A comparative study of monotone nonparametric kernel estimates

In this paper we present a detailed numerical comparison of three monotone nonparametric kernel regression estimates, which isotonize a nonparametric curve estimator. The first estimate is the classical smoothed isotone estimate of Brunk (1958). The second method has recently been proposed by Hall and Huang (2001) and modifies the weights of a commonly used kernel estimate such that the resulting estimate is monotone. The third estimate was recently proposed by Dette, Neumeyer and Pilz (2003) and combines density and regression estimation techniques to obtain a monotone curve estimate of the inverse of the isotone regression function. The three concepts are briefly reviewed and their finite sample properties are studied by means of a simulation study. Although all estimates are first order asymptotically equivalent (provided that the unknown regression function is isotone) some differences for moderate samples are observed. --isotonic regression,order restricted inference,Nadaraya-Watson estimator,local linear regression,monte carlo simulation

Nonparametric option pricing with no-arbitrage constraints

We propose a completely kernel based method of estimating the call price function or the state price density of options. The new estimator of the call price function fulfills the constraints like monotonicity and convexity given in Breeden and Litzenberger (1978) without necessarily estimating the state price density for an underlying asset price from its option prices. It can be shown that the estimator is pointwise consistent and asymptotically normal. In a simulation study we compare the new estimator to the unconstrained kernel estimator and to the estimator given in Aït-Sahalia and Duarte (2003). --call pricing function b,constrained nonparametric estimation,monotone rearrangements,state price density

A note on nonparametric estimation of the effective dose in quantal bioassay

For the common binary response model we propose a direct method for the nonparametric estimation of the effective dose level ED? (0Binary response model,effective dose level,nonparametric regression,isotonic regression,order restricted inference,local linear regression

A simple nonparametric estimator of a monotone regression function

In this paper a new method for monotone estimation of a regression function is proposed. The estimator is obtained by the combination of a density and a regression estimate and is appealing to users of conventional smoothing methods as kernel estimators, local polynomials, series estimators or smoothing splines. The main idea of the new approach is to construct a density estimate from the estimated values ˆm(i/N) (i = 1, . . . ,N) of the regression function to use these “data” for the calculation of an estimate of the inverse of the regression function. The final estimate is then obtained by a numerical inversion. Compared to the conventially used techniques for monotone estimation the new method is computationally more efficient, because it does not require constrained optimization techniques for the calculation of the estimate. We prove asymptotic normality of the new estimate and compare the asymptotic properties with the unconstrained estimate. In particular it is shown that for kernel estimates or local polynomials the monotone estimate is first order asymptotically equivalent to the unconstrained estimate. We also illustrate the performance of the new procedure by means of a simulation study. --isotonic regression,order restricted inference,Nadaraya-Watson estimator,local linear regression

Parameterized Neural Networks for Finance

We discuss and analyze a neural network architecture, that enables learning a model class for a set of different data samples rather than just learning a single model for a specific data sample. In this sense, it may help to reduce the overfitting problem, since, after learning the model class over a larger data sample consisting of such different data sets, just a few parameters need to be adjusted for modeling a new, specific problem. After analyzing the method theoretically and by regression examples for different one-dimensional problems, we finally apply the approach to one of the standard problems asset managers and banks are facing: the calibration of spread curves. The presented results clearly show the potential that lies within this method. Furthermore, this application is of particular interest to financial practitioners, since nearly all asset managers and banks which are having solutions in place may need to adapt or even change their current methodologies when ESG ratings additionally affect the bond spreads.Comment: 24 pages, 17 figure

Genome-wide association study in 79,366 European-ancestry individuals informs the genetic architecture of 25-hydroxyvitamin D levels

Vitamin D is a steroid hormone precursor that is associated with a range of human traits and diseases. Previous GWAS of serum 25-hydroxyvitamin D concentrations have identified four genome-wide significant loci (GC, NADSYN1/DHCR7, CYP2R1, CYP24A1). In this study, we expand the previous SUNLIGHT Consortium GWAS discovery sample size from 16,125 to 79,366 (all European descent). This larger GWAS yields two additional loci harboring genome-wide significant variants (P = 4.7x10(-9) at rs8018720 in SEC23A, and P = 1.9x10(-14) at rs10745742 in AMDHD1). The overall estimate of heritability of 25-hydroxyvitamin D serum concentrations attributable to GWAS common SNPs is 7.5%, with statistically significant loci explaining 38% of this total. Further investigation identifies signal enrichment in immune and hematopoietic tissues, and clustering with autoimmune diseases in cell-type-specific analysis. Larger studies are required to identify additional common SNPs, and to explore the role of rare or structural variants and gene-gene interactions in the heritability of circulating 25-hydroxyvitamin D levels.Peer reviewe

Genome-wide association study identifies six new loci influencing pulse pressure and mean arterial pressure.

Numerous genetic loci have been associated with systolic blood pressure (SBP) and diastolic blood pressure (DBP) in Europeans. We now report genome-wide association studies of pulse pressure (PP) and mean arterial pressure (MAP). In discovery (N = 74,064) and follow-up studies (N = 48,607), we identified at genome-wide significance (P = 2.7 × 10(-8) to P = 2.3 × 10(-13)) four new PP loci (at 4q12 near CHIC2, 7q22.3 near PIK3CG, 8q24.12 in NOV and 11q24.3 near ADAMTS8), two new MAP loci (3p21.31 in MAP4 and 10q25.3 near ADRB1) and one locus associated with both of these traits (2q24.3 near FIGN) that has also recently been associated with SBP in east Asians. For three of the new PP loci, the estimated effect for SBP was opposite of that for DBP, in contrast to the majority of common SBP- and DBP-associated variants, which show concordant effects on both traits. These findings suggest new genetic pathways underlying blood pressure variation, some of which may differentially influence SBP and DBP

Genetic variants in novel pathways influence blood pressure and cardiovascular disease risk.

Blood pressure is a heritable trait influenced by several biological pathways and responsive to environmental stimuli. Over one billion people worldwide have hypertension (≥140 mm Hg systolic blood pressure or  ≥90 mm Hg diastolic blood pressure). Even small increments in blood pressure are associated with an increased risk of cardiovascular events. This genome-wide association study of systolic and diastolic blood pressure, which used a multi-stage design in 200,000 individuals of European descent, identified sixteen novel loci: six of these loci contain genes previously known or suspected to regulate blood pressure (GUCY1A3-GUCY1B3, NPR3-C5orf23, ADM, FURIN-FES, GOSR2, GNAS-EDN3); the other ten provide new clues to blood pressure physiology. A genetic risk score based on 29 genome-wide significant variants was associated with hypertension, left ventricular wall thickness, stroke and coronary artery disease, but not kidney disease or kidney function. We also observed associations with blood pressure in East Asian, South Asian and African ancestry individuals. Our findings provide new insights into the genetics and biology of blood pressure, and suggest potential novel therapeutic pathways for cardiovascular disease prevention

Prevalence and architecture of de novo mutations in developmental disorders.

The genomes of individuals with severe, undiagnosed developmental disorders are enriched in damaging de novo mutations (DNMs) in developmentally important genes. Here we have sequenced the exomes of 4,293 families containing individuals with developmental disorders, and meta-analysed these data with data from another 3,287 individuals with similar disorders. We show that the most important factors influencing the diagnostic yield of DNMs are the sex of the affected individual, the relatedness of their parents, whether close relatives are affected and the parental ages. We identified 94 genes enriched in damaging DNMs, including 14 that previously lacked compelling evidence of involvement in developmental disorders. We have also characterized the phenotypic diversity among these disorders. We estimate that 42% of our cohort carry pathogenic DNMs in coding sequences; approximately half of these DNMs disrupt gene function and the remainder result in altered protein function. We estimate that developmental disorders caused by DNMs have an average prevalence of 1 in 213 to 1 in 448 births, depending on parental age. Given current global demographics, this equates to almost 400,000 children born per year

The contribution of X-linked coding variation to severe developmental disorders

Abstract: Over 130 X-linked genes have been robustly associated with developmental disorders, and X-linked causes have been hypothesised to underlie the higher developmental disorder rates in males. Here, we evaluate the burden of X-linked coding variation in 11,044 developmental disorder patients, and find a similar rate of X-linked causes in males and females (6.0% and 6.9%, respectively), indicating that such variants do not account for the 1.4-fold male bias. We develop an improved strategy to detect X-linked developmental disorders and identify 23 significant genes, all of which were previously known, consistent with our inference that the vast majority of the X-linked burden is in known developmental disorder-associated genes. Importantly, we estimate that, in male probands, only 13% of inherited rare missense variants in known developmental disorder-associated genes are likely to be pathogenic. Our results demonstrate that statistical analysis of large datasets can refine our understanding of modes of inheritance for individual X-linked disorders