Two Stage Estimation Procedure of Non-Linear Regression Functions for Spatially-Dependent Data

2020 ◽  
Author(s):  
Ryuei Nishii ◽  
Shojiro Tanaka
Keyword(s):  
Linear Regression ◽  
Estimation Procedure ◽  
Dependent Data ◽  
Two Stage ◽  
Regression Functions ◽  
Non Linear ◽  
Stage Estimation

scholarly journals A two-stage estimation procedure for non-linear structural equation models

Biostatistics ◽  
2019 ◽  
Vol 21 (4) ◽  
pp. 676-691
Author(s):  
Klaus Kähler Holst ◽  
Esben Budtz-Jørgensen
Keyword(s):  
Linear Model ◽  
Latent Variables ◽  
Structural Equation ◽  
Structural Equation Models ◽  
Outcome Variable ◽  
Two Stage ◽  
Ml Estimation ◽  
Linear Effect ◽  
Non Linear ◽  
Stage Estimation

Summary Applications of structural equation models (SEMs) are often restricted to linear associations between variables. Maximum likelihood (ML) estimation in non-linear models may be complex and require numerical integration. Furthermore, ML inference is sensitive to distributional assumptions. In this article, we introduce a simple two-stage estimation technique for estimation of non-linear associations between latent variables. Here both steps are based on fitting linear SEMs: first a linear model is fitted to data on the latent predictor and terms describing the non-linear effect are predicted by their conditional means. In the second step, the predictions are included in a linear model for the latent outcome variable. We show that this procedure is consistent and identifies its asymptotic distribution. We also illustrate how this framework easily allows the association between latent variables to be modeled using restricted cubic splines, and we develop a modified estimator which is robust to non-normality of the latent predictor. In a simulation study, we compare the proposed method to MLE and alternative two-stage estimation techniques.

scholarly journals Validation of spectral sky radiance derived from all-sky camera images – a case study

2014 ◽  
Vol 7 (1) ◽  
pp. 69-97
Author(s):  
K. Tohsing ◽  
M. Schrempf ◽  
S. Riechelmann ◽  
G. Seckmeyer
Keyword(s):  
Linear Regression ◽  
Eye Lens ◽  
Charge Coupled Device ◽  
Regression Functions ◽  
Non Linear ◽  
Sky Radiance ◽  
Sky Imager ◽  
Sky Conditions ◽  
Fish Eye

Abstract. Spectral sky radiance (380–760 nm) is derived from measurements with a Hemispherical Sky Imager (HSI) system. The HSI consists of a commercial compact CCD (charge coupled device) camera equipped with a fish-eye lens and provides hemispherical sky images in three reference bands such as red, green and blue. To obtain the spectral sky radiance from these images non-linear regression functions for various sky conditions have been derived. The camera-based spectral sky radiance was validated by spectral sky radiance measured with a CCD spectroradiometer. The spectral sky radiance for complete distribution over the hemisphere between both instruments deviates by less than 20% at 500 nm for all sky conditions and for zenith angles less than 80°. The reconstructed spectra of the wavelength 380 nm to 760 nm between both instruments at various directions deviate by less then 20% for all sky conditions.

Bounded Risk Two-stage Estimation Procedure for a U(aq, bq) Distribution

2020 ◽  
pp. 000806832096334
Author(s):  
V. N. Kadam ◽  
H.S. Patil
Keyword(s):  
Stopping Time ◽  
Estimation Procedure ◽  
Sampling Procedure ◽  
Two Stage ◽  
Assigned Value ◽  
Q Model ◽  
Bounded Risk ◽  
Stage Estimation ◽  
Assigned Number ◽  
Uniformly Bounded

In the literature, an extensive work on sequential fixed-width confidence interval for the parameter of U( q, m q) model, where m > 1 is known, is available. In this article, we propose a two-stage sampling procedure for estimating the parameter q of U( aq, bq) distribution, where a < b are positive and known. Here, the risk of an estimator [Formula: see text] of q is less than a pre-assigned number w (>0), that is, [Formula: see text], 0 < A < ∞ is known. We determine the parameter Bk of stopping variable so that the risk is uniformly bounded by a pre-assigned value w. We have also tabulated the values of the expected stopping time and its standard deviation (SD).

scholarly journals Simar and Wilson two-stage efficiency analysis for Stata

2019 ◽  
Vol 19 (4) ◽  
pp. 950-988 ◽  
Author(s):  
Oleg Badunenko ◽  
Harald Tauchmann
Keyword(s):  
Production Efficiency ◽  
Estimation Procedure ◽  
Data Envelopment ◽  
Two Stage ◽  
Global Competitiveness ◽  
Explanatory Variables ◽  
World Economic ◽  
Original Procedure ◽  
Stage Estimation

When one analyzes the determinants of production efficiency, regressing efficiency scores estimated by data envelopment analysis on explanatory variables has much intuitive appeal. Simar and Wilson (2007, Journal of Econometrics 136: 31–64) show that this conventional two-stage estimation procedure suffers from severe flaws that render its results, and particularly statistical inference based on them, questionable. They additionally propose a statistically grounded bootstrap-based two-stage estimator that eliminates the above-mentioned weaknesses of its conventional predecessors and comes in two variants. In this article, we introduce the new command simarwilson, which implements either variant of the suggested estimator in Stata. The command allows for various options and extends the original procedure in some respects. For instance, it allows for analyzing both outputand input-oriented efficiency. To demonstrate the capabilities of simarwilson, we use data from the Penn World Tables and the Global Competitiveness Report by the World Economic Forum to perform a cross-country empirical study about the importance of quality of governance in a country for its efficiency of output production.

Modeling out-Migration from Depressed Regions: The Significance of Origin and Destination Characteristics

1980 ◽  
Vol 12 (7) ◽  
pp. 799-812 ◽  
Author(s):  
G L Clark ◽  
K P Ballard
Keyword(s):  
Estimation Procedure ◽  
The United States ◽  
Migration Decision ◽  
Two Stage ◽  
Cross Sectional ◽  
Capital Theory ◽  
Testing Procedures ◽  
Stage Estimation ◽  
Theory Use ◽  
Depressed Regions

Many migration models, whether derived from the Hicksian macroadjustment approach or from human capital theory, use simultaneously origin and destination variables in their empirical testing procedures. In this paper it is hypothesized that the actual out-migration decision process has two separate but interrelated stages—the decision to leave and the decision as to the destination. A two-stage estimation procedure is used to analyze the significance of origin characteristics as determinants of out-migration, and the factors that allocate migrants to particular destinations. The model is applied to understanding the patterns and determinants of out-migration from a depressed region, the Central Appalachians of the United States of America. Time-series and cross-sectional models are utilized to evaluate the hypothesized two-stage process over the period 1958–1975.

Speeding up estimation of the Hurst exponent by a two-stage procedure from a large to small range

2017 ◽  
Vol 34 (1) ◽  
pp. 3-17 ◽  
Author(s):  
Yen-Ching Chang
Keyword(s):  
Discrete Time ◽  
Hurst Exponent ◽  
Estimation Procedure ◽  
Computational Time ◽  
Small Range ◽  
Two Stage ◽  
Content Type ◽  
Computational Performance ◽  
The Difference ◽  
Stage Estimation

Purpose The Hurst exponent has been very important in telling the difference between fractal signals and explaining their significance. For estimators of the Hurst exponent, accuracy and efficiency are two inevitable considerations. The main purpose of this study is to raise the execution efficiency of the existing estimators, especially the fast maximum likelihood estimator (MLE), which has optimal accuracy. Design/methodology/approach A two-stage procedure combining a quicker method and a more accurate one to estimate the Hurst exponent from a large to small range will be developed. For the best possible accuracy, the data-induction method is currently ideal for the first-stage estimator and the fast MLE is the best candidate for the second-stage estimator. Findings For signals modeled as discrete-time fractional Gaussian noise, the proposed two-stage estimator can save up to 41.18 per cent the computational time of the fast MLE while remaining almost as accurate as the fast MLE, and even for signals modeled as discrete-time fractional Brownian motion, it can also save about 35.29 per cent except for smaller data sizes. Originality/value The proposed two-stage estimation procedure is a novel idea. It can be expected that other fields of parameter estimation can apply the concept of the two-stage estimation procedure to raise computational performance while remaining almost as accurate as the more accurate of two estimators.

Pairwise estimation of multivariate longitudinal outcomes in a Bayesian setting with extensions to the joint model

2020 ◽  
pp. 1471082X2094506
Author(s):  
Katya Mauff ◽  
Nicole S. Erler ◽  
Isabella Kardys ◽  
Dimitris Rizopoulos
Keyword(s):  
Importance Sampling ◽  
Estimation Procedure ◽  
Joint Model ◽  
Limited Information ◽  
Time To Event ◽  
Two Stage ◽  
Bivariate Model ◽  
Longitudinal Outcomes ◽  
Credible Intervals ◽  
Stage Estimation

Multiple longitudinal outcomes are theoretically easily modelled via extension of the generalized linear mixed effects model. However, due to computational limitations in high dimensions, in practice these models are applied only in situations with relatively few outcomes. We adapt the solution proposed by Fieuws and Verbeke (2006) to the Bayesian setting: fitting all pairwise bivariate models instead of a single multivariate model, and combining the Markov Chain Monte Carlo (MCMC) realizations obtained for each pairwise bivariate model for the relevant parameters. We explore importance sampling as a method to more closely approximate the correct multivariate posterior distribution. Simulation studies show satisfactory results in terms of bias, RMSE and coverage of the 95% credible intervals for multiple longitudinal outcomes, even in scenarios with more limited information and non-continuous outcomes, although the use of importance sampling is not successful. We further examine the incorporation of a time-to-event outcome, proposing the use of Bayesian pairwise estimation of a multivariate GLMM in an adaptation of the corrected two-stage estimation procedure for the joint model for multiple longitudinal outcomes and a time-to-event outcome ( Mauff et al., 2020 , Statistics and Computing). The method does not work as well in the case of the corrected two-stage joint model; however, the results are promising and should be explored further.

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