in Catalonia: Some highlights from the empirical research

The results of the examinations taken by graduated high school studentswho want to enrol at a Catalan university are here studied. To do so,the authors address several issues related to the equity of the system:reliability of grading, difficulty and discrimination power of the exams.The general emphasis is put upon the concurrent research and empiricalevidence about the properties of the examination items and scores. Aftera discussion about the limitations of the exams' format and appropriatenessof the instruments used in the study, the article concludes with somesuggestions to improve such examinations.

Inference with the lognormal distribution

Several estimators of the expectation, median and mode of the lognormal distribution are derived. They aim to be approximately unbiased, efficient, or have a minimax property in the class of estimators we introduce. The small-sample properties of these estimators are assessed by simulations and, when possible, analytically. Some of these estimators of the expectation are far more efficient than the maximum likelihood or the minimum-variance unbiased estimator, even for substantial samplesizes.

On the short-time behavior of the implied volatility for jump-diffusion models with stochastic volatility

In this paper we use Malliavin calculus techniques to obtain an expression for the short-time behavior of the at-the-money implied volatility skew for a generalization of the Bates model, where the volatility does not need to be neither a difussion, nor a Markov process as the examples in section 7 show. This expression depends on the derivative of the volatility in the sense of Malliavin calculus.

Improving small area estimation by combining surveys: new perspectives in regional statistics

A national survey designed for estimating a specific population quantity is sometimes used for estimation of this quantity also for a small area, such as a province. Budget constraints do not allow a greater sample size for the small area, and so other means of improving estimation have to be devised. We investigate such methods and assess them by a Monte Carlo study. We explore how a complementary survey can be exploited in small area estimation. We use the context of the Spanish Labour Force Survey (EPA) and the Barometer in Spain for our study.

Subsampling inference in threshold autoregressive models

This paper discusses inference in self exciting threshold autoregressive (SETAR)models. Of main interest is inference for the threshold parameter. It iswell-known that the asymptotics of the corresponding estimator depend uponwhether the SETAR model is continuous or not. In the continuous case, thelimiting distribution is normal and standard inference is possible. Inthe discontinuous case, the limiting distribution is non-normal and cannotbe estimated consistently. We show valid inference can be drawn by theuse of the subsampling method. Moreover, the method can even be extendedto situations where the (dis)continuity of the model is unknown. In thiscase, also the inference for the regression parameters of the modelbecomes difficult and subsampling can be used advantageously there aswell. In addition, we consider an hypothesis test for the continuity ofthe SETAR model. A simulation study examines small sample performance.

A BPE model for the Burgers' equation

We study the BPE (Brownian particle equation) model of the Burgers equationpresented in the preceeding article [6]. More precisely, we are interestedin establishing the existence and uniqueness properties of solutions usingprobabilistic techniques.

An empirical evaluation of small area estimators

This paper investigates the comparative performance of five small areaestimators. We use Monte Carlo simulation in the context of boththeoretical and empirical populations. In addition to the direct andindirect estimators, we consider the optimal composite estimator withpopulation weights, and two composite estimators with estimatedweights: one that assumes homogeneity of within area variance andsquare bias, and another one that uses area specific estimates ofvariance and square bias. It is found that among the feasibleestimators, the best choice is the one that uses area specificestimates of variance and square bias.

Almost sure testability of classes of densities

Let a class $\F$ of densities be given. We draw an i.i.d.\ sample from a density $f$ which may or may not be in $\F$. After every $n$, one must make a guess whether $f \in \F$ or not. A class is almost surely testable if there exists such a testing sequence such that for any $f$, we make finitely many errors almost surely. In this paper, several results are given that allowone to decide whether a class is almost surely testable. For example, continuity and square integrability are not testable, but unimodality, log-concavity, and boundedness by a given constant are.

A zero-delay sequential scheme for lossy coding of individual sequences

We consider adaptive sequential lossy coding of bounded individual sequences when the performance is measured by the sequentially accumulated mean squared distortion. Theencoder and the decoder are connected via a noiseless channel of capacity $R$ and both are assumed to have zero delay. No probabilistic assumptions are made on how the sequence to be encoded is generated. For any bounded sequence of length $n$, the distortion redundancy is defined as the normalized cumulative distortion of the sequential scheme minus the normalized cumulative distortion of the best scalarquantizer of rate $R$ which is matched to this particular sequence. We demonstrate the existence of a zero-delay sequential scheme which uses common randomization in the encoder and the decoder such that the normalized maximum distortion redundancy converges to zero at a rate $n^{-1/5}\log n$ as the length of the encoded sequence $n$ increases without bound.

A simple optimised search heuristic for the job-shop scheduling problem

This paper presents a simple Optimised Search Heuristic for the Job Shop Scheduling problem that combines a GRASP heuristic with a branch-and-bound algorithm. The proposed method is compared with similar approaches and leads to better results in terms of solution quality and computing times.