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.

Two-stage sequential procedure for nonparametric regression estimation

In nonparametric statistics the functional form of the relationship between the response variable and its associated predictor variables is unspecified but it is assumed to be a smooth function. We develop a procedure for constructing a fixed width confidence interval for the predicted value at a specified point of the independent variable. The optimal sample size for constructing this interval is obtained using a two stage sequential procedure which relies on some asymptotic properties of the Nadaraya--Watson and local linear estimators. Finally, a large scale simulation study demonstrates the applicability of the developed procedure for small and moderate sample sizes. The procedure developed here should find wide applicability since many practical problems which arise in industry involve estimating an unknown function.

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.

Missing value estimation for mixed-attribute data sets

Missing data imputation is a key issue in learning from incomplete data. Various techniques have been developed with great successes on dealing with missing values in data sets with homogeneous attributes (their independent attributes are all either continuous or discrete). This paper studies a new setting of missing data imputation, i.e., imputing missing data in data sets with heterogeneous attributes (their independent attributes are of different types), referred to as imputing mixed-attribute data sets. Although many real applications are in this setting, there is no estimator designed for imputing mixed-attribute data sets. This paper first proposes two consistent estimators for discrete and continuous missing target values, respectively. And then, a mixture-kernel-based iterative estimator is advocated to impute mixed-attribute data sets. The proposed method is evaluated with extensive experiments compared with some typical algorithms, and the result demonstrates that the proposed approach is better than these existing imputation methods in terms of classification accuracy and root mean square error (RMSE) at different missing ratios.

Wavelets/multiwavelets bases and correspondence estimation problem : an analytic study

Correspondence estimation in one of the most active research areas in the field of computer vision and number of techniques has been proposed, possessing both advantages and shortcomings. Among the techniques reported, multiresolution analysis based stereo correspondence estimation has gained lot of research focus in recent years. Although, the most widely employed medium for multiresolution analysis is wavelets and multiwavelets bases, however, relatively little work has been reported in this context. In this work we have tried to address some of the issues regarding the work done in this domain and the inherited shortcomings. In the light of these shortcomings, we propose a new technique to overcome some of the flaws that could have significantly impact on the algorithm performance and has not been addressed in the earlier propositions. Proposed algorithm uses multiresolution analysis enforced with wavelets/multiwavelts transform modulus maxima to establish correspondences between the stereo pair of images. Variety of wavelets and multiwavelets bases, possessing distinct properties such as orthogonality, approximation order, short support and shape are employed to analyse their effect on the performance of correspondence estimation. The idea is to provide knowledge base to understand and establish relationships between wavelets and multiwavelets properties and their effect on the quality of stereo correspondence estimation.

Channel estimation scheme for 3.9G wireless communication systems using RLS algorithm

Main challenges for a terminal implementation are efficient realization of the receiver, especially for channel estimation (CE) and equalization. In this paper, training based recursive least square (RLS) channel estimator technique is presented for a long term evolution (LTE) single carrier-frequency division multiple access (SC-FDMA) wireless communication system. This CE scheme uses adaptive RLS estimator which is able to update parameters of the estimator continuously, so that knowledge of channel and noise statistics are not required. Simulation results show that the RLS CE scheme with 500 Hz Doppler frequency has 3 dB better performances compared with 1.5 kHz Doppler frequency.

Maximum-likelihood based estimation for Q-ball imaging using diffusion-weighted MRI data

Q-ball imaging has been presented to reconstruct diffusion orientation distribution function using diffusion weighted MRI. In this thesiis, we present a novel and robust approach to satisfy the smoothness constraint required in Q-ball imaging. Moreover, we developed an improved estimator based on the actual distribution of the MR data.

Characterization of supported cylinder-planar germanium waveguide sensors with synchrotron Infrared radiation

Cylinder-planar Ge waveguides are being developed as evanescent-wave sensors for chemical microanalysis. The only non-planar surface is a cylinder section having a 300-mm radius of curvature. This confers a symmetric taper, allowing for direct coupling into and out of the waveguide's 1-mm² end faces while obtaining multiple reflections at the central <30-μm-thick sensing region. Ray-optic calculations indicate that the propagation angle at the central minimum has a strong nonlinear dependence on both angle and vertical position of the input ray. This results in rather inefficient coupling of input light into the off-axis modes that are most useful for evanescent-wave absorption spectroscopy. Mode-specific performance of the cylinder-planar waveguides has also been investigated experimentally. As compared to a blackbody source, the much greater brightness of synchrotron-generated infrared (IR) radiation allows a similar total energy throughput, but restricted to a smaller fraction of the allowed waveguide modes. However, such angle-selective excitation results in a strong oscillatory interference pattern in the transmission spectra. These spectral oscillations are the principal technical limitation on using synchrotron radiation to measure evanescent-wave absorption spectra with the thin waveguides.

Phylogeny affects estimation of metabolic scaling in mammals

The relationship between body size and metabolic rate is a crucial issue in organismal biology and evolution. There has been considerable debate over whether the scaling exponent of the relationship is 0.75 (Kleiber’s Law) or 0.67. Here we show that determination of this exponent for mammals depends on both the evolutionary tree and the regression model used in the comparative analysis. For example, more recent molecular-based phylogenies tend to support a 0.67 exponent, whereas older phylogenies, mostly based on morphological data, suggest a 0.75 exponent. However, molecular phylogenies yield more variable results than morphological phylogenies and thus are not currently helping to resolve the issue.

Determinants of local abundance in a major radiation of Australian passerines (Aves: Meliphagoidea)

Aim  To identify the factors that contribute to variation in abundance (population density), and to investigate whether habitat breadth and diet breadth predict macroecological patterns in a suborder of passerine birds (Meliphagoidea).
Location  Australia (including Tasmania).
Methods  Mean abundance data were collated from site surveys of bird abundance (the Australian Bird Count); range size and latitudinal position data from published distribution maps; and body mass and diet breadth information from published accounts. A diversity index of habitats used (habitat breadth) was calculated from the bird census data. We used bivariate correlation and multiple regression techniques, employing two phylogenetic comparative methods: phylogenetic generalized least squares and independent contrasts.

Results  Body mass and latitude were the only strong predictors of abundance, with larger-bodied and lower-latitude species existing at lower densities. Together, however, body mass and latitude explained only 11.1% of the variation in mean abundance. Range size and habitat breadth were positively correlated, as were diet breadth and body mass. However, neither range size, nor habitat breadth and diet breadth, explained patterns in abundance either directly or indirectly.
Main conclusions  Levels of abundance (population density) in meliphagoid birds are most closely linked to body mass and latitudinal position, but not range size. As with many other macroecological analyses, we find little evidence for aspects of niche breadth having an effect on patterns of abundance. We hypothesize that evolutionary age may also have a determining effect on why species tend to be rarer (less abundant) in the tropics.

Earliest Wuchiapingian (Lopingian, Late Permian) brachiopods in southern Hunan, South China : implications for the Pre-Lopingian crisis and onset of Lopingian recovery / radiation

The uppermost 5-15 m of the Douling Formation in the southern Hunan area. South China, yields a diverse fauna comprised of ammonoids, bivalves, and brachiopods. The brachiopods reported in this paper consist of 51 species in 34 genera and are dominated by the Lopingian (Late Permian) species associated with a few species persisting from the underlying Maokouan (Late Guadalupian). This fauna is of earliest Wuchiapingian in age as precisely constrained by the associated conodont Clarkina postbitteri postbitteri and the Guadalupian-type ammonoid fauna of the Roadoceras-Doulingoceras Zone in the brachiopod horizon. The discovery of the Lopingian species-dominated brachiopod fauna in the earliest Wuchiapingian in southern Hunan suggests a much less pronounced effect of the pre-Lopingian crisis (end-Guadalupian mass extinction) than the end-Changhsingian mass extinction in terms of brachiopods, a contemporaneous onset of the Lopingian recovery/radiation during the pre-Lopingian crisis period, and taxonomic selectivity of the pre-Lopingian crisis in terms of different fossil groups. New taxa are Echinauris doulingensis n. sp., Pararigbyella quadrilobata n. gen. and n. sp. and P. doulingensis n. gen. and n. sp.

CM-based blind equalization of time-varying SIMO-FIR channel with single pulsation estimation

It is known that the constant modulus (CM) property of the source signal can be exploited to blindly equalize time-invariant single-inputmultiple-output (SIMO) and finite-impulse-response (FIR) channels. However, the time-invariance assumption about the channel cannot be satisfied in several practical applications, e.g., mobile communication. In this paper, we show that, under some mild conditions, the CM criterion can be extended to the blind equalization of a time-varying channel that is described by the complex exponential basis expansion model (CE-BEM). Although several existing blind equalization methods that are based on the CE-BEM have to employ higher order statistics to estimate all nonzero channel pulsations, the CM-based method only needs to estimate one pulsation using second-order statistics, which yields better estimation results. It also relaxes the restriction on the source signal and is applicable to some classes of signals with which the existing methods cannot deal.

Fusion based 3D tracking of mobile transmitters via robust set-valued state estimation with RSS measurements

This paper investigates the problem of location and velocity detection of a mobile agent using Received Signal Strength (RSS) measurements captured by geographically distributed seed nodes. With inherently nonlinear power measurements, we derive a powerful linear measurement scheme using an analytical measurement conversion technique which can readily be used with RSS measuring sensors. We also employ the concept of sensor fusion in conjunction for the case of redundant measurements to further enhance the estimation accuracy.