IDENTIFICATION OF LINEAR REGRESSIONS WITH ERRORS IN ALL VARIABLES

Derivatives Of ◽

Linear Regressions

This paper analyzes the classical linear regression model with measurement errors in all the variables. First, we provide necessary and sufficient conditions for identification of the coefficients. We show that the coefficients are not identified if and only if an independent normally distributed linear combination of regressors can be transferred from the regressors to the errors. Second, we introduce a new estimator for the coefficients using a continuum of moments that are based on second derivatives of the log characteristic function of the observables. In Monte Carlo simulations, the estimator performs well and is robust to the amount of measurement error and number of mismeasured regressors. In an application to firm investment decisions, the estimates are similar to those produced by a generalized method of moments estimator based on third to fifth moments.

VARIATION PROBLEM CONTAINING SECOND DERIVATIVES OF UNKNOWN FUNCTIONS

Chronos: natural and technical sciences ◽

10.52013/2712-9691-34-1-6 ◽

2021 ◽

Vol 6 (1(34)) ◽

pp. 30-42

Author(s):

Misraddin Allahverdi oglu Sadigov

Keyword(s):

Variational Problem ◽

Sufficient Conditions ◽

Continuous Functions ◽

Necessary Condition ◽

Absolutely Continuous Functions ◽

Absolutely Continuous ◽

Variation Problem ◽

Second Derivatives ◽

The property subdifferential of an integral and terminal functional in a space of the type of absolutely continuous functions is studied. Necessary and sufficient conditions for an extremum for a variational problem containing the second derivatives of unknown functions are obtained. With the help of the subdifferential introduced by the author, a nonconvex generalized variational problem containing the second derivatives of unknown functions is considered, and the necessary condition for an extremum is obtained.

REDUNDANCY OF MOMENT CONDITIONS AND THE EFFICIENCY OF OLS IN SUR MODELS

Econometric Theory ◽

10.1017/s0266466608080687 ◽

2008 ◽

Vol 24 (5) ◽

pp. 1456-1460 ◽

Cited By ~ 1

Author(s):

Hailong Qian

Keyword(s):

Least Squares ◽

Asymptotic Efficiency ◽

Generalized Method Of Moments ◽

Sufficient Conditions ◽

Generalized Least Squares ◽

Ordinary Least Squares ◽

American Statistical Association ◽

Orthogonality Condition ◽

Moment Conditions ◽

Necessary And Sufficient

In this note, based on the generalized method of moments (GMM) interpretation of the usual ordinary least squares (OLS) and feasible generalized least squares (FGLS) estimators of seemingly unrelated regressions (SUR) models, we show that the OLS estimator is asymptotically as efficient as the FGLS estimator if and only if the cross-equation orthogonality condition is redundant given the within-equation orthogonality condition. Using the condition for redundancy of moment conditions of Breusch, Qian, Schmidt, and Wyhowski (1999, Journal of Econometrics 99, 89–111), we then derive the necessary and sufficient condition for the equal asymptotic efficiency of the OLS and FGLS estimators of SUR models. We also provide several useful sufficient conditions for the equal asymptotic efficiency of OLS and FGLS estimators that can be interpreted as various mixings of the two famous sufficient conditions of Zellner (1962, Journal of the American Statistical Association 57, 348–368).

Automatic choice of parameters at approximation of functions by rational splines

Researches in Mathematics ◽

10.15421/248709 ◽

1987 ◽

pp. 52

Author(s):

A.D. Malysheva

Keyword(s):

Sufficient Conditions ◽

Order Of Approximation ◽

Approximation Of Functions ◽

Smooth Functions ◽

Higher Derivatives ◽

Automatic Choice ◽

Derivatives Of ◽

Best Parameters ◽

Approximation Of A Function

We obtain necessary and sufficient conditions put on the parameters of rational splines that provide given order of approximation of smooth functions. We point out the formulas of asymptotically the best parameters of rational splines that, while providing the best order of approximation of a function by rational splines, do not contain information about the values of higher derivatives of a function.

Monotonicity and complete monotonicity of two functions constituted via three derivatives of a function involving trigamma function

10.31219/osf.io/whb2q ◽

2020 ◽

Author(s):

Feng Qi

Keyword(s):

Sufficient Conditions ◽

Laplace Transforms ◽

Complete Monotonicity ◽

Convolution Theorem ◽

Monotonic Functions ◽

Completely Monotonic ◽

Completely Monotonic Functions ◽

In the paper, by convolution theorem of the Laplace transforms, a monotonicity rule for the ratio of two Laplace transforms, Bernstein's theorem for completely monotonic functions, and other analytic techniques, the author (1) presents the decreasing monotonicity of a ratio constituted via three derivatives of a function involving trigamma function; (2) discovers necessary and sufficient conditions for a function constituted via three derivatives of a function involving trigamma function to be completely monotonic. These results conform previous guesses posed by the author.

Lagrangian for Circuits with Higher-Order Elements

Entropy ◽

10.3390/e21111059 ◽

2019 ◽

Vol 21 (11) ◽

pp. 1059 ◽

Cited By ~ 2

Author(s):

Zdenek Biolek ◽

Dalibor Biolek ◽

Viera Biolkova

Keyword(s):

Variational Principle ◽

Equations Of Motion ◽

Sufficient Conditions ◽

Higher Order ◽

The State ◽

Even Order ◽

Independent Variable ◽

Derivatives Of ◽

State Functions

The necessary and sufficient conditions of the validity of Hamilton’s variational principle for circuits consisting of (α,β) elements from Chua’s periodical table are derived. It is shown that the principle holds if and only if all the circuit elements lie on the so-called Σ-diagonal with a constant sum of the indices α and β. In this case, the Lagrangian is the sum of the state functions of the elements of the L or +R types minus the sum of the state functions of the elements of the C or −R types. The equations of motion generated by this Lagrangian are always of even-order. If all the elements are linear, the equations of motion contain only even-order derivatives of the independent variable. Conclusions are illustrated on an example of the synthesis of the Pais–Uhlenbeck oscillator via the elements from Chua’s table.

Higher-order conditions for strict local Pareto minima for problems with partial order introduced by a polyhedral cone

Journal of Applied Analysis ◽

10.1515/jaa-2018-0005 ◽

2018 ◽

Vol 24 (1) ◽

pp. 45-54

Author(s):

Aleksandra Stasiak

Keyword(s):

Partial Order ◽

Optimization Problems ◽

Sufficient Conditions ◽

Polyhedral Cone ◽

Directional Derivatives ◽

Pareto Minima ◽

Vector Valued Functions ◽

Vector Valued ◽

Abstract Using the definitions of μ-th order lower and upper directional derivatives of vector-valued functions, introduced in Rahmo and Studniarski (J. Math. Anal. Appl. 393 (2012), 212–221), we provide some necessary and sufficient conditions for strict local Pareto minimizers of order μ for optimization problems where the partial order is introduced by a pointed polyhedral cone with non-empty interior.

Necessary and sufficient conditions for two functions defined by two derivatives of a function involving trigamma function to be completely monotonic or monotonic

10.31219/osf.io/6ar4p ◽

2020 ◽

Author(s):

Feng Qi

Keyword(s):

Exponential Function ◽

Sufficient Conditions ◽

Laplace Transforms ◽

Convolution Theorem ◽

Completely Monotonic ◽

In the paper, by convolution theorem for the Laplace transforms, some properties of a function involving exponential function, and other analytic techniques, the author finds necessary and sufficient conditions for two functions defined by two derivatives of a function involving trigamma function to be completely monotonic or monotonic.

Complete monotonicity of a difference constituted by four derivatives of a function involving trigamma function

10.20944/preprints202011.0343.v1 ◽

2020 ◽

Author(s):

Feng Qi

Keyword(s):

Sufficient Conditions ◽

Laplace Transforms ◽

Complete Monotonicity ◽

Convolution Theorem ◽

Monotonic Functions ◽

Completely Monotonic ◽

Completely Monotonic Functions ◽

In the paper, by virtue of convolution theorem for the Laplace transforms, Bernstein's theorem for completely monotonic functions, and other techniques, the author finds necessary and sufficient conditions for a difference constituted by four derivatives of a function involving trigamma function to be completely monotonic.

Necessary and sufficient conditions for complete monotonicity and monotonicity of two functions defined by two derivatives of a function involving trigamma function

Applicable Analysis and Discrete Mathematics ◽

10.2298/aadm191111014q ◽

2021 ◽

pp. 14-14

Author(s):

Feng Qi

Keyword(s):

Exponential Function ◽

Sufficient Conditions ◽

Laplace Transforms ◽

Complete Monotonicity ◽

Monotonic Functions ◽

Completely Monotonic ◽

Completely Monotonic Functions ◽

In the paper, by virtue of convolution theorem for the Laplace transforms, Bernstein's theorem for completely monotonic functions, some properties of a function involving exponential function, and other analytic techniques, the author finds necessary and sufficient conditions for two functions defined by two derivatives of a function involving trigamma function to be completely monotonic or monotonic. These results generalize corresponding known ones.

Behavioral-related firm characteristics, risks and determinants of stock returns

Review of Accounting and Finance ◽

10.1108/raf-03-2017-0060 ◽

2019 ◽

Vol 18 (1) ◽

pp. 95-112

Author(s):

Wikrom Prombutr ◽

Chanwit Phengpis

Keyword(s):

Stock Returns ◽

Behavioral Finance ◽

Measurement Errors ◽

Sufficient Conditions ◽

Portfolio Analysis ◽

Firm Characteristics ◽

Content Type ◽

Stock Portfolio ◽

Investment Growth

PurposeThis paper aims to investigate a relatively new anomaly of investment growth and revisits well-known anomalies of size and value. It aims to answer two main research questions. First, can covariance risks (i.e. factor loadings) be excluded from being determining variables that drive return premiums and explain stock returns? Second, from a behavioral finance standpoint, the authors examine whether using firm characteristics is a more practical and accessible approach and also meets the necessary and sufficient conditions to analyze stock returns.Design/methodology/approachThe authors create the investment-growth-based factor (LMH) which is defined as the return difference between low and high investment growth portfolios. The authors then incorporate the LMH factor along with other characteristic-based factors and their loadings into characteristic-balanced portfolio and three-factor model tests.FindingsThe authors find that covariance risks on investment growth, size and value are not necessary as determining variables. Instead, they find that behavioral-related firm characteristics of investment growth, size and value are necessary and sufficient as determinants of return premiums and stock returns.Practical implicationsThe results have practical and useful implications for investors in their stock portfolio analysis and selection because firm characteristics are relatively more available than covariance risks that need estimation and typically contain measurement errors.Originality/valueThe paper has practical value to investors in their stock portfolio analysis and selection. Methodologically, in contrast to prior studies that do not directly use the investment growth to control for portfolio characteristics, the use of the newly created LMH factor and its loadings allows us to directly and properly test if the investment growth anomaly is related to the investment growth characteristic that is hypothesized to drive return premiums and determine stock returns from behavioral finance perspectives.