Linear Restrictions Research Articles

A class of Stein‐rules in multivariate regression model with structural changes

AbstractIn this paper, we consider an estimation problem of the matrix of the regression coefficients in multivariate regression models with unknown change‐points. More precisely, we consider the case where the target parameter satisfies an uncertain linear restriction. Under general conditions, we propose a class of estimators that includes as special cases shrinkage estimators (SEs) and both the unrestricted and restricted estimator. We also derive a more general condition for the SEs to dominate the unrestricted estimator. To this end, we extend some results underlying the multidimensional version of the mixingale central limit theorem as well as some important identities for deriving the risk function of SEs. Finally, we present some simulation studies that corroborate the theoretical findings.

Linear growth and child development in low- and middle-income countries: a meta-analysis.

The initial years of life are critical for physical growth and broader cognitive, motor, and socioemotional development, but the magnitude of the link between these processes remains unclear. Our objective was to produce quantitative estimates of the cross-sectional and prospective association of height-for-age z score (HAZ) with child development. Observational studies conducted in low- and middle-income countries (LMICs) presenting data on the relationship of linear growth with any measure of child development among children <12 years of age were identified from a systematic search of PubMed, Embase, and PsycINFO. Two reviewers then extracted these data by using a standardized form. A total of 68 published studies conducted in 29 LMICs were included in the final database. The pooled adjusted standardized mean difference in cross-sectional cognitive ability per unit increase in HAZ for children ≤ 2 years old was +0.24 (95% confidence interval [CI], 0.14-0.33; I(2) = 53%) and +0.09 for children > 2 years old (95% CI, 0.05-0.12; I(2) = 78%). Prospectively, each unit increase in HAZ for children ≤ 2 years old was associated with a +0.22-SD increase in cognition at 5 to 11 years after multivariate adjustment (95% CI, 0.17-0.27; I(2) = 0%). HAZ was also significantly associated with earlier walking age and better motor scores (P < .05). Observational evidence suggests a robust positive association between linear growth during the first 2 years of life with cognitive and motor development. Effective interventions that reduce linear growth restriction may improve developmental outcomes; however, integration with environmental, educational, and stimulation interventions may produce larger positive effects.

How to define relaxed V2 languages and how to distinguish them from non-V2 languages: A reply to Brandtler (2014)

This paper provides evidence for the idea that relaxed verb-second (V2) languages exist and exhibt specific properties which distinguish them from both strict V2 and non-V2 languages. The identification of the relaxed subtype of V2 languages implies that V2 should not be understood as a linear restriction, but as an abstract rule involving the movement of the finite verb to a head of the left periphery in all main clauses.

Energy Efficient Throughput Maximization for Wireless Networks Using Piece Wise Linear Approximation

The amount of power requirement is a main issue in wireless network nodes. We recommend a new piece-wise linear approximation to convert nonlinearities into linear restrictions. In this paper, we considered the energy required for the battery, which is most important. We proposed that this issue can be overcome by a mixed-integer nonlinear program (MINLP). To make our concept as energy efficient, we characterize its scientific expressions, then suggest a new piece-wise linear approximation which will give prime solution. This method allows converting the nonlinearities into linear constraints. In this paper both network throughput and energy requirement were optimized through a multi criteria framework which is optimized, i.e., by optimizing the network output by reducing the maximum power consumption. In telecommunication the source coding, channel coding, and finally the, line coding are at the transmitting point to generate the baseband signal. In some systems they use modulation to multiplex these signal to generate many baseband signals. During the active wireless link for communication, the energy consumption is in the form of two thins 1. Energy required for the purpose of broad casting and the other is energy required for the instruments involved during the communication. The utilization of power depends upon the whether the link is active or not. From the above consideration our work is vary from the existing work in the same area. The energy used by the LCD for the existing is always used and hence the usage of power for one node is more when compared to proposed system. Keywords: Piece-wise linear approximation, MINLP, Energy efficiency, Energy consumption, Network through put, PIC Microcontroller.

Linear Restriction Estimates for Schrödinger Equation on Metric Cones

In this paper, we study some modified linear restriction estimates of the dynamics generated by Schrödinger operator on metric cone M, where the metric cone M is of the form M = (0, ∞) r × Σ, with the cross section Σ being a compact (n − 1)-dimensional Riemannian manifold (Σ, h) and the equipped metric being g = dr 2 + r 2 h. Assuming the initial data possesses additional regularity in angular variable θ ∈ Σ, we show some linear restriction estimates for the solutions. In terms of their applications, we obtain global-in-time Strichartz estimates for radial initial data and show small initial data scattering theory for the mass-critical nonlinear Schrödinger equation on two-dimensional metric cones.

Forces Between Conductors: The “50/50 Rule” About the Partition of Supplied Energy

We prove the 50/50 rule of Fig. 1 by a Lagrangian technique (all fields pulled back to the reference configuration at time 0) which exposes the necessity of two circumstances for the result to hold: 1) time-invariance of currents, when expressed in “material form” and 2) equality of (magnetic) coenergy and energy, which excludes nonlinear $\boldsymbol {B}$ – $\boldsymbol {H}$ laws. A dual result, which holds in case of time-invariance of “flux linkages” (but without the linearity restriction), is found along the way.

Is the Ex-Ante Equity Risk Premium Always Positive? Evidence from a New Conditional Expectations Model

In this paper, we propose a new two-stage method, including Principal Component Analysis and Boosted Regression Tree, to model conditional expected returns. With this technique, we address two potential criticisms on how to capture the true identity of the investors’ information set, and how investors use the information in forming expected returns. Applying this risk premium proxy, we test whether risk premium is always positive. A number of asset pricing studies have focused on testing linear restrictions imposed by asset pricing models and largely ignore this important restriction. We find evidence that the positivity condition of the risk premium is violated for the US (CRSP index) in some states of the economy; these states are associated with periods of low corporate returns, low long term government bond returns, lagged negative risk premium, and downward sloping term structure.

A restricted $$r{-}k$$ r - k class estimator in the mixed regression model with autocorrelated disturbances

In this paper, a new estimator is proposed by combining basically the ordinary ridge regression estimator and the principal component regression estimator for a regression model which has multicollinearity and which satisfies some a priori stochastic linear restrictions. The performance of the proposed \(r{-}k\) class estimator in this mixed regression model is compared with those of the mixed regression estimator, ridge regression estimator and the stochastic restricted ridge regression estimator in terms of the mean squared error matrix criterion. Tests for verifying the conditions of dominance of the proposed estimator over the others are also proposed. Furthermore, a Monte Carlo study and a numerical illustration are carried out to empirically study the performance of the estimators by the mean squared error values, and then to perform tests to verify if the conditions for superiority of the proposed estimator over the others hold.

Shrinkage ridge estimators in semiparametric regression models

In this paper, ridge and non-ridge type shrinkage estimators and their positive parts are defined in the semiparametric regression model when the errors are dependent and some non-stochastic linear restrictions are imposed under a multicollinearity setting. The exact risk expressions in addition to biases are derived for the estimators under study and the region of optimality of each estimator is exactly determined. Also, necessary and sufficient conditions, for the superiority of the ridge type estimator over its counterpart, for selecting the ridge parameter k are obtained. Lastly, a simulation study and real data analysis are performed to illustrate the efficiency of proposed estimators based on the minimum risk criterion. In this regard, kernel smoothing and modified cross-validation methods for estimating the non-parametric function are used.

Independence distribution-preserving covariance structures for the likelihood ratio test for LXB=0 in the general linear model

We derive an explicit representation of the general non-i.i.d. error covariance matrix of the general linear model vector such that the likelihood ratio test statistic for testing certain linear restrictions on the parameter vector is robust against certain forms of dependency and heteroscedasticity. In doing so, we correct two proposed explicit covariance matrix characterizations given in Khatri (1981).

Green's Hyperplane Restriction Theorem: An extension to modules

In this paper, we prove a generalization of Green's Hyperplane Restriction Theorem to the case of modules over the polynomial ring, providing in particular an upper bound for the Hilbert function of the general linear restriction of a module M in a degree d by the corresponding Hilbert function of a lexicographic module.

Stochastic Restricted Maximum Likelihood Estimator in Logistic Regression Model

In the presence of multicollinearity in logistic regression, the variance of the Maximum Likelihood Estimator (MLE) becomes inflated. Siray et al. (2015) [1] proposed a restricted Liu estimator in logistic regression model with exact linear restrictions. However, there are some situations, where the linear restrictions are stochastic. In this paper, we propose a Stochastic Restricted Maximum Likelihood Estimator (SRMLE) for the logistic regression model with stochastic linear restrictions to overcome this issue. Moreover, a Monte Carlo simulation is conducted for comparing the performances of the MLE, Restricted Maximum Likelihood Estimator (RMLE), Ridge Type Logistic Estimator(LRE), Liu Type Logistic Estimator(LLE), and SRMLE for the logistic regression model by using Scalar Mean Squared Error (SMSE).

Testing for A Set of Linear Restrictions in VARMA Models Using Autoregressive Metric: An Application to Granger Causality Test

In this paper we propose a test for a set of linear restrictions in a Vector Autoregressive Moving Average (VARMA) model. This test is based on the autoregressive metric, a notion of distance between two univariate ARMA models, M0 and M1, introduced by Piccolo in 1990. In particular, we show that this set of linear restrictions is equivalent to a null distance d(M0,M1 ) between two given ARMA models. This result provides the logical basis for using d(M0,M1) = 0 as a null hypothesis in our test. Some Monte Carlo evidence about the finite sample behavior of our testing procedure is provided and two empirical examples are presented.

A new MM algorithm for constrained estimation in the proportional hazards model

The constrained estimation in Cox’s model for the right-censored survival data is studied and the asymptotic properties of the constrained estimators are derived by using the Lagrangian method based on Karush–Kuhn–Tucker conditions. A novel minorization–maximization (MM) algorithm is developed for calculating the maximum likelihood estimates of the regression coefficients subject to box or linear inequality restrictions in the proportional hazards model. The first M-step of the proposed MM algorithm is to construct a surrogate function with a diagonal Hessian matrix, which can be reached by utilizing the convexity of the exponential function and the negative logarithm function. The second M-step is to maximize the surrogate function with a diagonal Hessian matrix subject to box constraints, which is equivalent to separately maximizing several one-dimensional concave functions with a lower bound and an upper bound constraint, resulting in an explicit solution via a median function. The ascent property of the proposed MM algorithm under constraints is theoretically justified. Standard error estimation is also presented via a non-parametric bootstrap approach. Simulation studies are performed to compare the estimations with and without constraints. Two real data sets are used to illustrate the proposed methods.

Efficiency of a stochastic restricted two-parameter estimator in linear regression

Sakallıoğlu and Kaçiranlar (2008) proposed an estimator, two-parameter estimator, as an alternative to the ordinary least squares, the ordinary ridge and the Liu estimators in the presence of multicollinearity. In this paper, we introduce a new class estimator by combining the ideas underlying the mixed estimator and the two-parameter estimator when stochastic linear restrictions are assumed to hold. The necessary and sufficient conditions for the superiority of the new estimator over the two-parameter estimator, modified mixed estimator and stochastic restricted two-parameter estimator Yang and Wu (2012) are derived by the matrix mean square error criterion. Furthermore, selections of the biasing parameters are discussed and two numerical examples and a Monte Carlo simulation are given to evaluate the performance of mentioned estimators in the theoretical results.

Intuitionistic Fuzzy Weighted Linear Regression Model with Fuzzy Entropy under Linear Restrictions.

In fuzzy set theory, it is well known that a triangular fuzzy number can be uniquely determined through its position and entropies. In the present communication, we extend this concept on triangular intuitionistic fuzzy number for its one-to-one correspondence with its position and entropies. Using the concept of fuzzy entropy the estimators of the intuitionistic fuzzy regression coefficients have been estimated in the unrestricted regression model. An intuitionistic fuzzy weighted linear regression (IFWLR) model with some restrictions in the form of prior information has been considered. Further, the estimators of regression coefficients have been obtained with the help of fuzzy entropy for the restricted/unrestricted IFWLR model by assigning some weights in the distance function.

Construction of a recombinant vector for site-directed mutagenesis in Salmonella typhimurium

BACKGROUND: Among all common techniques in sitedirectedmutagenesis, λ Red recombinase system has beenwidely used to knock out chromosomal genes in bacteria. In thismethod, there is always the risk of DNA Linear digestion byhost's restriction enzymes that leads to the low frequency ofrecombination. OBJECTIVES:To overcome this, we constructeda recombinant vector to disrupt phoP gene in Salmonellatyphimurium. METHODS: The SOEing PCR method andrestriction enzymes were used to construct the vector. RESULTS:The resulting plasmid, pTAAZ92, contains a Kanamycincassette with two long homologous arms flanking of the phoPgene. CONCLUSIONS: After electrotransformation of thepTAAZ92 into the Salmonella typhimurium , the phoP gene isreplaced by the Kanamycin cassette through homologousrecombination. According to the high homology of the phoPgene in many of Salmonella species the pTAAZ92 can be used todisrupt the phoP gene in most of these species.

A Generalized Stochastic Restricted Ridge Regression Estimator

In this article, we introduce a new stochastic restricted estimator for the unknown vector parameter in the linear regression model when stochastic linear restrictions on the parameters hold. We show that the new estimator is a generalization of the ordinary mixed estimator (OME), Liu estimator (LE), ordinary ridge estimator (ORR), (k-d) class estimator, stochastic restricted Liu estimator (SRLE), and stochastic restricted ridge estimator (SRRE). Performance of the new estimator in comparison to other estimators in terms of the mean squares error matrix (MMSE) is examined. Numerical example from literature have been given to illustrate the results.

Optimisation of substrate blends in anaerobic co-digestion using adaptive linear programming

Anaerobic co-digestion of multiple substrates has the potential to enhance biogas productivity by making use of the complementary characteristics of different substrates. A blending strategy based on a linear programming optimisation method is proposed aiming at maximising COD conversion into methane, but simultaneously maintaining a digestate and biogas quality. The method incorporates experimental and heuristic information to define the objective function and the linear restrictions. The active constraints are continuously adapted (by relaxing the restriction boundaries) such that further optimisations in terms of methane productivity can be achieved. The feasibility of the blends calculated with this methodology was previously tested and accurately predicted with an ADM1-based co-digestion model. This was validated in a continuously operated pilot plant, treating for several months different mixtures of glycerine, gelatine and pig manure at organic loading rates from 1.50 to 4.93gCOD/Ld and hydraulic retention times between 32 and 40days at mesophilic conditions.

A Method of Multi-View Images 3D Restructuring of Discrete Line Segments

In this paper, the average reprojection geometrical errors on all images of a spatial straight line is taken as the restructuring and optimization target function to ensure the optimal result to be acquired; a spatial straight line is expressed by use of the Plücker coordinates for the proposal of the analytical method of correcting the double linear restriction on the Plücker coordinates of noise-included spatial straight lines; during the optimization process, to ensure parameters that meet double linear restriction, the iteration renewal process is expressed by at least 4 parameters, to increase the precision of restructuring results. Experiments results derived from simulation data and real images have all demonstrated the high efficiency and precision of the algorithm proposed in this paper.