Optimal Weight Matrix Research Articles

Alternative Over-Identifying Restriction Test in GMM Estimation of Panel Data Models

This paper proposes a new over-identifying restriction test called the diagonal J test in the generalized method of moments (GMM) framework. Different from the conventional over-identifying restriction test, where the sample covariance matrix of moment conditions is used in the weighting matrix, the proposed test uses a block diagonal weighting matrix constructed from the efficient optimal weighting matrix. We show that the proposed test statistic asymptotically follows a weighted sum of chi-square distributions with one degree of freedom. Since we need to decompose the moment conditions into groups when implementing the proposed test, we propose two methods to split the moment conditions. The first is to use K-means method that is widely used in the cluster analysis. The second is to utilize the special structure of moment conditions where they are available sequentially. Such a case typically appears in the panel data models. We also conduct a local power analysis of the diagonal J test in the context of dynamic panel data models, and show that the proposed test has almost the same power as the standard J test in some specific cases. Monte Carlo simulation reveals that the proposed test has substantially better size property than the standard test does, while having almost no power loss in comparison to the standard test when it has no size distortions.

Performance Evaluation of Pattern Storage Network of Associative memory with Sub-optimal GA for Hand written Hindi SWARS

In this paper we are performing the evaluation of Hopfield neural network as Associative memory for recalling of memorized patterns from the Sub-optimal genetic algorithm for Handwritten of Hindi language. In this process the genetic algorithm is employed from sub-optimal form for recalling of memorized patterns corresponding to the presented noisy prototype input patterns. The sub-optimal form of GA is considered as the non-random initial population or solution. So, rather than random start, the GA explores from the sum of correlated weight matrices for the input patterns of training set. The objective of this study is to determine the optimal weight matrix for correct recalling corresponds to approximate prototype input pattern of Hindi ‘SW. In this study the performance of neural network is evaluated in terms of the rate of success for recalling of memorized Hindi for presented approximate prototype input pattern with GA in two aspects. The first aspect reflects the random nature of the GA and the second one exhibit the suboptimal nature of the GA for its exploration.The simulated results demonstrate the better performance of network for recalling of the memorized Hindi SWARS using genetic algorithm to evolve the population of weights from sub-optimal weight matrix.

Estimation and testing of higher-order spatial autoregressive panel data error component models

This paper develops an estimator for higher-order spatial autoregressive panel data error component models with spatial autoregressive disturbances, SARAR(R,S). We derive the moment conditions and optimal weighting matrix without distributional assumptions for a generalized moments (GM) estimation procedure of the spatial autoregressive parameters of the disturbance process and define a generalized two-stage least squares estimator for the regression parameters of the model. We prove consistency of the proposed estimators, derive their joint asymptotic distribution, and provide Monte Carlo evidence on their small sample performance.

Inference for Income Distributions Using Grouped Data

We develop a general approach to estimation and inference for income distributions using grouped or aggregate data that are typically available in the form of population shares and class mean incomes, with unknown group bounds. We derive generic moment conditions and an optimal weight matrix that can be used for generalized method-of-moments (GMM) estimation of any parametric income distribution. Our derivation of the weight matrix and its inverse allows us to express the seemingly complex GMM objective function in a relatively simple form that facilitates estimation. We show that our proposed approach, which incorporates information on class means as well as population proportions, is more efficient than maximum likelihood estimation of the multinomial distribution, which uses only population proportions. In contrast to the earlier work of Chotikapanich, Griffiths, and Rao, and Chotikapanich, Griffiths, Rao, and Valencia, which did not specify a formal GMM framework, did not provide methodology for obtaining standard errors, and restricted the analysis to the beta-2 distribution, we provide standard errors for estimated parameters and relevant functions of them, such as inequality and poverty measures, and we provide methodology for all distributions. A test statistic for testing the adequacy of a distribution is proposed. Using eight countries/regions for the year 2005, we show how the methodology can be applied to estimate the parameters of the generalized beta distribution of the second kind (GB2), and its special-case distributions, the beta-2, Singh–Maddala, Dagum, generalized gamma, and lognormal distributions. We test the adequacy of each distribution and compare predicted and actual income shares, where the number of groups used for prediction can differ from the number used in estimation. Estimates and standard errors for inequality and poverty measures are provided. Supplementary materials for this article are available online.

Maximum-SNR Optimal Weighting Matrix for Multiple Relay-Antenna-Assisted Orthogonal Space Time Block Codes

An optimal linear weighting matrix is proposed for nonregenerative multiple relay-antenna-assisted orthogonal space time block codes, which results in the maximum received signal-to-noise ratio (SNR) at the destination. The proposed optimal design of the linear weighting matrix achieves an approximately-15-dB SNR gain over the naive weighting matrix at the bit error rate (BER) of 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-3</sup> as a benefit of efficiently exploiting the diversity gain provided by the multiple relay antennas.

A sparse recovery algorithm for DOA estimation using weighted subspace fitting

A new algorithm involving sparse recovery is proposed to address the problem of direction-of-arrival (DOA) estimation using weighted subspace fitting (WSF). The proposed algorithm proves to be a modified version of ℓ1-SVD by using an optimal weighting matrix, wherein a scheme of regularization between sparsity penalty and subspace fitting error is also given for all SNR range. Numerical simulations verify the efficiency of the proposed algorithm and illustrate the performance improvement in low SNR.

Study of Hopfield neural network with sub-optimal and random GA for pattern recalling of English characters

In this paper we are studying the performance of Hopfield neural network for recalling of memorized patterns from the Hebbian rule and genetic algorithm for English characters. In this process the genetic algorithm is employed in random form and sub-optimal form for recalling of memorized patterns corresponding to the presented noisy prototype input patterns. The objective of this study is to determine the optimal weight matrix for correct recalling corresponding to noisy form of the English characters. In this study the performance of neural network is evaluated in terms of the rate of success for recalling of noisy input patterns of the English characters with GA in two aspects. The first aspect reflects the random nature of the GA and the second one exhibits the suboptimal nature of the GA for its exploration. The simulated results demonstrate the better performance of network for recalling of the stored letters of English alphabets using genetic algorithm on the suboptimal weight matrix.

Empirical Policy Functions as Benchmarks for Evaluation of Dynamic Capital Structure Models

We assess the finite sample performance of simulation estimators that are used to estimate the parameters of dynamic corporate finance models. We formulate an out-of-sample specification test and propose a new set of statistical benchmarks that can be used to estimate and evaluate these models. These benchmarks are based on model policy functions. Our Monte Carlo simulations show that the estimators are largely unbiased with low root mean squared errors. When computed with an optimal weight matrix, the t-tests and specification tests associated with the estimators are close to correctly sized. The specification tests have excellent power to detect misspecification.

Robust Relaying Schemes for Multiple-Antenna Multi-Relay Networks

The optimal beamforming weight matrix for amplify and forward multiple-antenna multiple-relay network is investigated. It is assumed that the partial first and second hop channel state information (CSI) is available at relays. In order to minimize the mean square error (MSE) at destination, all relay weight matrices must be designed simultaneously under individual relay power constraints. Using the Lagrange dual variables, it is shown that this general vector optimization problem can be converted into a scalar optimization problem whose scalar Lagrange multipliers can be obtained numerically. This is the generalized version of the scheme suggested for complete CSI. The proposed scheme is evaluated through computer simulation with various numbers of relays and antennas to obtain MSE and bit error rate (BER) metrics. It is also shown that the resulting MSE and BER are less than those of the schemes available in the literature by a good margin depending upon the amount of the utilized relay and antennas as well as the estimation error.

Weight matrix based identification of terpene synthases conserved motifs in Arabidopsis thaliana proteome

AbstractTerpenes comprise the most diverse collection of natural products. Out of more than 30,000 individual terpenoids identified, at least half are synthesized by plants. A relatively small, but quantitatively significant, number of terpenoids are involved in primary plant metabolism. However, the vast majorities are classified as secondary metabolites; compounds not required for plant growth and development but presumed to have an ecological function in communication or defense and are widely used in industrial applications. Terpene hydrocarbon scaffolds are generated by the action of the mechanistically intriguing family of mono-, sesqui-, and diterpene synthases collectively termed as terpene synthases, that catalyze multistep reactions with diphosphorylated substrates of 10 (geranyl diphosphate), 15 (farnesyl diphosphate) or 20 (geranylgeranyl diphosphate) carbons. In the studied work, we performed a computational study on proteome wide identification of terpene synthase motifs in Arabidopsis thaliana proteome on the basis of weight matrix approach. We have developed an optimal weight matrix for the identification of terpene synthase motifs in the plant’s proteome. Weight matrix was constructed by aligning orthologous sequences of known terpene synthases originated from diverse plant species viz., Abies grandis, Nicotiana tobaccum etc. Sequences of detected domains &amp; motifs were retrieved through SwissProtKB/NCBI on the basis of specific conservation IDs of Prosite, Pfam, Interpro, Prodom, COG, TIGR databases, while position specific scoring matrices were made through MEME, MotifSampler, PossuMsearch tools. Weight matrix based search of conserved motifs in the proteome of A. thaliana was done through ESA, Lahead and Simple algorithm based search tools of PossuMsearch biosuite in Linux system. Prediction was first validated by using positive control data set and optimized the method to reach prediction accuracy upto &gt;90%. After tool performance evaluation, prediction was made on whole proteome at specific threshold/score value. Significant results were found in A. thaliana with motif similarity ranges from 80% to 100%. This proteome wide search model paves the path to identify more terpene synthases genes in A. thaliana, as well as in other plant systems.

Weight matrix based identification of terpene synthases conserved motifs in Arabidopsis thaliana proteome

Terpenes comprise the most diverse collection of natural products. Out of more than 30,000 individual terpenoids identified, at least half are synthesized by plants. A relatively small, but quantitatively significant, number of terpenoids are involved in primary plant metabolism. However, the vast majorities are classified as secondary metabolites; compounds not required for plant growth and development but presumed to have an ecological function in communication or defense and are widely used in industrial applications. Terpene hydrocarbon scaffolds are generated by the action of the mechanistically intriguing family of mono-, sesqui-, and diterpene synthases collectively termed as terpene synthases, that catalyze multistep reactions with diphosphorylated substrates of 10 (geranyl diphosphate), 15 (farnesyl diphosphate) or 20 (geranylgeranyl diphosphate) carbons. In the studied work, we performed a computational study on proteome wide identification of terpene synthase motifs in Arabidopsis thaliana proteome on the basis of weight matrix approach. We have developed an optimal weight matrix for the identification of terpene synthase motifs in the plant’s proteome. Weight matrix was constructed by aligning orthologous sequences of known terpene synthases originated from diverse plant species viz., Abies grandis, Nicotiana tobaccum etc. Sequences of detected domains & motifs were retrieved through SwissProtKB/NCBI on the basis of specific conservation IDs of Prosite, Pfam, Interpro, Prodom, COG, TIGR databases, while position specific scoring matrices were made through MEME, MotifSampler, PossuMsearch tools. Weight matrix based search of conserved motifs in the proteome of A. thaliana was done through ESA, Lahead and Simple algorithm based search tools of PossuMsearch biosuite in Linux system. Prediction was first validated by using positive control data set and optimized the method to reach prediction accuracy upto >90%. After tool performance evaluation, prediction was made on whole proteome at specific threshold/score value. Significant results were found in A. thaliana with motif similarity ranges from 80% to 100%. This proteome wide search model paves the path to identify more terpene synthases genes in A. thaliana, as well as in other plant systems.

Amplify-forward relaying for multiple-antenna multiple relay networks under individual power constraint at each relay

This article considers the design of an optimal beamforming weight matrix of multiple-antenna multiple-relay networks. It is assumed that each relay utilizes the amplify and forward strategy, i.e., it multiplies the received signal vector by a matrix, dubbed the relay weight matrix, and forwards the resulting vector to the destination. Furthermore, we assume that the source and the destination have the same number of antennas and that each transmit antenna is virtually paired to a different destination antenna. The relay weight matrices are concurrently designed to optimize the mean square error (MSE) criterion at the destination, assuming each relay node is subject to a power constraint. Accordingly, it is demonstrated that this problem can be cast as a convex optimization problem in which the individual power constraints are tackled by employing the method of Lagrange multipliers in two stages. First, the relay gain matrix is computed analytically in terms of Lagrange dual variables, thereby converting the original problem into a scalar optimization problem. Then, these scalar variables are computed numerically. The proposed scheme is evaluated through simulation with various numbers of relays and antennas to obtain MSE and bit error rate (BER) metrics and it is shown that the resulting MSE and BER achieved through using the proposed method outperforms that of MMSE-MMSE method introduced by Oyman et.al., which is regarded as the best known method for the underlying problem.

Reference-free time-based localization for an asynchronous target

Low-complexity least-squares (LS) estimators based on time-of-arrival (TOA) or time-difference-of-arrival (TDOA) measurements have been developed to locate a target node with the help of anchors (nodes with known positions). They require to select a reference anchor in order to cancel nuisance parameters or relax stringent synchronization requirements. Thus, their localization performance relies heavily on the reference selection. In this article, we propose several reference-free localization estimators based on TOA measurements for a scenario, where anchor nodes are synchronized, and the clock of the target node runs freely. The reference-free LS estimators that are different from the reference-based ones do not suffer from a poor reference selection. Furthermore, we generalize existing reference-based localization estimators using TOA or TDOA measurements, which are scattered over different research areas, and we shed new light on their relations. We justify that the optimal weighting matrix can compensate the influence of the reference selection for reference-based weighted LS (WLS) estimators using TOA measurements, and make all those estimators identical. However, the optimal weighting matrix cannot decouple the reference dependency for reference-based WLS estimators using a nonredundant set of TDOA measurements, but can make the estimators using the same set identical as well. Moreover, the Cramér-Rao bounds are derived as benchmarks. Simulation results corroborate our analysis.

Prioritization and Evaluation of Depression Candidate Genes by Combining Multidimensional Data Resources

BackgroundLarge scale and individual genetic studies have suggested numerous susceptible genes for depression in the past decade without conclusive results. There is a strong need to review and integrate multi-dimensional data for follow up validation. The present study aimed to apply prioritization procedures to build-up an evidence-based candidate genes dataset for depression.MethodsDepression candidate genes were collected in human and animal studies across various data resources. Each gene was scored according to its magnitude of evidence related to depression and was multiplied by a source-specific weight to form a combined score measure. All genes were evaluated through a prioritization system to obtain an optimal weight matrix to rank their relative importance with depression using the combined scores. The resulting candidate gene list for depression (DEPgenes) was further evaluated by a genome-wide association (GWA) dataset and microarray gene expression in human tissues.ResultsA total of 5,055 candidate genes (4,850 genes from human and 387 genes from animal studies with 182 being overlapped) were included from seven data sources. Through the prioritization procedures, we identified 169 DEPgenes, which exhibited high chance to be associated with depression in GWA dataset (Wilcoxon rank-sum test, p = 0.00005). Additionally, the DEPgenes had a higher percentage to express in human brain or nerve related tissues than non-DEPgenes, supporting the neurotransmitter and neuroplasticity theories in depression.ConclusionsWith comprehensive data collection and curation and an application of integrative approach, we successfully generated DEPgenes through an effective gene prioritization system. The prioritized DEPgenes are promising for future biological experiments or replication efforts to discoverthe underlying molecular mechanisms for depression.

A note on improving quadratic inference functions using a linear shrinkage approach

In some commonly used longitudinal clinical trials designs, the quadratic inference functions (QIF) method fails to work due to non-invertible estimation of the optimal weighting matrix. We propose a modified QIF method, in which the optimal weighting matrix is estimated by a linear shrinkage estimator, replacing the sample covariance matrix. We prove that the linear shrinkage estimator is consistent and asymptotically optimal under the expected quadratic loss, and will have more stable numerical performance than the sample covariance matrix. Simulations show that numerical improvements are acquired in light of a higher percentage of convergence, and smaller standard errors and mean square errors of parameter estimates.

The Asymptotical Stability Analysis for Switched Descriptor Systems

This paper is concerned with the asymptotical stability analysis for a class of switched uncertain descriptor systems with time-delay. The robustly asymptotical stability of this system is proven by making use of the generalized Lyapunov Stability theory, linear matrix inequality (LMI) tools and multiple Lyapunov function techniques. The conservation of result is greatly reduced by means of introducing the optimal weight matrix and avoiding vector matrix inequality in deducing procedure, in which there is no need of transformation and hypothesis for descriptor systems. The designed control law could surely make switched Descriptor Systems quickly approach the balanceable point. Experimentally, one numerical simulation verifies the effectiveness of this method.

Pattern recall analysis of the Hopfield neural network with a genetic algorithm

This paper describes the implementation of a genetic algorithm to evolve the population of weight matrices for storing and recalling the patterns in a Hopfield type neural network model. In the Hopfield type neural network of associative memory, the appropriate arrangement of synaptic weights provides an associative function in the network. The energy function associated with the stable state of this model represents the appropriate storage of the input patterns. The aim is to obtain the optimal weight matrix for efficient recall of any prototype input pattern. For this, we explore the population generation technique (mutation and elitism), crossover and the fitness evaluation function for generating the new population of the weight matrices. This process continues until the selection of the last weight matrix or matrices has been performed. The experiments incorporate a neural network trained with multiple numbers of patterns using the Hebbian learning rule. In most cases, the recalling of patterns using a genetic algorithm seems to give better results than the conventional recalling with the Hebbian rule. The simulated results suggest that the genetic algorithm is the better searching technique for recalling noisy prototype input patterns.

The Effects of Dynamic Feedbacks on LS and MM Estimator Accuracy in Panel Data Models: Some Additional Results

In this paper, we show that the order of magnitude of the finite sample bias of the GMMld^{(2)} estimator of Bun and Kiviet (2006) can be reduce from O(T/N) to O(1/N) if the optimal weighting matrix is used. To demonstrate this result, we consider a model transformed by the upper triangular Cholesky factorization of the inverse of the variance matrix of error component u_i. Some variants of the system GMM estimator that are associated with the Cholesky-transformed model are also discussed.

Pattern recalling analysis of English alphabets using Hopfield model of feedback neural network with evolutionary searching

In this paper, we are analysing the performance of Hopfield model of feedback neural networks (NNs) with general Hebbian learning rule and genetic algorithm (GA) for pattern recognition. In the Hopfield type of NNs, the weighted code of input patterns provides an auto-associative function in the network, which exhibits its associative memory feature. The objective is to determine the optimal weight matrix for efficient recalling of any approximate input pattern. For this, we explore the population generation technique (mutation and elitism), crossover and setting up of proper fitness evaluation functions to generate the new population of the weight matrices. This process will continue until the last weight matrix has been selected. The experiments consider a neural network architecture that stores all letters of English alphabets (capitals only) using Hebbian rule and then accomplishes the recalling of these stored patterns on presentation of any prototype input pattern of the already stored patterns using both conventional Hebbian rule and evolutionary algorithm. The simulated results demonstrate the better performance of network for recalling of the stored letters of English alphabets using GA and minimise the randomness from the GA.

A multi-dimensional evidence-based candidate gene prioritization approach for complex diseases–schizophrenia as a case

During the past decade, we have seen an exponential growth of vast amounts of genetic data generated for complex disease studies. Currently, across a variety of complex biological problems, there is a strong trend towards the integration of data from multiple sources. So far, candidate gene prioritization approaches have been designed for specific purposes, by utilizing only some of the available sources of genetic studies, or by using a simple weight scheme. Specifically to psychiatric disorders, there has been no prioritization approach that fully utilizes all major sources of experimental data. Here we present a multi-dimensional evidence-based candidate gene prioritization approach for complex diseases and demonstrate it in schizophrenia. In this approach, we first collect and curate genetic studies for schizophrenia from four major categories: association studies, linkage analyses, gene expression and literature search. Genes in these data sets are initially scored by category-specific scoring methods. Then, an optimal weight matrix is searched by a two-step procedure (core genes and unbiased P-values in independent genome-wide association studies). Finally, genes are prioritized by their combined scores using the optimal weight matrix. Our evaluation suggests this approach generates prioritized candidate genes that are promising for further analysis or replication. The approach can be applied to other complex diseases. The collected data, prioritized candidate genes, and gene prioritization tools are freely available at http://bioinfo.mc.vanderbilt.edu/SZGR/.