scholarly journals Zipf's Law for cities: estimation of regression function parameters based on the weight of American urban areas and Polish towns

2021 ◽  
Vol 53 (53) ◽  
pp. 147-156
Author(s):  
Dariusz Sokołowski ◽  
Iwona Jażdżewska
Keyword(s):  
Linear Regression ◽  
Regression Model ◽  
Urban Areas ◽  
Empirical Distribution ◽  
Urban System ◽  
Regression Function ◽  
Estimation Methods ◽  
Weighted Regression ◽  
The Usa ◽  
Parameter Estimation Methods

Abstract The paper aims at presentation of a methodology where the classical linear regression model is modified to guarantee more realistic estimations and lower parameter oscillations for a specific urban system. That can be achieved by means of the weighted regression model which is based on weights ascribed to individual cities. The major shortcoming of the methods used so far – especially the classical simple linear regression – is the treatment of individual cities as points carrying the same weight, in consequence of which the linear regression poorly matches the empirical distribution of cities. The aim is reached in a several-stage process: demonstration of the drawbacks of the linear parameter estimation methods traditionally used for the purposes of urban system analyses; introduction of the weighted regression which to a large extent diminishes specific drawbacks; and empirical verification of the method with the use of the input data for the USA and Poland

scholarly journals A time series analysis of bulk tank somatic cell counts of dairy herds located in Brazil and the United States

2017 ◽  
Vol 47 (4) ◽  
Author(s):  
Liz Gonçalves Rodrigues ◽  
Maria Helena Cosendey de Aquino ◽  
Márcio Roberto Silva ◽  
Letícia Caldas Mendonça ◽  
Juliana França Monteiro de Mendonça ◽  
...  
Keyword(s):  
Time Series ◽  
Linear Regression ◽  
Regression Model ◽  
Linear Regression Model ◽  
Southeastern Brazil ◽  
Dairy Herds ◽  
Somatic Cell Counts ◽  
Cell Counts ◽  
The Usa ◽  
Bulk Tank

ABSTRACT: Bulk tank somatic cell counts (BTSCC) is widely used to monitore the mammary gland health at the herd and regional level. The BTSCC time series from specific regions or countries can be used to compare the mammary gland health and estimate the trend of subclinical mastitis at the regional level. Three time series of BTSCC from dairy herds located in the USA and the Southeastern Brazil were evaluated from 1995 to 2014. Descriptive statistics and a linear regression model were used to evaluate the data of the BTSCC time series. The mean of annual geometric mean of BTSCC (AGM) and the percentage of dairy herds with a BTSCC greater than 400,000 cells mL-1 (%>400) were significantly different (P<0.05) according to the countries and the times series. Linear regression model used for the USA time series was statistically significant for AGM and the %>400 (P<0.05). The first and second USA time series presented an increasing and decreasing trend for AGM and the %>400, respectively. The linear regression model for the Brazil time series was not significant (P>0.05) for both dependent variables (AGM and %>400). The Brazil time series showed no increasing or decreasing trend for the AGM and %>400. Consequently, approximately 40 to 50% of the dairy herds from southeastern Brazil will not achieve the regulatory limits for BTSCC over the next years.

Detecting a Change in School Performance: A Bayesian Analysis for a Multilevel Join Point Problem

2001 ◽  
Vol 26 (4) ◽  
pp. 443-468 ◽  
Author(s):  
Yeow Meng Thum ◽  
Suman K. Bhattacharya
Keyword(s):  
Linear Regression ◽  
Regression Model ◽  
Test Scores ◽  
Evaluation Studies ◽  
Regression Function ◽  
Hierarchical Bayes ◽  
Bayes Estimation ◽  
Point Problem ◽  
Two Phase ◽  
Multilevel Linear Regression

A substantial literature on switches in linear regression functions considers situations in which the regression function is discontinuous at an unknown value of the regressor, Xk , where k is the so-called unknown “change point.” The regression model is thus a two-phase composite of yi ∼ N(β01 + β11xi, σ12), i=1, 2,..., k and yi ∼ N(β02 + β12xi, σ22), i= k + 1, k + 2,..., n. Solutions to this single series problem are considerably more complex when we consider a wrinkle frequently encountered in evaluation studies of system interventions, in that a system typically comprises multiple members (j = 1, 2, . . . , m ) and that members of the system cannot all be expected to change synchronously. For example, schools differ not only in whether a program, implemented system-wide, improves their students’ test scores, but depending on the resources already in place, schools may also differ in when they start to show effects of the program. If ignored, heterogeneity among schools in when the program takes initial effect undermines any program evaluation that assumes that change points are known and that they are the same for all schools. To describe individual behavior within a system better, and using a sample of longitudinal test scores from a large urban school system, we consider hierarchical Bayes estimation of a multilevel linear regression model in which each individual regression slope of test score on time switches at some unknown point in time, kj. We further explore additional results employing models that accommodate case weights and shorter time series.

scholarly journals A Comparative Study of Some Estimation Methods in Simple Linear Regression Model for Different Sample Sizes in Presence of Outliers

2015 ◽  
Vol 3 (6) ◽  
pp. 380
Author(s):  
Soner Çankaya ◽  
Samet Hasan Abacı
Keyword(s):  
Linear Regression ◽  
Regression Model ◽  
Sample Size ◽  
Linear Regression Model ◽  
Estimation Methods ◽  
Simple Linear Regression ◽  
Sample Sizes ◽  
Simple Linear Regression Model ◽  
Body Weights ◽  
Chest Girth

The aim of this study was to compare some estimation methods (LS, M, S, LTS and MM) for estimating the parameters of simple linear regression model in the presence of outlier and different sample size (10, 20, 30, 50 and 100). To compare methods, the effect of chest girth on body weights of Karayaka lambs at weaning period was examined. Chest girth of lambs was used as independent variable and body weight at weaning period was used as dependent variable in the study. Also, it was taken consideration that there were 10-20% outliers of data set for different sample sizes. Mean square error (MSE) and coefficient of determination (R2) values were used as criteria to evaluate the estimator performance. Research findings showed that LTS estimator is the best models with minimum MSE and maximum R2 values for different size of sample in the presence of outliers. Thereby, LTS method can be proposed, to predict best-fitted model for relationship between chest girth and body weights of Karayaka lambs at weaning period, to the researches who are studying on small ruminants as an alternative way to estimate the regression parameters in the presence of outliers for different sample size.

scholarly journals Adaptively Unified Semi-supervised Learning for Cross-Modal Retrieval

2017 ◽  
Author(s):  
Liang Zhang ◽  
Bingpeng Ma ◽  
Jianfeng He ◽  
Guorong Li ◽  
Qingming Huang ◽  
...  
Keyword(s):  
Linear Regression ◽  
Regression Model ◽  
Semantic Information ◽  
State Of The Art ◽  
Unlabeled Data ◽  
Weighted Regression ◽  
Discriminant Ability ◽  
Novel Method ◽  
Class Labels ◽  
Relevant Class

Motivated by the fact that both relevancy of class labels and unlabeled data can help to strengthen multi-modal correlation, this paper proposes a novel method for cross-modal retrieval. To make each sample moving to the direction of its relevant label while far away from that of its irrelevant ones, a novel dragging technique is fused into a unified linear regression model. By this way, not only the relation between embedded features and relevant class labels but also the relation between embedded features and irrelevant class labels can be exploited. Moreover, considering that some unlabeled data contain specific semantic information, a weighted regression model is designed to adaptively enlarge their contribution while weaken that of the unlabeled data with non-specific semantic information. Hence, unlabeled data can supply semantic information to enhance discriminant ability of classifier. Finally, we integrate the constraints into a joint minimization formulation and develop an efficient optimization algorithm to learn a discriminative common subspace for different modalities. Experimental results on Wiki, Pascal and NUS-WIDE datasets show that the proposed method outperforms the state-of-the-art methods even when we set 20% samples without class labels.

scholarly journals A new regression model for bounded response variable: An alternative to the beta and unit-Lindley regression models

PLoS ONE ◽  
2021 ◽  
Vol 16 (1) ◽  
pp. e0245627
Author(s):  
Emrah Altun ◽  
M. El-Morshedy ◽  
M. S. Eliwa
Keyword(s):  
Parameter Estimation ◽  
Regression Model ◽  
Regression Models ◽  
Real Data ◽  
Quantile Function ◽  
Distribution Functions ◽  
Cumulative Distribution ◽  
Estimation Methods ◽  
Response Variable ◽  
Parameter Estimation Methods

A new distribution defined on (0,1) interval is introduced. Its probability density and cumulative distribution functions have simple forms. Thanks to its simple forms, the moments, incomplete moments and quantile function of the proposed distribution are derived and obtained in explicit forms. Four parameter estimation methods are used to estimate the unknown parameter of the distribution. Besides, simulation study is implemented to compare the efficiencies of these parameter estimation methods. More importantly, owing to the proposed distribution, we provide an alternative regression model for the bounded response variable. The proposed regression model is compared with the beta and unit-Lindley regression models based on two real data sets.

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