Maximum-likelihood estimation of specific differential phase and attenuation in rain

Precise estimation of propagation parameters inprecipitation media is of interest to improve the performanceof communications systems and in remote sensing applications.In this paper, we present maximum-likelihood estimators ofspecific attenuation and specific differential phase in rain. Themodel used for obtaining the cited estimators assumes coherentpropagation, reflection symmetry of the medium, and Gaussianstatistics of the scattering matrix measurements. No assumptionsabout the microphysical properties of the medium are needed.The performance of the estimators is evaluated through simulateddata. Results show negligible estimators bias and variances closeto Cramer–Rao bounds.

Unemployment dynamics and NAIRU estimates for CEECs : a univariate approach

In this paper we test for the hysteresis versus the natural rate hypothesis on the unemployment rates of the EU new members using unit root tests that account for the presence of level shifts. As a by product, the analysis proceeds to the estimation of a NAIRU measure from a univariate point of view. The paper also focuses on the precision of these NAIRU estimates studying the two sources of inaccuracy that derive from the break points estimation and the autoregressive parameters estimation. The results point to the existence of up to four structural breaks in the transition countries NAIRU that can be associated with institutional changes implementing market-oriented reforms. Moreover, the degree of persistence in unemployment varies dramatically among the individual countries depending on the stage reached in the transition process

Unemployment dynamics and NAIRU estimates for CEECs : a univariate approach

In this paper we test for the hysteresis versus the natural rate hypothesis on the unemployment rates of the EU new members using unit root tests that account for the presence of level shifts. As a by product, the analysis proceeds to the estimation of a NAIRU measure from a univariate point of view. The paper also focuses on the precision of these NAIRU estimates studying the two sources of inaccuracy that derive from the break points estimation and the autoregressive parameters estimation. The results point to the existence of up to four structural breaks in the transition countries NAIRU that can be associated with institutional changes implementing market-oriented reforms. Moreover, the degree of persistence in unemployment varies dramatically among the individual countries depending on the stage reached in the transition process

A finite-population revenue management model and a risk-ratio procedure for the joint estimation of population size and parameters

Many dynamic revenue management models divide the sale period into a finite number of periods T and assume, invoking a fine-enough grid of time, that each period sees at most one booking request. These Poisson-type assumptions restrict the variability of the demand in the model, but researchers and practitioners were willing to overlook this for the benefit of tractability of the models. In this paper, we criticize this model from another angle. Estimating the discrete finite-period model poses problems of indeterminacy and non-robustness: Arbitrarily fixing T leads to arbitrary control values and on the other hand estimating T from data adds an additional layer of indeterminacy. To counter this, we first propose an alternate finite-population model that avoids this problem of fixing T and allows a wider range of demand distributions, while retaining the useful marginal-value properties of the finite-period model. The finite-population model still requires jointly estimating market size and the parameters of the customer purchase model without observing no-purchases. Estimation of market-size when no-purchases are unobservable has rarely been attempted in the marketing or revenue management literature. Indeed, we point out that it is akin to the classical statistical problem of estimating the parameters of a binomial distribution with unknown population size and success probability, and hence likely to be challenging. However, when the purchase probabilities are given by a functional form such as a multinomial-logit model, we propose an estimation heuristic that exploits the specification of the functional form, the variety of the offer sets in a typical RM setting, and qualitative knowledge of arrival rates. Finally we perform simulations to show that the estimator is very promising in obtaining unbiased estimates of population size and the model parameters.

Estimation of the parameters of the gravitational-wage signal of a coalescing binary system

The statistical theory of signal detection and the estimation of its parameters are reviewed and applied to the case of detection of the gravitational-wave signal from a coalescing binary by a laser interferometer. The correlation integral and the covariance matrix for all possible static configurations are investigated numerically. Approximate analytic formulas are derived for the case of narrow band sensitivity configuration of the detector.

Estimation of the viscoelastic properties of vessel walls using a computational model and Doppler ultrasound

Human arteries affected by atherosclerosis are characterized by altered wall viscoelastic properties. The possibility of noninvasively assessing arterial viscoelasticity in vivo would significantly contribute to the early diagnosis and prevention of this disease. This paper presents a noniterative technique to estimate the viscoelastic parameters of a vascular wall Zener model. The approach requires the simultaneous measurement of flow variations and wall displacements, which can be provided by suitable ultrasound Doppler instruments. Viscoelastic parameters are estimated by fitting the theoretical constitutive equations to the experimental measurements using an ARMA parameter approach. The accuracy and sensitivity of the proposed method are tested using reference data generated by numerical simulations of arterial pulsation in which the physiological conditions and the viscoelastic parameters of the model can be suitably varied. The estimated values quantitatively agree with the reference values, showing that the only parameter affected by changing the physiological conditions is viscosity, whose relative error was about 27% even when a poor signal-to-noise ratio is simulated. Finally, the feasibility of the method is illustrated through three measurements made at different flow regimes on a cylindrical vessel phantom, yielding a parameter mean estimation error of 25%.

Multiuser detection in a dynamic environment — Part II: Joint user identification and parameter estimation

The problem of jointly estimating the number, the identities, and the data of active users in a time-varying multiuser environment was examined in a companion paper (IEEE Trans. Information Theory, vol. 53, no. 9, September 2007), at whose core was the use of the theory of finite random sets on countable spaces. Here we extend that theory to encompass the more general problem of estimating unknown continuous parameters of the active-user signals. This problem is solved here by applying the theory of random finite sets constructed on hybrid spaces. We doso deriving Bayesian recursions that describe the evolution withtime of a posteriori densities of the unknown parameters and data.Unlike in the above cited paper, wherein one could evaluate theexact multiuser set posterior density, here the continuous-parameter Bayesian recursions do not admit closed-form expressions. To circumvent this difficulty, we develop numerical approximationsfor the receivers that are based on Sequential Monte Carlo (SMC)methods (“particle filtering”). Simulation results, referring to acode-divisin multiple-access (CDMA) system, are presented toillustrate the theory.

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.

Using composite estimators to improve both domain and total area estimation

In this article we propose using small area estimators to improve the estimatesof both the small and large area parameters. When the objective is to estimateparameters at both levels accurately, optimality is achieved by a mixed sampledesign of fixed and proportional allocations. In the mixed sample design, oncea sample size has been determined, one fraction of it is distributedproportionally among the different small areas while the rest is evenlydistributed among them. We use Monte Carlo simulations to assess theperformance of the direct estimator and two composite covariant-freesmall area estimators, for different sample sizes and different sampledistributions. Performance is measured in terms of Mean Squared Errors(MSE) of both small and large area parameters. It is found that the adoptionof small area composite estimators open the possibility of 1) reducingsample size when precision is given, or 2) improving precision for a givensample size.

On the performance of small-area estimators: Fixed vs. random area parameters

Most methods for small-area estimation are based on composite estimators derived from design- or model-based methods. A composite estimator is a linear combination of a direct and an indirect estimator with weights that usually depend on unknown parameters which need to be estimated. Although model-based small-area estimators are usually based on random-effects models, the assumption of fixed effects is at face value more appropriate.Model-based estimators are justified by the assumption of random (interchangeable) area effects; in practice, however, areas are not interchangeable. In the present paper we empirically assess the quality of several small-area estimators in the setting in which the area effects are treated as fixed. We consider two settings: one that draws samples from a theoretical population, and another that draws samples from an empirical population of a labor force register maintained by the National Institute of Social Security (NISS) of Catalonia. We distinguish two types of composite estimators: a) those that use weights that involve area specific estimates of bias and variance; and, b) those that use weights that involve a common variance and a common squared bias estimate for all the areas. We assess their precision and discuss alternatives to optimizing composite estimation in applications.

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.

Firm investment in imperfect capital markets: A structural estimation

We set up a dynamic model of firm investment in which liquidity constraintsenter explicity into the firm's maximization problem. The optimal policyrules are incorporated into a maximum likelihood procedure which estimatesthe structural parameters of the model. Investment is positively related tothe firm's internal financial position when the firm is relatively poor. This relationship disappears for wealthy firms, which can reach theirdesired level of investment. Borrowing is an increasing function of financial position for poor firms. This relationship is reversed as a firm's financial position improves, and large firms hold little debt.Liquidity constrained firms may be unused credits lines and the capacity toinvest further if they desire. However the fear that liquidity constraintswill become binding in the future induces them to invest only when internalresources increase.We estimate the structural parameters of the model and use them to quantifythe importance of liquidity constraints on firms' investment. We find thatliquidity constraints matter significantly for the investment decisions of firms. If firms can finance investment by issuing fresh equity, rather than with internal funds or debt, average capital stock is almost 35% higher overa period of 20 years. Transitory shocks to internal funds have a sustained effect on the capital stock. This effect lasts for several periods and ismore persistent for small firms than for large firms. A 10% negative shock to firm fundamentals reduces the capital stock of firms which face liquidityconstraints by almost 8% over a period as opposed to only 3.5% for firms which do not face these constraints.

Minimum distance estimation of stationary and non-stationary ARFIMA processes

A new parametric minimum distance time-domain estimator for ARFIMA processes is introduced in this paper. The proposed estimator minimizes the sum of squared correlations of residuals obtained after filtering a series through ARFIMA parameters. The estimator iseasy to compute and is consistent and asymptotically normally distributed for fractionallyintegrated (FI) processes with an integration order d strictly greater than -0.75. Therefore, it can be applied to both stationary and non-stationary processes. Deterministic components are also allowed in the DGP. Furthermore, as a by-product, the estimation procedure provides an immediate check on the adequacy of the specified model. This is so because the criterion function, when evaluated at the estimated values, coincides with the Box-Pierce goodness of fit statistic. Empirical applications and Monte-Carlo simulations supporting the analytical results and showing the good performance of the estimator in finite samples are also provided.

Using spatially distributed parameters and multi-response objective functions to solve parameterization of complex applications of semi-distributed hydrological models

Application of semi-distributed hydrological models to large, heterogeneous watersheds deals with several problems. On one hand, the spatial and temporal variability in catchment features should be adequately represented in the model parameterization, while maintaining the model complexity in an acceptable level to take advantage of state-of-the-art calibration techniques. On the other hand, model complexity enhances uncertainty in adjusted model parameter values, therefore increasing uncertainty in the water routing across the watershed. This is critical for water quality applications, where not only streamflow, but also a reliable estimation of the surface versus subsurface contributions to the runoff is needed. In this study, we show how a regularized inversion procedure combined with a multiobjective function calibration strategy successfully solves the parameterization of a complex application of a water quality-oriented hydrological model. The final value of several optimized parameters showed significant and consistentdifferences across geological and landscape features. Although the number of optimized parameters was significantly increased by the spatial and temporal discretization of adjustable parameters, the uncertainty in water routing results remained at reasonable values. In addition, a stepwise numerical analysis showed that the effects on calibration performance due to inclusion of different data types in the objective function could be inextricably linked. Thus caution should be taken when adding or removing data from an aggregated objective function.

ML approaches to channel estimation for pilot-aided multi-rate DS/CDMA systems

This paper analyzes the asymptotic performance of maximum likelihood (ML) channel estimation algorithms in wideband code division multiple access (WCDMA) scenarios. We concentrate on systems with periodic spreading sequences (period larger than or equal to the symbol span) where the transmitted signal contains a code division multiplexed pilot for channel estimation purposes. First, the asymptotic covariances of the training-only, semi-blind conditional maximum likelihood (CML) and semi-blind Gaussian maximum likelihood (GML) channelestimators are derived. Then, these formulas are further simplified assuming randomized spreading and training sequences under the approximation of high spreading factors and high number of codes. The results provide a useful tool to describe the performance of the channel estimators as a function of basicsystem parameters such as number of codes, spreading factors, or traffic to training power ratio.