Speed of wave-front solutions to hyperbolic reaction-diffusion equations

The asymptotic speed problem of front solutions to hyperbolic reaction-diffusion (HRD) equations is studied in detail. We perform linear and variational analyses to obtain bounds for the speed. In contrast to what has been done in previous work, here we derive upper bounds in addition to lower ones in such a way that we can obtain improved bounds. For some functions it is possible to determine the speed without any uncertainty. This is also achieved for some systems of HRD (i.e., time-delayed Lotka-Volterra) equations that take into account the interaction among different species. An analytical analysis is performed for several systems of biological interest, and we find good agreement with the results of numerical simulations as well as with available observations for a system discussed recently

Non-peaky signals in wideband fading channels: achievable bit rates and optimal bandwidth

In the context of fading channels it is well established that, with a constrained transmit power, the bit rates achievable by signals that are not peaky vanish as the bandwidth grows without bound. Stepping back from the limit, we characterize the highest bit rate achievable by such non-peaky signals and the approximate bandwidth where that apex occurs. As it turns out, the gap between the highest rate achievable without peakedness and the infinite-bandwidth capacity (with unconstrained peakedness) is small for virtually all settings of interest to wireless communications. Thus, although strictly achieving capacity in wideband fading channels does require signal peakedness, bit rates not far from capacity can be achieved with conventional signaling formats that do not exhibit the serious practical drawbacks associated with peakedness. In addition, we show that the asymptotic decay of bit rate in the absence of peakedness usually takes hold at bandwidths so large that wideband fading models are called into question. Rather, ultrawideband models ought to be used.

Federalism and democracy. The case of minority nations: a federalist deficit

In this chapter, after pointing out the different logics that lie behind the familiar ideas of democracy and federalism, I have dealt with the case of plurinational federal democracies. Having put forward a double criterion of an empirical nature with which to differentiate between the existence of minority nations within plurinational democracies (section 2), I suggest three theoretical criteria for the political accommodation of these democracies. In the following section, I show the agonistic nature of the normative discussion of the political accommodation of this kind of democracies, which bring monist and pluralist versions of the demos of the polity into conflict (section 3.1), as well as a number of conclusions which are the result of a comparative study of 19 federal and regional democracies using four analytical axes: the uninational/plurinational axis; the unitarianism-federalism axis; the centralisation-decentralisation axis; and the symmetry-asymmetry axis (section 3.2). This analysis reveals shortcomings in the constitutional recognition of national pluralism in federal and regional cases with a large number of federated units/regions with political autonomy; a lower degree of constitutional federalism and a greater asymmetry in the federated entities or regions of plurinational democracies. It also reveals difficulties to establish clear formulas in these democracies in order to encourage a “federalism of trust” based on the participation and protection of national minorities in the shared government of plurinational federations/regional states. Actually, there is a federal deficit in this kind polities according to normative liberal-democratic patterns and to what comparative analysis show. Finally, this chapter advocates the need for a greater normative and institutional refinement in plurinational federal democracies. In order to achieve this, it is necessary to introduce a deeper form of “ethical” pluralism -which displays normative agonistic trends, as well as a more “confederal/asymmetrical” perspective, congruent with the national pluralism of these kind of polities.

Life-Cycle Effects on Household Expenditures: A Latent-Variable Approach

Using data from the Spanish household budget survey, we investigate life- cycle effects on several product expenditures. A latent-variable model approach is adopted to evaluate the impact of income on expenditures, controlling for the number of members in the family. Two latent factors underlying repeated measures of monetary and non-monetary income are used as explanatory variables in the expenditure regression equations, thus avoiding possible bias associated to the measurement error in income. The proposed methodology also takes care of the case in which product expenditures exhibit a pattern of infrequent purchases. Multiple-group analysis is used to assess the variation of key parameters of the model across various household life-cycle typologies. The analysis discloses significant life-cycle effects on the mean levels of expenditures; it also detects significant life-cycle effects on the way expenditures are affected by income and family size. Asymptotic robust methods are used to account for possible non-normality of the data.

Lyfe-cycle effects on household expenditures: A latent-variable approach

Using data from the Spanish household budget survey, we investigate life-cycle effects on several product expenditures. A latent-variable model approach is adopted to evaluate the impact of income on expenditures, controlling for the number of members in the family. Two latent factors underlying repeated measures of monetary and non-monetary income are used as explanatory variables in the expenditure regression equations, thus avoiding possible bias associated to the measurement error in income. The proposed methodology also takes care of the case in which product expenditures exhibit a pattern of infrequent purchases. Multiple-group analysis is used to assess the variation of key parameters of the model across various household life-cycle typologies. The analysis discloses significant life-cycle effects on the mean levels of expenditures; it also detects significant life-cycle effects on the way expenditures are affected by income and family size. Asymptotic robust methods are used to account for possible non-normality of the data.

Fusion of data sets in multivariate linear regression with errors-in-variables

We consider the application of normal theory methods to the estimation and testing of a general type of multivariate regressionmodels with errors--in--variables, in the case where various data setsare merged into a single analysis and the observable variables deviatepossibly from normality. The various samples to be merged can differ on the set of observable variables available. We show that there is a convenient way to parameterize the model so that, despite the possiblenon--normality of the data, normal--theory methods yield correct inferencesfor the parameters of interest and for the goodness--of--fit test. Thetheory described encompasses both the functional and structural modelcases, and can be implemented using standard software for structuralequations models, such as LISREL, EQS, LISCOMP, among others. An illustration with Monte Carlo data is presented.

A generalization of histogram type estimators

We introduce simple nonparametric density estimators that generalize theclassical histogram and frequency polygon. The new estimators are expressed as linear combination of density functions that are piecewisepolynomials, where the coefficients are optimally chosen in order to minimize the integrated square error of the estimator. We establish the asymptotic behaviour of the proposed estimators, and study theirperformance in a simulation study.

Minimax lower bounds for the two-armed bandit problem

We obtain minimax lower bounds on the regret for the classicaltwo--armed bandit problem. We provide a finite--sample minimax version of the well--known log $n$ asymptotic lower bound of Lai and Robbins. Also, in contrast to the log $n$ asymptotic results on the regret, we show that the minimax regret is achieved by mere random guessing under fairly mild conditions on the set of allowable configurations of the two arms. That is, we show that for {\sl every} allocation rule and for {\sl every} $n$, there is a configuration such that the regret at time $n$ is at least 1 -- $\epsilon$ times the regret of random guessing, where $\epsilon$ is any small positive constant.

On the closed-form approximation of short-time random strike options

In this paper we propose a general technique to develop first and second order closed-form approximation formulas for short-time options withrandom strikes. Our method is based on Malliavin calculus techniques andallows us to obtain simple closed-form approximation formulas dependingon the derivative operator. The numerical analysis shows that these formulas are extremely accurate and improve some previous approaches ontwo-assets and three-assets spread options as Kirk's formula or the decomposition mehod presented in Alòs, Eydeland and Laurence (2011).

Finite sample nonparametric tests for linear regressions

We introduce several exact nonparametric tests for finite sample multivariatelinear regressions, and compare their powers. This fills an important gap inthe literature where the only known nonparametric tests are either asymptotic,or assume one covariate only.

Compact matrix expressions for generalized Wald tests of equality of moment vectors

Asymptotic chi-squared test statistics for testing the equality ofmoment vectors are developed. The test statistics proposed aregeneralizedWald test statistics that specialize for different settings by inserting andappropriate asymptotic variance matrix of sample moments. Scaled teststatisticsare also considered for dealing with situations of non-iid sampling. Thespecializationwill be carried out for testing the equality of multinomial populations, andtheequality of variance and correlation matrices for both normal andnon-normaldata. When testing the equality of correlation matrices, a scaled versionofthe normal theory chi-squared statistic is proven to be an asymptoticallyexactchi-squared statistic in the case of elliptical data.

Option pricing under stochastic volatility and stochastic interest rate in the Spanish case

Among the underlying assumptions of the Black-Scholes option pricingmodel, those of a fixed volatility of the underlying asset and of aconstantshort-term riskless interest rate, cause the largest empirical biases. Onlyrecently has attention been paid to the simultaneous effects of thestochasticnature of both variables on the pricing of options. This paper has tried toestimate the effects of a stochastic volatility and a stochastic interestrate inthe Spanish option market. A discrete approach was used. Symmetricand asymmetricGARCH models were tried. The presence of in-the-mean and seasonalityeffectswas allowed. The stochastic processes of the MIBOR90, a Spanishshort-terminterest rate, from March 19, 1990 to May 31, 1994 and of the volatilityofthe returns of the most important Spanish stock index (IBEX-35) fromOctober1, 1987 to January 20, 1994, were estimated. These estimators wereused onpricing Call options on the stock index, from November 30, 1993 to May30, 1994.Hull-White and Amin-Ng pricing formulas were used. These prices werecomparedwith actual prices and with those derived from the Black-Scholesformula,trying to detect the biases reported previously in the literature. Whereasthe conditional variance of the MIBOR90 interest rate seemed to be freeofARCH effects, an asymmetric GARCH with in-the-mean and seasonalityeffectsand some evidence of persistence in variance (IEGARCH(1,2)-M-S) wasfoundto be the model that best represent the behavior of the stochasticvolatilityof the IBEX-35 stock returns. All the biases reported previously in theliterature were found. All the formulas overpriced the options inNear-the-Moneycase and underpriced the options otherwise. Furthermore, in most optiontrading, Black-Scholes overpriced the options and, because of thetime-to-maturityeffect, implied volatility computed from the Black-Scholes formula,underestimatedthe actual volatility.

Variable Kernel estimates: On the impossibility of tuning the parameters

For the standard kernel density estimate, it is known that one can tune the bandwidth such that the expected L1 error is within a constant factor of the optimal L1 error (obtained when one is allowed to choose the bandwidth with knowledge of the density). In this paper, we pose the same problem for variable bandwidth kernel estimates where the bandwidths are allowed to depend upon the location. We show in particular that for positive kernels on the real line, for any data-based bandwidth, there exists a densityfor which the ratio of expected L1 error over optimal L1 error tends to infinity. Thus, the problem of tuning the variable bandwidth in an optimal manner is ``too hard''. Moreover, from the class of counterexamples exhibited in the paper, it appears thatplacing conditions on the densities (monotonicity, convexity, smoothness) does not help.

Scaled and adjusted restricted tests in multi-sample analysis of moment structures

We extend to score, Wald and difference test statistics the scaled and adjusted corrections to goodness-of-fit test statistics developed in Satorra and Bentler (1988a,b). The theory is framed in the general context of multisample analysis of moment structures, under general conditions on the distribution of observable variables. Computational issues, as well as the relation of the scaled and corrected statistics to the asymptotic robust ones, is discussed. A Monte Carlo study illustrates thecomparative performance in finite samples of corrected score test statistics.

Social security and democracy

Many political economic theories use and emphasize the process of votingin their explanation of the growth of Social Security, governmentspending, and other public policies. But is there an empirical connectionbetween democracy and Social Security program size or design? Using somenew international data sets to produce both country-panel econometricestimates as well as case studies of South American and southern Europeancountries, we find that Social Security policy varies according toeconomic and demographic factors, but that very different politicalhistories can result in the same Social Security policy. We find littlepartial effect of democracy on the size of Social Security budgets, onhow those budgets are allocated, or how economic and demographic factorsaffect Social Security. If there is any observed difference, democraciesspend a little less of their GDP on Social Security, grow their budgetsa bit more slowly, and cap their payroll tax more often, than doeconomically and demographically similar nondemocracies. Democracies andnondemocracies are equally likely to have benefit formulas inducingretirement and, conditional on GDP per capita, equally likely to induceretirement with a retirement test vs. an earnings test.