Restricted Linear Model Research Articles

Methodology for Inventory Management in Neighborhood Stores Using Machine Learning and Integer Linear Programming

Context: Nowadays, inventory management poses a challenge given the constant demands related to temporality, geographic location, price variability, and budget availability, among others. In neighborhood shops, this process is manually done based on experience (the data generated are ignored), which is sometimes not enough to respond to changes. This shows the need to develop new strategies and tools that use data analysis techniques. Method: Our methodology predicts the weekly demand for 14 common products in neighborhood stores, which is later refined based on investment capital. The method is validated using a database built with synthetic information extracted from statistical sampling. For the prediction model, three supervised learning models are used: support vector machines (SVM), AutoRegressive models (Arx), and Gaussian processes (GP). This work proposes a restricted linear model given an inversion and the predicted quantity of products; the aim is to refine the prediction while maximizing the shopkeeper's profit. Finally, the problem is solved by applying an integer linear programming paradigm. Results: Tests regarding the prediction and inventory adjustment stages are conducted, showing that the methodology can predict the temporal dynamics of the data by inferring the statistical moments of the distributions used. It is shown that it is possible to obtain a maximum profit with a lower investment. Conclusions: Our method allows predicting and refining inventory management in a neighborhood store model where quantities are managed to maximize the shopkeeper's profits. This opens the way to explore this approach in a real scenario or to introduce new techniques that can improve its performance.

Dispersion matrix comparisons among estimators under two competing restricted linear regression models

Dispersion matrix comparisons among estimators under two competing restricted linear regression models

Generalized ridge shrinkage estimation in restricted linear model

Generalized ridge shrinkage estimation in restricted linear model

Statistical inference of a stochastically restricted linear mixed model

<abstract><p>This article compares a predictor with the best linear unbiased predictor (BLUP) for a unified form of all unknown parameters under a stochastically restricted linear mixed model (SRLMM) in terms of the mean squared error matrix (MSEM) criterion. The methodology of block matrix inertias and ranks is employed to compare the MSEMs of these predictors. The comparison results are also demonstrated for a linear mixed model with and without an exact restriction, as well as special cases of the unified form of all unknown parameters in the SRLMM.</p></abstract>

R-Software for the Assessment of Structural Changes in Fisheries Production of Andhra Pradesh and Tamil Nadu for Indian GDP

A Chow test was applied to analyze the structural changes in GDP of India with respect to Fisheries GDP obtained from the states of Andhra Pradesh and Tamil Nadu using Unrestricted and Restricted Linear Regression models in matrix notation for the period of 2000–01 to 2013–14. The GDP and Fisheries GDP data pertaining to the state of Andhra Pradesh and Tamil Nadu for the periods 2000–01 to 2006–07 and 2007–08 to 2013–14 were also collected for analyzing the structural changes between earmarked two periods as well as states from 2000–01 to 2013–14. In this study, the Chow test revealed that there was no structural change between the total GDP of India and Fisheries GDP with respect to the states Andhra Pradesh and Tamil Nadu during the periods 2001–2007 and 2008 –2014. However, significant structural changes could be observed between the GDP of India and Fisheries GDP obtained from the states of Andhra Pradesh and Tamil Nadu during the period 2000–2001 to 2013–14.However, there was a positive trend of structural change observed in the states Andhra Pradesh and Tamil Nadu with respect to the GDP of India and Fisheries GDP during the period 2000–2001 to 2012–14. Owing to theses, it is concluded that the contribution of fisheries with respect to the country’s GDP between the periods made a significant structural change however no many structural changes were observed in two time periods within the states.

A Simulation Study of Some Restricted Estimators in Restricted Linear Regression Model

When the multicollinearity exists in linear regression model, the result of the Restricted Least Square estimator (RLS) is unstable. So that, more researchers proposed the restricted biased estimators to improve the efficiency of RLS estimator. In this paper, Some of biased restricted estimators have been introduced to study the performance of them. The simulation study has been given to compare these estimators. According to simulation study, we found that, the shrinkage restricted ridge regression (SRRE) estimator which proposed by Baber and Mustafa [1], has good properties comparing with other restricted estimators that given in this study. A Numerical example has been considered to illustrate the performance of these estimators

The Performance of Some Restricted Estimators In Restricted Linear Regression Model

In the linear regression model, the restricted biased estimation as one of important methods to addressing the high variance and the multicollinearity problems. In this paper, we make the simulation study of the some restricted biased estimators. The mean square error (MME) criteria are used to make a comparison among them. According to the simulation study we observe that, the performance of the restricted modified unbiased ridge regression estimator (RMUR) was proposed by Bader and Alheety (2020) is better than of these estimators. Numerical example have been considered to illustrate the performance of the estimators.

Robust estimation in restricted linear regression

Linear regression is a well-known method to predict further values for dependent variable given observed independent variables. Sometimes, there is prior information about regression coefficients. Therefore, restricted regression takes into account prior information and combines it with the sample information. Unfortunately, restricted regression has same assumptions as a linear regression. In this paper, we propose robust estimation of restricted linear models. In the application part, it is demonstrated that the proposed methods are convenient method to give impressive results in the presence of outliers with stochastic or nonstochastic restriction.

Revising the BFIHOST catchment descriptor to improve UK flood frequency estimates

Abstract The estimate of the base flow index (BFI) based on the Hydrology of Soil Types (HOST) classification, BFIHOST, provides a measure of catchment responsiveness. BFIHOST is used with other variables to estimate the median annual maximum flood (QMED) in the UK standard Flood Estimation Handbook (FEH) statistical method and is also an explanatory variable in ReFH2, the FEH design hydrograph package. The current estimates of BFIHOST are derived from a restricted linear model, and a number of issues in the catchment dataset have been identified since the original work in 1995. The BFI calculated through base flow separation tends to be underestimated in clay-dominated catchments, and the calculation technique performs poorly in ephemeral catchments or those with missing data. The pragmatic bounding of BFI coefficients for permeable soils overlying aquifer outcrops is also problematic for small catchments. This paper investigates alternative regression methods to improve base flow estimates using the HOST class data for 991 stations (compared to 575 in the original); beta regression was found to give the best performance. Combining multiple rare classes into single classes is also shown to improve performance. The new version of BFIHOST was applied to the QMED equation, showing improved performance.

A new version of unbiased ridge regression estimator under the stochastic restricted linear regression model

Crouse et al. (Commun Stat Theory Methods 24:2341–2354, 1995) proposed the unbiased ridge regression estimator for the multicollinear regression model. Jibo Wu (The Scientific World Journal; Volume 2014, Article ID 206943, 1–8) introduced an unbiased two-parameter estimator based on prior information and two-parameter estimator proposed by Özkale and Kacıranlar, 2007. A new version of unbiased two-parameter estimator for the stochastic restricted linear regression model is proposed in this paper. The properties and the performance of the proposed estimator compared to other common estimators using the mean squares error criterion for the goodness of fit have been studied. Finally; A numerical example and a simulation study has been given to illustrate the performance of the proposed estimator.

One-block train formation in large-scale railway networks: An exact model and a tree-based decomposition algorithm

We investigate the one-block train formation problem (TFP) in the railway freight transportation industry. The input to this problem is a railway network and a set of demands for transportation. Each demand is a request for shipping a number of rail cars from one station to another. The one-block TFP now addresses two subproblems in the tactical level: Which pairs of stations are directly connected via a block (or: train service); and which demands are transported by each block. The aim is to service all demands against minimal costs. Moving beyond current researches on service network design, the unitary rule and the intree rule are taken into account in this study based on the Chinese railway background. We develop a linear binary programming formulation to minimize the total sum of train accumulation costs and car classification costs, subject to limitations on the classification capacity and the number of sort tracks at each station. Furthermore, we propose a novel solution methodology that applies a tree-based decomposition algorithm. Here, we first decompose the whole network into a series of rooted trees for each destination separately. Then, we divide the trees further into sufficiently small subtrees, whose size is regulated by a node size parameter. Finally, we construct a restricted linear binary model for each subtree and solve these models sequentially to find their optimal solutions. The algorithm ensures that an overall feasible solution is obtained if one exists. Our computational results on a realistic network from the Chinese railway system with 83 stations, 158 links and 5700 randomly generated demands show that the proposed algorithm can derive high-quality solutions within a few hours of computation time. These solutions are on average 48.05% better than those obtained after solving the linear binary program with a commercial solver for 1 day.

Estimation and test of restricted linear EV model with nonignorable missing covariates

This paper deals with estimation and test procedures for restricted linear errors-invariables (EV) models with nonignorable missing covariates. We develop a restricted weighted corrected least squares (WCLS) estimator based on the propensity score, which is fitted by an exponentially tilted likelihood method. The limiting distributions of the proposed estimators are discussed when tilted parameter is known or unknown. To test the validity of the constraints, we construct two test procedures based on corrected residual sum of squares and empirical likelihood method and derive their asymptotic properties. Numerical studies are conducted to examine the finite sample performance of our proposed methods.

고정효과의 제한선형모형

본 논문은 고정효과의 선형모형에서 추정가능함수로 주어지는 제한모형의 모수추론에 관한 방법을 다루고 있다. 모형의 일부분으로 부과되는 제한식이 추정가능함수들로 구성될 때 모수의 추론을 위한 Lagrange 배수법과 제한식이 모형에 병합되어 변환된 제한모형을 이용하여 모수를 추론하는 방법으로 주어지는 두 분석이 동일함을 입증하고 있다. 제한모형의 모수 추정에 이용된 두 방법에서 주어지는 모수 추정치는 같지 않으나 추정가능함수의 추정값은 불변임을 보여주고 있다. 또한, 선형모형에 모형의 일부로 추가되는 제한이 추정가능함수인 가의 판단으로 사영행렬을 이용할 수 있음을 나타내며 추정가능함수가 제한식에 포함될 때 잔차의 변동량과 자유도의 변화를 다루었다. 제한모형에서 제한식에 따른 변환된 제한모형의 형태를 제시하였으며 검정가능함수에 대한 가설검정을 위한 축소제한모형으로부터 변환된 축소제한모형을 제시하고 사영에 의한 분산분석결과가 Lagrange 배수법에 의한 결과와 동일함을 다루었다.

ON EQUALITIES OF BLUES FOR A MULTIPLE RESTRICTED PARTITIONED LINEAR MODEL

For the multiple restricted partitioned linear model M={y,X1 β1 + …+ Xsβs | A1β1=b1,…,Asβs=bs,Σ}, the relationships between the restricted partitioned linear model M and the corresponding s small restricted linear models Mi={y,Xiβi | Aiβi=bi,Σ},i=1,…,s are studied. The necessary and sufficient conditions for the best linear unbiased estimators (BLUEs) under the full restricted model to be the sums of BLUEs under the s small restricted model are derived. Some statistical properties of the BLUEs are also described.

Statistical inference on restricted linear regression models with partial distortion measurement errors

We consider statistical inference for linear regression models when some variables are distorted with errors by some unknown functions of commonly observable confounding variables. The proposed estimation procedure is designed to accommodate undistorted as well as distorted variables. To test a hypothesis on the parametric components, a restricted least squares estimator is proposed for unknown parameters under some restricted conditions. Asymptotic properties for the estimators are established. A test statistic based on the difference between the residual sums of squares under the null and alternative hypotheses is proposed, and we also obtain the asymptotic properties of the test statistic. A wild bootstrap procedure is proposed to calculate critical values. Simulation studies are conducted to demonstrate the performance of the proposed procedure and a real example is analysed for an illustration.

Difference-based ridge-type estimator of parameters in restricted partial linear model with correlated errors.

In this article, a generalized difference-based ridge estimator is proposed for the vector parameter in a partial linear model when the errors are dependent. It is supposed that some additional linear constraints may hold to the whole parameter space. Its mean-squared error matrix is compared with the generalized restricted difference-based estimator. Finally, the performance of the new estimator is explained by a simulation study and a numerical example.

On Diagnostics in Stochastic Restricted Linear Regression Models

The aim of this paper is to propose some diagnostic methods in stochastic restricted linear regression models. A review of stochastic restricted linear regression models is given. For the model, this paper studies the method and application of the diagnostic mostly. Firstly, review the estimators of this model. Secondly, show that the case deletion model is equivalent to the mean shift outlier model for diagnostic purpose. Then, some diagnostic statistics are given. At last, example is given to illustrate our results.

The Optimal Selection for Restricted Linear Models with Average Estimator

The essential task of risk investment is to select an optimal tracking portfolio among various portfolios. Statistically, this process can be achieved by choosing an optimal restricted linear model. This paper develops a statistical procedure to do this, based on selecting appropriate weights for averaging approximately restricted models. The method of weighted average least squares is adopted to estimate the approximately restricted models under dependent error setting. The optimal weights are selected by minimizing ak-class generalized information criterion (k-GIC), which is an estimate of the average squared error from the model average fit. This model selection procedure is shown to be asymptotically optimal in the sense of obtaining the lowest possible average squared error. Monte Carlo simulations illustrate that the suggested method has comparable efficiency to some alternative model selection techniques.

GSCA: New Software and Algorithms to Analyse Diallel Mating Designs Based on Restricted Linear Model

Abstract The diallel mating designs have been extensively employed to gain genetic information by crop and tree breeders, but analysis of diallel data faces some challenges because the same parent acts both male and female roles. Theoretically, little attention was paid to the statistical inference and hypothesis testing for a fixed diallel linear model. In this paper we provide a uniform solution to any fixed diallel linear model with matrix expression based on the theory of restricted linear models. We derive formulae for estimating diallel parameters and their standard errors, and obtain uniform statistics for hypothesis testing of parameters, factors and differences between general combining abilities (GCA) or specific combining abilities (SCA). To put the result into practice, we have developed a Windows®software program “GSCA” for analyzing a flexible diallel linear model that could contain the GCA, SCA, reciprocal, block and environment effects as well as interaction effects such as GCA by environment. GSCA can perform analyses not only for Griffing’s four types of diallel crosses but also for more complicated diallel crosses whether the data structure is balanced or unbalanced. A real example is given to illustrate the convenience, flexibility and power of our software for diallel analysis.

Characterizing Relationships Between Estimations Under a General Linear Model with Explicit and Implicit Restrictions by Rank of Matrix

In the investigation of the restricted linear model ℳ r = {y, X β | A β = b, σ2 Σ}, the parameter constraints A β = b are often handled by transforming the model into certain implicitly restricted model. Any estimation derived from the explicitly and implicitly restricted models on the vector β and its functions should be equivalent, although the expressions of the estimation under the two models may be different. However, people more likely want to directly compare different expressions of estimations and yield a conclusion on their equivalence by using some algebraic operations on expressions of estimations. In this article, we give some results on equivalence of the well-known OLSEs and BLUEs under the explicitly and implicitly restricted linear models by using some expansion formulas for ranks of matrices.