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.

25-hydroxyvitamin D concentration is inversely associated with serum MMP-9 in a cross-sectional study of African American ESRD patients.

BACKGROUND: Circulating 25-hydroxyvitamin D [25(OH)D] concentration is inversely associated with peripheral arterial disease and hypertension. Vascular remodeling may play a role in this association, however, data relating vitamin D level to specific remodeling biomarkers among ESRD patients is sparse. We tested whether 25(OH)D concentration is associated with markers of vascular remodeling and inflammation in African American ESRD patients.METHODS: We conducted a cross-sectional study among ESRD patients receiving maintenance hemodialysis within Emory University-affiliated outpatient hemodialysis units. Demographic, clinical and dialysis treatment data were collected via direct patient interview and review of patients records at the time of enrollment, and each patient gave blood samples. Associations between 25(OH)D and biomarker concentrations were estimated in univariate analyses using Pearson's correlation coefficients and in multivariate analyses using linear regression models. 25(OH) D concentration was entered in multivariate linear regression models as a continuous variable and binary variable (<15 ng/ml and =15 ng/ml). Adjusted estimate concentrations of biomarkers were compared between 25(OH) D groups using analysis of variance (ANOVA). Finally, results were stratified by vascular access type.RESULTS: Among 91 patients, mean (standard deviation) 25(OH)D concentration was 18.8 (9.6) ng/ml, and was low (<15 ng/ml) in 43% of patients. In univariate analyses, low 25(OH) D was associated with lower serum calcium, higher serum phosphorus, and higher LDL concentrations. 25(OH) D concentration was inversely correlated with MMP-9 concentration (r = -0.29, p = 0.004). In multivariate analyses, MMP-9 concentration remained negatively associated with 25(OH) D concentration (P = 0.03) and anti-inflammatory IL-10 concentration positively correlated with 25(OH) D concentration (P = 0.04).CONCLUSIONS: Plasma MMP-9 and circulating 25(OH) D concentrations are significantly and inversely associated among ESRD patients. This finding may suggest a potential mechanism by which low circulating 25(OH) D functions as a cardiovascular risk factor.

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.

Econometrics and decision making: Effects of presentation mode

Much of empirical economics involves regression analysis. However, does thepresentation of results affect economists ability to make inferences for decision makingpurposes? In a survey, 257 academic economists were asked to make probabilisticinferences on the basis of the outputs of a regression analysis presented in a standardformat. Questions concerned the distribution of the dependent variable conditional onknown values of the independent variable. However, many respondents underestimateduncertainty by failing to take into account the standard deviation of the estimatedresiduals. The addition of graphs did not substantially improve inferences. On the otherhand, when only graphs were provided (i.e., with no statistics), respondents weresubstantially more accurate. We discuss implications for improving practice in reportingresults of regression analyses.

In vivo targeting of an anti-tumor antibody coupled to antigenic MHC class I complexes induces specific growth inhibition and regression of established syngeneic tumor grafts.

The concept of antibody-mediated targeting of antigenic MHC/peptide complexes on tumor cells in order to sensitize them to T-lymphocyte cytotoxicity represents an attractive new immunotherapy strategy. In vitro experiments have shown that an antibody chemically conjugated or fused to monomeric MHC/peptide can be oligomerized on the surface of tumor cells, rendering them susceptible to efficient lysis by MHC-peptide restricted specific T-cell clones. However, this strategy has not yet been tested entirely in vivo in immunocompetent animals. To this aim, we took advantage of OT-1 mice which have a transgenic T-cell receptor specific for the ovalbumin (ova) immunodominant peptide (257-264) expressed in the context of the MHC class I H-2K(b). We prepared and characterized conjugates between the Fab' fragment from a high-affinity monoclonal antibody to carcinoembryonic antigen (CEA) and the H-2K(b) /ova peptide complex. First, we showed in OT-1 mice that the grafting and growth of a syngeneic colon carcinoma line transfected with CEA could be specifically inhibited by systemic injections of the conjugate. Next, using CEA transgenic C57BL/6 mice adoptively transferred with OT-1 spleen cells and immunized with ovalbumin, we demonstrated that systemic injections of the anti-CEA-H-2K(b) /ova conjugate could induce specific growth inhibition and regression of well-established, palpable subcutaneous grafts from the syngeneic CEA-transfected colon carcinoma line. These results, obtained in a well-characterized syngeneic carcinoma model, demonstrate that the antibody-MHC/peptide strategy can function in vivo. Further preclinical experimental studies, using an anti-viral T-cell response, will be performed before this new form of immunotherapy can be considered for clinical use.

Testing financing constraints on firm investment using variable capital

We consider a dynamic multifactor model of investment with financing imperfections,adjustment costs and fixed and variable capital. We use the model to derive a test offinancing constraints based on a reduced form variable capital equation. Simulation resultsshow that this test correctly identifies financially constrained firms even when the estimationof firms investment opportunities is very noisy. In addition, the test is well specified inthe presence of both concave and convex adjustment costs of fixed capital. We confirmempirically the validity of this test on a sample of small Italian manufacturing companies.

Solving higher-dimensional continuous time stochastic control problems by value function regression

The paper develops a method to solve higher-dimensional stochasticcontrol problems in continuous time. A finite difference typeapproximation scheme is used on a coarse grid of low discrepancypoints, while the value function at intermediate points is obtainedby regression. The stability properties of the method are discussed,and applications are given to test problems of up to 10 dimensions.Accurate solutions to these problems can be obtained on a personalcomputer.

Weighted Kernel regression

In the fixed design regression model, additional weights areconsidered for the Nadaraya--Watson and Gasser--M\"uller kernel estimators.We study their asymptotic behavior and the relationships between new andclassical estimators. For a simple family of weights, and considering theIMSE as global loss criterion, we show some possible theoretical advantages.An empirical study illustrates the performance of the weighted estimatorsin finite samples.

How wide is the gap? An investigation of gender wage differences using quantile regression

In this paper we examine the determinants of wages and decompose theobserved differences across genders into the "explained by differentcharacteristics" and "explained by different returns components"using a sample of Spanish workers. Apart from the conditionalexpectation of wages, we estimate the conditional quantile functionsfor men and women and find that both the absolute wage gap and thepart attributed to different returns at each of the quantiles, farfrom being well represented by their counterparts at the mean, aregreater as we move up in the wage range.

Exact tests for correlation and for the slope in simple linear regressions without making assumptions

We present an exact test for whether two random variables that have known bounds on their support are negatively correlated. The alternative hypothesis is that they are not negatively correlated. No assumptions are made on the underlying distributions. We show by example that the Spearman rank correlation test as the competing exact test of correlation in nonparametric settings rests on an additional assumption on the data generating process without which it is not valid as a test for correlation.We then show how to test for the significance of the slope in a linear regression analysis that invovles a single independent variable and where outcomes of the dependent variable belong to a known bounded set.

Early disturbances of gamma band dynamics in mild cognitive impairment.

Recent studies have indicated that gamma band oscillations participate in the temporal binding needed for the synchronization of cortical networks involved in short-term memory and attentional processes. To date, no study has explored the temporal dynamics of gamma band in the early stages of dementia. At baseline, gamma band analysis was performed in 29 cases with mild cognitive impairment (MCI) during the n-back task. Based on phase diagrams, multiple linear regression models were built to explore the relationship between the cognitive status and gamma oscillation changes over time. Individual measures of phase diagram complexity were made using fractal dimension values. After 1 year, all cases were assessed neuropsychologically using the same battery. A total of 16 MCI patients showed progressive cognitive decline (PMCI) and 13 remained stable (SMCI). When adjusted for gamma values at lag -2, and -3 ms, PMCI cases displayed significantly lower average changes in gamma values than SMCI cases both in detection and 2-back tasks. Gamma fractal dimension of PMCI cases displayed significantly higher gamma fractal dimension values compared to SMCI cases. This variable explained 11.8% of the cognitive variability in this series. Our data indicate that the progression of cognitive decline in MCI is associated with early deficits in temporal binding that occur during the activation of selective attention processes.

The spiritual distress assessment tool: an instrument to assess spiritual distress in hospitalised elderly persons.

BACKGROUND: Although spirituality is usually considered a positive resource for coping with illness, spiritual distress may have a negative influence on health outcomes. Tools are needed to identify spiritual distress in clinical practice and subsequently address identified needs. This study describes the first steps in the development of a clinically acceptable instrument to assess spiritual distress in hospitalized elderly patients. METHODS: A three-step process was used to develop the Spiritual Distress Assessment Tool (SDAT): 1) Conceptualisation by a multidisciplinary group of a model (Spiritual Needs Model) to define the different dimensions characterizing a patient's spirituality and their corresponding needs; 2) Operationalisation of the Spiritual Needs Model within geriatric hospital care leading to a set of questions (SDAT) investigating needs related to each of the defined dimensions; 3) Qualitative assessment of the instrument's acceptability and face validity in hospital chaplains. RESULTS: Four dimensions of spirituality (Meaning, Transcendence, Values, and Psychosocial Identity) and their corresponding needs were defined. A formalised assessment procedure to both identify and subsequently score unmet spiritual needs and spiritual distress was developed. Face validity and acceptability in clinical practice were confirmed by chaplains involved in the focus groups. CONCLUSIONS: The SDAT appears to be a clinically acceptable instrument to assess spiritual distress in elderly hospitalised persons. Studies are ongoing to investigate the psychometric properties of the instrument and to assess its potential to serve as a basis for integrating the spiritual dimension in the patient's plan of care.

Heidelberg Retina Tomograph in Glaucoma Case-finding

Purpose: To compare the disease classification using optic nerve head imaging against clinical examination combined with perimetry in the case-finding environment.Methods: During a glaucoma screening event at the University Hospital in Lausanne 148 attendees opted to undergo an extended screening exam consisting of perimetry with Octopus (Haag-Streit, Koeniz, Switzerland), tonometry, gonioscopy, slit-lamp optic nerve head examination and Heidelberg Retinal Tomorgraph (HRT, Heidelberg engineering). Classification criteria of an abnormal clinical exam consisted of a cup to disc ratio > 0.6, other disc abnormality (e.g. notching), closed angles, Van Herrick < ¼ and intraocular pressure >21mmHg. In perimetry a square root loss variance (sLV) >3.0 dB was considered abnormal. Those cases with both an abnormal clinical exam and abnormal perimetric results were considered to be glaucoma suspects. An abnormal HRT exam was a global Moorfields Regression Analysis (MRA) result of "outside normal limits". The results from the worse eye for each instrument are reported.Results: The mean age of the patients was 59.9 years (SD ±14.8years). 46 subjects failed the clinical exam. 55 subjects had sLV>3.0dB. 86 subjects failed one or more of the testing components, 21 subjects failed both the clinical exam and perimetry. Two cases of advanced glaucoma were diagnosed on the day of the event. 20 subjects were referred due to other ocular pathology (10 cataract; 2 AMD; 8 other). 16 subjects were outside normal limits with the HRT, of which 11 failed the clinical exam, 9 failed the perimetric exam and 7 failed all three. HRT had a sensitivity of 33% CI [15%,57%] with a specificity of 93% CI [87%,97%].Conclusions: HRT shows good specificity, however the low sensitivity makes it of limited use in the proposed case finding scenario.

Local-scale spatial variation in diversity of social wasps in an Amazonian rain forest in Caxiuanã, Pará, Brazil (Hymenoptera, Vespidae, Polistinae)

Polistine wasps are important in Neotropical ecosystems due to their ubiquity and diversity. Inventories have not adequately considered spatial attributes of collected specimens. Spatial data on biodiversity are important for study and mitigation of anthropogenic impacts over natural ecosystems and for protecting species. We described and analyzed local-scale spatial patterns of collecting records of wasp species, as well as spatial variation of diversity descriptors in a 2500-hectare area of an Amazon forest in Brazil. Rare species comprised the largest fraction of the fauna. Close range spatial effects were detected for most of the more common species, with clustering of presence-data at short distances. Larger spatial lag effects could also be identified in some species, constituting probably cases of exogenous autocorrelation and candidates for explanations based on environmental factors. In a few cases, significant or near significant correlations were found between five species (of Agelaia, Angiopolybia, and Mischocyttarus) and three studied environmental variables: distance to nearest stream, terrain altitude, and the type of forest canopy. However, association between these factors and biodiversity variables were generally low. When used as predictors of polistine richness in a linear multiple regression, only the coefficient for the forest canopy variable resulted significant. Some level of prediction of wasp diversity variables can be attained based on environmental variables, especially vegetation structure. Large-scale landscape and regional studies should be scheduled to address this issue.