Robust response transformations based on optimal prediction

Nonlinear regression problems can often be reduced to linearity by transforming the response variable (e.g., using the Box-Cox family of transformations). The classic estimates of the parameter defining the transformation as well as of the regression coefficients are based on the maximum likelihood criterion, assuming homoscedastic normal errors for the transformed response. These estimates are nonrobust in the presence of outliers and can be inconsistent when the errors are nonnormal or heteroscedastic. This article proposes new robust estimates that are consistent and asymptotically normal for any unimodal and homoscedastic error distribution. For this purpose, a robust version of conditional expectation is introduced for which the prediction mean squared error is replaced with an M scale. This concept is then used to develop a nonparametric criterion to estimate the transformation parameter as well as the regression coefficients. A finite sample estimate of this criterion based on a robust version of smearing is also proposed. Monte Carlo experiments show that the new estimates compare favorably with respect to the available competitors.

Constant coefficient tests for random coefficient regression

Random coefficient regression models have been applied in differentfields and they constitute a unifying setup for many statisticalproblems. The nonparametric study of this model started with Beranand Hall (1992) and it has become a fruitful framework. In thispaper we propose and study statistics for testing a basic hypothesisconcerning this model: the constancy of coefficients. The asymptoticbehavior of the statistics is investigated and bootstrapapproximations are used in order to determine the critical values ofthe test statistics. A simulation study illustrates the performanceof the proposals.

Structural changes in the US economy: is there a role for monetary policy?

This paper investigates the contribution of monetary policy to the changes in outputgrowth and inflation dynamics in the US. We identify a policy shock and a policy rule ina time-varying coefficients VAR using robust sign restrictions. The transmission of policyshocks has been relatively stable. The variance of the policy shock has decreased over time,but policy shocks account for a small fraction of the level and of the variations in inflationand output growth volatility and persistence. We find little evidence of a significant increasein the long run response of the interest rate to inflation. A more aggressive inflation policyin the 1970s would have produced large output growth costs.

Asymptotic behaviour of the density in a parabolic SPDE

Consider the density of the solution $X(t,x)$ of a stochastic heat equation with small noise at a fixed $t\in [0,T]$, $x \in [0,1]$.In the paper we study the asymptotics of this density as the noise is vanishing. A kind of Taylor expansion in powers of the noiseparameter is obtained. The coefficients and the residue of the expansion are explicitly calculated.In order to obtain this result some type of exponential estimates of tail probabilities of the difference between the approximatingprocess and the limit one is proved. Also a suitable local integration by parts formula is developped.

Honey, I shrunk the sample covariance matrix

The central message of this paper is that nobody should be using the samplecovariance matrix for the purpose of portfolio optimization. It containsestimation error of the kind most likely to perturb a mean-varianceoptimizer. In its place, we suggest using the matrix obtained from thesample covariance matrix through a transformation called shrinkage. Thistends to pull the most extreme coefficients towards more central values,thereby systematically reducing estimation error where it matters most.Statistically, the challenge is to know the optimal shrinkage intensity,and we give the formula for that. Without changing any other step in theportfolio optimization process, we show on actual stock market data thatshrinkage reduces tracking error relative to a benchmark index, andsubstantially increases the realized information ratio of the activeportfolio manager.

On certain greedoid polyhedra, partially indexable scheduling problems and extended restless bandit allocation indices

We present a polyhedral framework for establishing general structural properties on optimal solutions of stochastic scheduling problems, where multiple job classes vie for service resources: the existence of an optimal priority policy in a given family, characterized by a greedoid(whose feasible class subsets may receive higher priority), where optimal priorities are determined by class-ranking indices, under restricted linear performance objectives (partial indexability). This framework extends that of Bertsimas and Niño-Mora (1996), which explained the optimality of priority-index policies under all linear objectives (general indexability). We show that, if performance measures satisfy partial conservation laws (with respect to the greedoid), which extend previous generalized conservation laws, then theproblem admits a strong LP relaxation over a so-called extended greedoid polytope, which has strong structural and algorithmic properties. We present an adaptive-greedy algorithm (which extends Klimov's) taking as input the linear objective coefficients, which (1) determines whether the optimal LP solution is achievable by a policy in the given family; and (2) if so, computes a set of class-ranking indices that characterize optimal priority policies in the family. In the special case of project scheduling, we show that, under additional conditions, the optimal indices can be computed separately for each project (index decomposition). We further apply the framework to the important restless bandit model (two-action Markov decision chains), obtaining new index policies, that extend Whittle's (1988), and simple sufficient conditions for their validity. These results highlight the power of polyhedral methods (the so-called achievable region approach) in dynamic and stochastic optimization.

The persistence of inflation in OECD countries: A fractionally integrated approach

The statistical properties of inflation and, in particular, its degree of persistence and stability over time is a subject of intense debate and no consensus has been achieved yet. The goal of this paper is to analyze this controversy using a general approach, with the aim of providing a plausible explanation for the existing contradictory results. We consider the inflation rates of 21 OECD countries which are modelled as fractionally integrated (FI) processes. First, we show analytically that FI can appear in inflation rates after aggregating individual prices from firms that face different costs of adjusting their prices. Then, we provide robust empirical evidence supporting the FI hypothesis using both classical and Bayesian techniques. Next, we estimate impulse response functions and other scalar measures of persistence, achieving an accurate picture of this property and its variation across countries. It is shown that the application of some popular tools for measuring persistence, such as the sum of the AR coefficients, could lead to erroneous conclusions if fractional integration is present. Finally, we explore the existence of changes in inflation inertia using a novel approach. We conclude that the persistence of inflation is very high (although non-permanent) in most post-industrial countries and that it has remained basically unchanged over the last four decades.

Estimating multi-country VAR models

This paper describes a methodology to estimate the coefficients, to test specification hypothesesand to conduct policy exercises in multi-country VAR models with cross unit interdependencies, unit specific dynamics and time variations in the coefficients. The framework of analysis is Bayesian: a prior flexibly reduces the dimensionality of the model and puts structure on the time variations; MCMC methods are used to obtain posterior distributions; and marginal likelihoods to check the fit of various specifications. Impulse responses and conditional forecasts are obtained with the output of MCMC routine. The transmission of certain shocks across countries is analyzed.

Analysis of the enantiomers of citalopram and its demethylated metabolites using chiral liquid chromatography.

A procedure using a chirobiotic V column is presented which allows separation of the enantiomers of citalopram and its two N-demethylated metabolites, and of the internal standard, alprenolol, in human plasma. Citalopram, demethylcitalopram and didemethylcitalopram, as well as the internal standard, were recovered from plasma by liquid-liquid extraction. The limits of quantification were found to be 5 ng/ml for each enantiomer of citalopram and demethylcitalopram, and 7.5 ng/ml for each enantiomer of didemethylcitalopram. Inter- and intra-day coefficients of variation varied from 2.4% to 8.6% for S- and R-citalopram, from 2.9% to 7.4% for S- and R-demethylcitalopram, and from 5.6% to 12.4% for S- and R- didemethylcitalopram. No interference was observed from endogenous compounds following the extraction of plasma samples from 10 different patients treated with citalopram. This method allows accurate quantification for each enantiomer and is, therefore, well suited for pharmacokinetic and drug interaction investigations. The presented method replaces a previously described highly sensitive and selective high-performance liquid chromatography procedure using an acetylated 3-cyclobond column which, because of manufactural problems, is no longer usable for the separation of the enantiomers of citalopram and its demethylated metabolites.

A new alternative method for testing skin irritation using a human skin model: a pilot study.

Studies assessing skin irritation to chemicals have traditionally used laboratory animals; however, such methods are questionable regarding their relevance for humans. New in vitro methods have been validated, such as the reconstructed human epidermis (RHE) model (Episkin®, Epiderm®). The comparison (accuracy) with in vivo results such as the 4-h human patch test (HPT) is 76% at best (Epiderm®). There is a need to develop an in vitro method that better simulates the anatomo-pathological changes encountered in vivo. To develop an in vitro method to determine skin irritation using human viable skin through histopathology, and compare the results of 4 tested substances to the main in vitro methods and in vivo animal method (Draize test). Human skin removed during surgery was dermatomed and mounted on an in vitro flow-through diffusion cell system. Ten chemicals with known non-irritant (heptylbutyrate, hexylsalicylate, butylmethacrylate, isoproturon, bentazon, DEHP and methylisothiazolinone (MI)) and irritant properties (folpet, 1-bromohexane and methylchloroisothiazolinone (MCI/MI)), a negative control (sodiumchloride) and a positive control (sodiumlaurylsulphate) were applied. The skin was exposed at least for 4h. Histopathology was performed to investigate irritation signs (spongiosis, necrosis, vacuolization). We obtained 100% accuracy with the HPT model; 75% with the RHE models and 50% with the Draize test for 4 tested substances. The coefficients of variation (CV) between our three test batches were <0.1, showing good reproducibility. Furthermore, we reported objectively histopathological irritation signs (irritation scale): strong (folpet), significant (1-bromohexane), slight (MCI/MI at 750/250ppm) and none (isoproturon, bentazon, DEHP and MI). This new in vitro test method presented effective results for the tested chemicals. It should be further validated using a greater number of substances; and tested in different laboratories in order to suitably evaluate reproducibility.

The overhang hangover

We revisit the debt overhang question. We first use non-parametric techniques to isolate a panel of countries on the downward sloping section of a debt Laffer curve. In particular, overhang countries are ones where a threshold level of debt is reached in sample, beyond which (initial) debt ends up lowering (subsequent)growth. On average, significantly negative coefficients appear when debt face value reaches 60 percent of GDP or 200 percent of exports, and when its present value reaches 40 percent of GDP or 140 percent of exports. Second, we depart from reduced form growth regressions and perform direct tests of the theory on the thus selected sample of overhang countries. In the spirit of event studies, we ask whether, as overhang level of debt is reached: (i)investment falls precipitously as it should when it becomes optimal to default, (ii) economic policy deteriorates observably, as it should when debt contracts become unable to elicit effort on the part of the debtor, and (iii) the terms of borrowing worsen noticeably, as they should when it becomes optimal for creditors to pre-empt default and exact punitive interest rates. We find a systematic response of investment, particularly when property rights are weakly enforced, some worsening of the policy environment, and a fall in interest rates. This easing of borrowing conditions happens because lending by the private sector virtually disappears in overhang situations, and multilateral agencies step in with concessional rates. Thus, while debt relief is likely to improve economic policy (and especially investment) in overhang countries, it is doubtful that it would ease their terms of borrowing, or the burden of debt.

Intra-individual stability of neuromotor tasks from 6 to 18 years: a longitudinal study.

This study investigates the intra-individual stability of the speed of several motor tasks and the intensity of associated movements in 256 children (131 girls, 125 boys) from the Zurich generational study using the Zurich neuromotor assessment battery (ZNA) over a 12-year period from the age of 6 to 18 years. The stability was assessed by correlograms of standard deviation scores calculated from age- and gender-adjusted normative values and compared with standing height and full scale intelligence quotient (IQ). While motor tasks of hand, finger and foot (HFT) and contralateral associated movements (CAM) exhibited a moderate stability (summary measure as correlation coefficients between two measurements made 4 years apart: .61 and .60), other tasks (dynamic balance, static balance and pegboard) were only weakly stable (.46, .47 and .49). IQ and height were more stable than neuromotor components (.72 and .86). We conclude that the moderately stable HFT and CAM may reflect "motor traits", while the stability of the pegboard and balance tasks is weaker because these skills are more experience related and state-dependent.

Random measurement error and regression dilution bias.

Summary points: - The bias introduced by random measurement error will be different depending on whether the error is in an exposure variable (risk factor) or outcome variable (disease) - Random measurement error in an exposure variable will bias the estimates of regression slope coefficients towards the null - Random measurement error in an outcome variable will instead increase the standard error of the estimates and widen the corresponding confidence intervals, making results less likely to be statistically significant - Increasing sample size will help minimise the impact of measurement error in an outcome variable but will only make estimates more precisely wrong when the error is in an exposure variable

Statistical discrimination of black gel pen inks analysed by laser desorption/ionization mass spectrometry

Pearson correlation coefficients were applied for the objective comparison of 30 black gel pen inks analysed by laser desorption ionization mass spectrometry (LDI-MS). The mass spectra were obtained for ink lines directly on paper using positive and negative ion modes at several laser intensities. This methodology has the advantage of taking into account the reproducibility of the results as well as the variability between spectra of different pens. A differentiation threshold could thus be selected in order to avoid the risk of false differentiation. Combining results from positive and negative mode yielded a discriminating power up to 85%, which was better than the one obtained previously with other optical comparison methodologies. The technique also allowed discriminating between pens from the same brand.

Systematic study of the static electrical properties of the CO molecule: influence of the basis set size and correlation energy

The influence of the basis set size and the correlation energy in the static electrical properties of the CO molecule is assessed. In particular, we have studied both the nuclear relaxation and the vibrational contributions to the static molecular electrical properties, the vibrational Stark effect (VSE) and the vibrational intensity effect (VIE). From a mathematical point of view, when a static and uniform electric field is applied to a molecule, the energy of this system can be expressed in terms of a double power series with respect to the bond length and to the field strength. From the power series expansion of the potential energy, field-dependent expressions for the equilibrium geometry, for the potential energy and for the force constant are obtained. The nuclear relaxation and vibrational contributions to the molecular electrical properties are analyzed in terms of the derivatives of the electronic molecular properties. In general, the results presented show that accurate inclusion of the correlation energy and large basis sets are needed to calculate the molecular electrical properties and their derivatives with respect to either nuclear displacements or/and field strength. With respect to experimental data, the calculated power series coefficients are overestimated by the SCF, CISD, and QCISD methods. On the contrary, perturbation methods (MP2 and MP4) tend to underestimate them. In average and using the 6-311 + G(3df) basis set and for the CO molecule, the nuclear relaxation and the vibrational contributions to the molecular electrical properties amount to 11.7%, 3.3%, and 69.7% of the purely electronic μ, α, and β values, respectively