Application of sequential nonparametric confidence bands in finance

In a nonparametric setting, the functional form of the relationship between the response variable and the associated predictor variables is assumed to be unknown when data is fitted to the model. Non-parametric regression models can be used for the same types of applications such as estimation, prediction, calibration, and optimization that traditional regression models are used for. The main aim of nonparametric regression is to highlight an important structure in the data without any assumptions about the shape of an underlying regression function. Hence the nonparametric approach allows the data to speak for itself. Applications of sequential procedures to a nonparametric regression model at a given point are considered.

The primary goal of sequential analysis is to achieve a given accuracy by using the smallest possible sample sizes. These sequential procedures allow an experimenter to make decisions based on the smallest number of observations without compromising accuracy. In the nonparametric regression model with a random design based on independent and identically distributed pairs of observations (X ,Y ), where the regression function m(x) is given bym(x) = E(Y X = x), estimation of the Nadaraya-Watson kernel estimator (m (x)) NW and local linear kernel estimator (m (x)) LL for the curve m(x) is considered. In order to obtain asymptotic confidence intervals form(x), two stage sequential procedure is used under which some asymptotic properties of Nadaraya-Watson and local linear estimators have been obtained.

The proposed methodology is first tested with the help of simulated data from linear and nonlinear functions. Encouraged by the preliminary findings from simulation results, the proposed method is applied to estimate the nonparametric regression curve of CAPM.

Sequential fixed-width confidence bands for kernel regression estimation

We consider a random design model based on independent and identically distributed (iid) pairs of observations (Xi, Yi), where the regression function m(x) is given by m(x) = E(Yi|Xi = x) with one independent variable. In a nonparametric setting the aim is to produce a reasonable approximation to the unknown function m(x) when we have no precise information about the form of the true density, f(x) of X. We describe an estimation procedure of non-parametric regression model at a given point by some appropriately constructed fixed-width (2d) confidence interval with the confidence coefficient of at least 1−. Here, d(> 0) and 2 (0, 1) are two preassigned values. Fixed-width confidence intervals are developed using both Nadaraya-Watson and local linear kernel estimators of nonparametric regression with data-driven bandwidths.

The sample size was optimized using the purely and two-stage sequential procedure together with asymptotic properties of the Nadaraya-Watson and local linear estimators. A large scale simulation study was performed to compare their coverage accuracy. The numerical results indicate that the confidence bands based on the local linear estimator have the best performance than those constructed by using Nadaraya-Watson estimator. However both estimators are shown to have asymptotically correct coverage properties.

Sample size determination for kernel regression estimation using sequential fixed-width confidence bands

We consider a random design model based on independent and identically distributed pairs of observations (Xi, Yi), where the regression function m(x) is given by m(x) = E(Yi|Xi = x) with one independent variable. In a nonparametric setting the aim is to produce a reasonable approximation to the unknown function m(x) when we have no precise information about the form of the true density, f(x) of X. We describe an estimation procedure of non-parametric regression model at a given point by some appropriately constructed fixed-width (2d) confidence interval with the confidence coefficient of at least 1−. Here, d(> 0) and 2 (0, 1) are two preassigned values. Fixed-width confidence intervals are developed using both Nadaraya-Watson and local linear kernel estimators of nonparametric regression with data-driven bandwidths. The sample size was optimized using the purely and two-stage sequential procedures together with asymptotic properties of the Nadaraya-Watson and local linear estimators. A large scale simulation study was performed to compare their coverage accuracy. The numerical results indicate that the confi dence bands based on the local linear estimator have the better performance than those constructed by using Nadaraya-Watson estimator. However both estimators are shown to have asymptotically correct coverage properties.

Field test study on the shear behaviour of stressed skin diaphragm spanning several purlins

Although profiled steel sheets have the diaphragm effect in steel structure, since there is no specific code to follow in China, it is only used as the reservation of the structural stiffness.So it results in economic wastes.In order to investigate the contribution of stressed skin to the overall stiffness, field tests are carried out to measure the lateral stiffness of the frames with and without stressed skin diaphgram.Based on the superposition principle and using the curve fitting method, the test results are quantified.The shear rigidity of stressed skin diaphgram spanning several purlins is gained indirectly.It shows that the shear rigidity of the diaphragm between two frames is even close to the lateral stiffness of one frame.

Development of adiabatic shear band in cold-rolled titanium

The evolution of adiabatic shear localization in commercial titanium subjected to heavy cold rolling was investigated. The evolution of the morphology, microhardness, local shear strain, and local temperature increments were systematically studied and estimated. A shear band with about 25m in width was formed and fine nanograins with a range of dimensions varying from 20 to 160nm and had a mean size of about 70nm were observed inside the centre of shear band after 83% cold-rolling. Microhardness test shows that hardness within the shear band is markedly higher than that of the surrounding matrix. The calculated shear strain and maximum temperature increase within the shear band are much higher than that of the overall deformed sample. The initiation of shear localization may depend on geometric perturbation instead of thermal ones.

Shear strength of composite plate girders with web cutouts

An experimental investigation of the shear strengths of composite plate girders, with centrally placed rectangular web cutouts, is described. A series of tests is conducted on short‐span girders having conventional welded stud shear connectors, connecting the composite concrete slabs to the top flanges of the plate girders. These tests indicated that it is the tensile or pullout capacity of the connectors that is primarily responsible for sustaining the composite action under predominantly shear loading. Subsequently, a further series of tests is conducted on short‐span girders with bolted tension connectors, designed to offer negligible resistance to horizontal shear forces at the interfaces between the concrete slabs and plate girders, which confirmed the previous conclusion. Both series of tests indicate that if adequate connectors are provided between a plate girder and a composite concrete slab, the shear strength of the composite girder is significantly higher than that of the plate girder alone. A simple analytical model for predicting the shear strengths of composite plate girders is also presented, which shows satisfactory correlation with the test results.

Shear-enhanced solution precipitation : a simple process to produce short polymeric nanofibers

The growing interest in polymeric nanofibers has been increasing the push for the development of simple and efficient nanofiber-preparation techniques. We herein describe how a conventional solution process is readapted to suit the needs for fast and efficient production of short polymeric nanofibers. Poly(ethylene-co-acrylic acid) (PEAA), a semi-crystalline polymer, was used as model. When a PEAA solution was injected into an alcoholic non-solvent while simultaneously applying high shear to the non-solvent system, PEAA nanofibers were obtained with average diameter as thin as 113 nm and length as short as 4.5 _m. The fiber diameter and length were also adjustable by varying the operating parameters. This one-step technique advances the currently available nanofabrication tools by adjusting a widely accepted concept to the nano-scale. It may constitute a viable method for large-scale production of short polymeric nanofibers.

Shear-free perfect fluids with a solenoidal electric curvature

We prove that the vorticity or the expansion vanishes for any shear-free perfect fluid solution of the Einstein field equations where the pressure satisfies a barotropic equation of state and the spatial divergence of the electric part of the Weyl tensor is zero.