scholarly journals NONPARAMETRIC ESTIMATION OF SEMIPARAMETRIC TRANSFORMATION MODELS

2016 ◽  
Vol 33 (4) ◽  
pp. 839-873 ◽  
Author(s):  
Jean-Pierre Florens ◽  
Senay Sokullu
Keyword(s):  
Nonparametric Estimation ◽  
Asymptotic Properties ◽  
Transformation Models ◽  
Dimensional Parameter ◽  
Independence Assumption ◽  
Finite Dimensional ◽  
The Mean ◽  
Semiparametric Transformation ◽  
Image Position ◽  
Nonparametric Estimates

In this paper we develop a nonparametric estimation technique for semiparametric transformation models of the form:H(Y) =φ(Z) +X′β+UwhereH,φare unknown functions,βis an unknown finite-dimensional parameter vector and the variables (Y,Z) are endogenous. Identification of the model and asymptotic properties of the estimator are analyzed under the mean independence assumption between the error term and the instruments. We show that the estimators are consistent, and a$\sqrt N$-convergence rate and asymptotic normality for$\hat \beta$can be attained. The simulations demonstrate that our nonparametric estimates fit the data well.

Regression for randomly sampled spatial series: the trigonometric case

1986 ◽  
Vol 23 (A) ◽  
pp. 275-289 ◽  
Author(s):  
David R. Brillinger
Keyword(s):  
Maximum Likelihood ◽  
Asymptotic Normality ◽  
Point Process ◽  
Maximum Likelihood Estimates ◽  
Dimensional Parameter ◽  
Finite Dimensional ◽  
Spatial Series ◽  
Consistency And Asymptotic Normality ◽  
Image Position ◽  
Asymptotically Efficient

The model Y(t) = s(t | θ) + ε(t) is studied in the case that observations are made at scattered points τ j in a subset of Rp and θ is a finite-dimensional parameter. The particular cases of 0 = (α, β) and (α, β, ω) are considered in detail. Consistency and asymptotic normality results are developed assuming that the spatial series ε(·) and the point process {τ j} are independent, stationary and mixing. The estimates considered are equivalent to least squares asymptotically and are not generally asymptotically efficient.Contributions of the paper include: study of the Rp case, management of irregularly placed observations, allowance for abnormal domains of observation and the discovery that aliasing complications do not arise when the point process {τ j} is mixing. There is a brief discussion of the construction and properties of maximum likelihood estimates for the spatial-temporal case.

Regression for randomly sampled spatial series: the trigonometric case

1986 ◽  
Vol 23 (A) ◽  
pp. 275-289
Author(s):  
David R. Brillinger
Keyword(s):  
Maximum Likelihood ◽  
Asymptotic Normality ◽  
Point Process ◽  
Maximum Likelihood Estimates ◽  
Dimensional Parameter ◽  
Finite Dimensional ◽  
Spatial Series ◽  
Consistency And Asymptotic Normality ◽  
Image Position ◽  
Asymptotically Efficient

The model Y(t) = s(t | θ) + ε(t) is studied in the case that observations are made at scattered points τ j in a subset of Rp and θ is a finite-dimensional parameter. The particular cases of 0 = (α, β) and (α, β, ω) are considered in detail. Consistency and asymptotic normality results are developed assuming that the spatial series ε(·) and the point process {τ j } are independent, stationary and mixing. The estimates considered are equivalent to least squares asymptotically and are not generally asymptotically efficient. Contributions of the paper include: study of the Rp case, management of irregularly placed observations, allowance for abnormal domains of observation and the discovery that aliasing complications do not arise when the point process {τ j } is mixing. There is a brief discussion of the construction and properties of maximum likelihood estimates for the spatial-temporal case.

CONSISTENCY AND ASYMPTOTIC NORMALITY OF SIEVE ML ESTIMATORS UNDER LOW-LEVEL CONDITIONS

2014 ◽  
Vol 30 (5) ◽  
pp. 1021-1076 ◽  
Author(s):  
Herman J. Bierens
Keyword(s):  
Asymptotic Normality ◽  
Density Function ◽  
Choice Model ◽  
Likelihood Estimation ◽  
Dimensional Parameter ◽  
Infinite Dimensional ◽  
Low Level ◽  
Asymptotically Normal ◽  
Finite Dimensional ◽  
Image Position

This paper considers sieve maximum likelihood estimation of seminonparametric (SNP) models with an unknown density function as non-Euclidean parameter, next to a finite-dimensional parameter vector. The density function involved is modeled via an infinite series expansion, so that the actual parameter space is infinite-dimensional. It will be shown that under low-level conditions the sieve estimators of these parameters are consistent, and the estimators of the Euclidean parameters are$\sqrt N$asymptotically normal, given a random sample of sizeN. The latter result is derived in a different way than in the sieve estimation literature. It appears that this asymptotic normality result is in essence the same as for the finite dimensional case. This approach is motivated and illustrated by an SNP discrete choice model.

scholarly journals Improvement of the Nonparametric Estimation of Functional Stationary Time Series Using Yeo-Johnson Transformation with Application to Temperature Curves

2021 ◽  
Vol 2021 ◽  
pp. 1-6
Author(s):  
Sameera Abdulsalam Othman ◽  
Haithem Taha Mohammed Ali
Keyword(s):  
Time Series ◽  
Nonparametric Estimation ◽  
Cox Model ◽  
Original Data ◽  
Stationary Time Series ◽  
Transformation Models ◽  
Response Variable ◽  
Functional Time Series ◽  
The Mean ◽  
Johnson Model

In this article, Box-Cox and Yeo-Johnson transformation models are applied to two time series datasets of monthly temperature averages to improve the forecast ability. An application algorithm was proposed to transform the positive original responses using the first model and the stationary responses using the second model to improve the nonparametric estimation of the functional time series. The Box-Cox model contributed to improving the results of the nonparametric estimation of the original data, but the results become somewhat confusing after attempting to make the transformed response variable stationary in the mean, while the functional time series predictions were more accurate using the transformed stationary datasets using the Yeo-Johnson model.

A GENERAL CLASS OF NON-NESTED TEST STATISTICS FOR MODELS DEFINED THROUGH MOMENT RESTRICTIONS

2017 ◽  
Vol 34 (2) ◽  
pp. 477-507
Author(s):  
Paulo M.D.C. Parente
Keyword(s):  
Asymptotic Properties ◽  
Monte Carlo Study ◽  
Test Statistics ◽  
Dimensional Parameter ◽  
New Class ◽  
Asymptotic Size ◽  
Finite Dimensional ◽  
Compound Model ◽  
Economic Journal ◽  
Moment Restrictions

In this article, we introduce a new class of Cox’s non-nested test statistics for models defined through overidentifying moment restrictions that depend on a finite dimensional parameter vector. In addition to showing that the GEL test statistics proposed in Smith (1997, Economic Journal 107, 503–519) and Ramalho and Smith (2002, Journal of Econometrics 107, 99–125) are members of this class, we reveal that further members can be constructed using the artificial compound model approach, which was originally applied by Atkinson (1970, Journal of the Royal Statistical Society, Series B 32, 323–335) in the parametric setting. We investigate the asymptotic properties of the statistics and propose tests based on modified versions of these statistics that have correct asymptotic size in a uniform sense, a requirement not satisfied by existing Cox’s non-nested tests. A Monte Carlo study examines the performance of the proposed tests.

The wigner property for CL-spaces and finite-dimensional polyhedral banach spaces

2021 ◽  
pp. 1-17
Author(s):  
Dongni Tan ◽  
Xujian Huang
Keyword(s):  
Banach Space ◽  
Banach Spaces ◽  
Phase Function ◽  
Linear Isometry ◽  
Basic Properties ◽  
Finite Dimensional ◽  
Image Position

Abstract We say that a map $f$ from a Banach space $X$ to another Banach space $Y$ is a phase-isometry if the equality \[ \{\|f(x)+f(y)\|, \|f(x)-f(y)\|\}=\{\|x+y\|, \|x-y\|\} \] holds for all $x,\,y\in X$ . A Banach space $X$ is said to have the Wigner property if for any Banach space $Y$ and every surjective phase-isometry $f : X\rightarrow Y$ , there exists a phase function $\varepsilon : X \rightarrow \{-1,\,1\}$ such that $\varepsilon \cdot f$ is a linear isometry. We present some basic properties of phase-isometries between two real Banach spaces. These enable us to show that all finite-dimensional polyhedral Banach spaces and CL-spaces possess the Wigner property.

scholarly journals AVERAGING OF AN INCREASING NUMBER OF MOMENT CONDITION ESTIMATORS

2014 ◽  
Vol 32 (1) ◽  
pp. 30-70 ◽  
Author(s):  
Xiaohong Chen ◽  
David T. Jacho-Chávez ◽  
Oliver Linton
Keyword(s):  
Moment Condition ◽  
Moment Conditions ◽  
Parameter Heterogeneity ◽  
Class Of Estimators ◽  
Optimal Weighting ◽  
The Mean ◽  
The Moment ◽  
Image Position ◽  
Nonlinear Estimators ◽  
Available Information

We establish the consistency and asymptotic normality for a class of estimators that are linear combinations of a set of$\sqrt n$-consistent nonlinear estimators whose cardinality increases with sample size. The method can be compared with the usual approaches of combining the moment conditions (GMM) and combining the instruments (IV), and achieves similar objectives of aggregating the available information. One advantage of aggregating the estimators rather than the moment conditions is that it yields robustness to certain types of parameter heterogeneity in the sense that it delivers consistent estimates of the mean effect in that case. We discuss the question of optimal weighting of the estimators.

The focusing of radiation by a random surface when the source is at a finite distance

1960 ◽  
Vol 56 (1) ◽  
pp. 27-40 ◽  
Author(s):  
M. S. Longuet-Higgins
Keyword(s):  
Mean Curvature ◽  
Joint Distribution ◽  
Total Curvature ◽  
Statistical Distribution ◽  
Constant Parameter ◽  
Random Surface ◽  
Second Derivatives ◽  
Finite Distance ◽  
The Mean ◽  
Image Position

Imagine a nearly horizontal, statistically uniform, random surface ζ(x, y), Gaussian in the sense that the second derivatives , , have a normal joint distribution. The problem considered is the statistical distribution of the quantitywhere J and Ω denote the mean curvature and total curvature of the surface, respectively, and ν is a constant parameter.

Asymptotic properties of the overall sound pressure level of subsonic jet flows using isotropy as a paradigm

2010 ◽  
Vol 664 ◽  
pp. 510-539 ◽  
Author(s):  
M. Z. AFSAR
Keyword(s):  
Reynolds Stress ◽  
Sound Pressure Level ◽  
Small Angle ◽  
Sound Pressure ◽  
Asymptotic Properties ◽  
Jet Noise ◽  
Pressure Level ◽  
Mean Flow ◽  
The Mean ◽  
Jet Axis

Measurements of subsonic air jets show that the peak noise usually occurs when observations are made at small angles to the jet axis. In this paper, we develop further understanding of the mathematical properties of this peak noise by analysing the properties of the overall sound pressure level with an acoustic analogy using isotropy as a paradigm for the turbulence. The analogy is based upon the hyperbolic conservation form of the Euler equations derived by Goldstein (Intl J. Aeroacoust., vol. 1, 2002, p. 1). The mean flow and the turbulence properties are defined by a Reynolds-averaged Navier–Stokes calculation, and we use Green's function based upon a parallel mean flow approximation. Our analysis in this paper shows that the jet noise spectrum can, in fact, be thought of as being composed of two terms, one that is significant at large observation angles and a second term that is especially dominant at small observation angles to the jet axis. This second term can account for the experimentally observed peak jet noise (Lush, J. Fluid Mech., vol. 46, 1971, p. 477) and was first identified by Goldstein (J. Fluid Mech., vol. 70, 1975, p. 595). We discuss the low-frequency asymptotic properties of this second term in order to understand its directional behaviour; we show, for example, that the sound power of this term is proportional to the square of the mean velocity gradient. We also show that this small-angle shear term does not exist if the instantaneous Reynolds stress source strength in the momentum equation itself is assumed to be isotropic for any value of time (as was done previously by Morris & Farrasat, AIAA J., vol. 40, 2002, p. 356). However, it will be significant if the auto-covariance of the Reynolds stress source, when integrated over the vector separation, is taken to be isotropic in all of its tensor suffixes. Although the analysis shows that the sound pressure of this small-angle shear term is sensitive to the statistical properties of the turbulence, this work provides a foundation for a mathematical description of the two-source model of jet noise.

scholarly journals VI.—The Body-Temperature of Fishes and other Marine Animals.

1908 ◽  
Vol 28 ◽  
pp. 66-84 ◽  
Author(s):  
Sutherland Simpson
Keyword(s):  
Body Temperature ◽  
Temperature Difference ◽  
Great Majority ◽  
The Body ◽  
Shore Crab ◽  
First Year ◽  
Marine Animals ◽  
Mean Temperature ◽  
The Mean ◽  
Image Position

SUMMARYThe body-temperature of the following fishes, crustaceans, and echinoderms has been examined and compared with the temperature of the water in which they live:—Cod-fish (Gadus morrhua), ling (Molva vulgaris), torsk (Brosmius brosme), coal-fish or saithe (Gadus virens), haddock (Gadus œgelfinus), flounder (Pleuronectes flesus), smelt (Osmerus eperlanus), dog-fish (Scyllium catulus), shore crab (Carcinus mœnas), edible crab (Cancer pagurus), lobster (Homarus vulgaris), sea-urchin (Echinus esculentus), and starfish (Asterias rubens). The minimum, maximum, and mean temperature difference for each species are given in the following table:—The excess of temperature is most evident in the larger specimens. This is well shown in the case of the coal-fish, where in the adult it was 0°·7 C., and in the great majority (11 out of 12) of the young of the first year, 0°·0 C. The body-weight and the conditions under which the fish are captured probably form the most important factors in determining the temperature difference.In 14 codfish, where the rectal, blood, and muscle temperatures were recorded in the same individual, it was found to be highest in the muscle and lowest in the rectum, the mean temperature difference being 0°·46 C. for the muscle, 0°·41 C for the blood, and 0°·36 C. for the rectum.

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