scholarly journals RELATIVE ERROR ACCURATE STATISTIC BASED ON NONPARAMETRIC LIKELIHOOD

2021 ◽  
pp. 1-24
Author(s):  
Lorenzo Camponovo ◽  
Yukitoshi Matsushita ◽  
Taisuke Otsu
Keyword(s):  
Relative Error ◽  
Generating Functions ◽  
Large Deviation ◽  
Moment Condition ◽  
Accurate Approximation ◽  
Test Statistic ◽  
Exponential Tilting ◽  
Moment Conditions ◽  
Nonparametric Likelihood ◽  
Relative Errors

This paper develops a new test statistic for parameters defined by moment conditions that exhibits desirable relative error properties for the approximation of tail area probabilities. Our statistic, called the tilted exponential tilting (TET) statistic, is constructed by estimating certain cumulant generating functions under exponential tilting weights. We show that the asymptotic p-value of the TET statistic can provide an accurate approximation to the p-value of an infeasible saddlepoint statistic, which admits a Lugannani–Rice style adjustment with relative errors of order n−1 both in normal and large deviation regions. Numerical results illustrate the accuracy of the proposed TET statistic. Our results cover both just- and overidentified moment condition models. A limitation of our analysis is that the theoretical approximation results are exclusively for the infeasible saddlepoint statistic, and closeness of the p-values for the infeasible statistic to the ones for the feasible TET statistic is only numerically assessed.

scholarly journals NONPARAMETRIC TESTS OF MOMENT CONDITION STABILITY

2012 ◽  
Vol 29 (1) ◽  
pp. 90-114 ◽  
Author(s):  
Ted Juhl ◽  
Zhijie Xiao
Keyword(s):  
Monte Carlo ◽  
Nonparametric Test ◽  
Nonparametric Tests ◽  
Moment Condition ◽  
Monte Carlo Experiment ◽  
Regularity Conditions ◽  
Test Statistic ◽  
Moment Conditions ◽  
The Moment ◽  
Over Time

This paper considers testing for moment condition instability for a wide variety of models that arise in econometric applications. We propose a nonparametric test based on smoothing the moment conditions over time. The resulting test takes the form of a U-statistic and has a limiting normal distribution. The proposed test statistic is not affected by changes in the distribution of the data, so long as certain simple regularity conditions hold. We examine the performance of the test through a small Monte Carlo experiment.

Application of pyrometer and standard sample to determine surface temperature of studied materials

2019 ◽  
pp. 9-13
Author(s):  
V.Ya. Mendeleyev ◽  
V.A. Petrov ◽  
A.V. Yashin ◽  
A.I. Vangonen ◽  
O.K. Taganov
Keyword(s):  
Composite Material ◽  
Surface Temperature ◽  
Relative Error ◽  
Wavelength Range ◽  
Standard Sample ◽  
A Priori ◽  
Temperature Changes ◽  
Surface Temperatures ◽  
Relative Errors ◽  
Normal Emissivity

Determining the surface temperature of materials with unknown emissivity is studied. A method for determining the surface temperature using a standard sample of average spectral normal emissivity in the wavelength range of 1,65–1,80 μm and an industrially produced Metis M322 pyrometer operating in the same wavelength range. The surface temperature of studied samples of the composite material and platinum was determined experimentally from the temperature of a standard sample located on the studied surfaces. The relative error in determining the surface temperature of the studied materials, introduced by the proposed method, was calculated taking into account the temperatures of the platinum and the composite material, determined from the temperature of the standard sample located on the studied surfaces, and from the temperature of the studied surfaces in the absence of the standard sample. The relative errors thus obtained did not exceed 1,7 % for the composite material and 0,5% for the platinum at surface temperatures of about 973 K. It was also found that: the inaccuracy of a priori data on the emissivity of the standard sample in the range (–0,01; 0,01) relative to the average emissivity increases the relative error in determining the temperature of the composite material by 0,68 %, and the installation of a standard sample on the studied materials leads to temperature changes on the periphery of the surface not exceeding 0,47 % for composite material and 0,05 % for platinum.

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.

scholarly journals Identification‐ and singularity‐robust inference for moment condition models

2019 ◽  
Vol 10 (4) ◽  
pp. 1703-1746 ◽  
Author(s):  
Donald W. K. Andrews ◽  
Patrik Guggenberger
Keyword(s):  
Moment Condition ◽  
Outer Product ◽  
Moment Conditions ◽  
Variance Matrix ◽  
Asymptotic Size ◽  
Moment Functions ◽  
Linear And Nonlinear ◽  
The Moment ◽  
Asymptotically Efficient ◽  
Iv Model

This paper introduces a new identification‐ and singularity‐robust conditional quasi‐likelihood ratio (SR‐CQLR) test and a new identification‐ and singularity‐robust Anderson and Rubin (1949) (SR‐AR) test for linear and nonlinear moment condition models. Both tests are very fast to compute. The paper shows that the tests have correct asymptotic size and are asymptotically similar (in a uniform sense) under very weak conditions. For example, in i.i.d. scenarios, all that is required is that the moment functions and their derivatives have 2 +  γ bounded moments for some γ > 0. No conditions are placed on the expected Jacobian of the moment functions, on the eigenvalues of the variance matrix of the moment functions, or on the eigenvalues of the expected outer product of the (vectorized) orthogonalized sample Jacobian of the moment functions. The SR‐CQLR test is shown to be asymptotically efficient in a GMM sense under strong and semi‐strong identification (for all k ≥  p, where k and p are the numbers of moment conditions and parameters, respectively). The SR‐CQLR test reduces asymptotically to Moreira's CLR test when p = 1 in the homoskedastic linear IV model. The same is true for p ≥ 2 in most, but not all, identification scenarios. We also introduce versions of the SR‐CQLR and SR‐AR tests for subvector hypotheses and show that they have correct asymptotic size under the assumption that the parameters not under test are strongly identified. The subvector SR‐CQLR test is shown to be asymptotically efficient in a GMM sense under strong and semi‐strong identification.

scholarly journals Limiting saddlepoint relative errors in large deviation regions under purely Tauberian conditions

Bernoulli ◽  
2019 ◽  
Vol 25 (4B) ◽  
pp. 3379-3399 ◽  
Author(s):  
Ronald W. Butler ◽  
Andrew T.A. Wood
Keyword(s):  
Large Deviation ◽  
Tauberian Conditions ◽  
Relative Errors

scholarly journals A robust method for shift detection in time series

Biometrika ◽  
2020 ◽  
Vol 107 (3) ◽  
pp. 647-660
Author(s):  
H Dehling ◽  
R Fried ◽  
M Wendler
Keyword(s):  
Time Series ◽  
Nonparametric Test ◽  
Test Statistic ◽  
Moment Conditions ◽  
Limit Theory ◽  
Dependent Observations ◽  
U Statistics ◽  
Shift Detection ◽  
Heavy Tailed ◽  
The Stability

Summary We present a robust and nonparametric test for the presence of a changepoint in a time series, based on the two-sample Hodges–Lehmann estimator. We develop new limit theory for a class of statistics based on two-sample U-quantile processes in the case of short-range dependent observations. Using this theory, we derive the asymptotic distribution of our test statistic under the null hypothesis of a constant level. The proposed test shows better overall performance under normal, heavy-tailed and skewed distributions than several other modifications of the popular cumulative sums test based on U-statistics, one-sample U-quantiles or M-estimation. The new theory does not involve moment conditions, so any transform of the observed process can be used to test the stability of higher-order characteristics such as variability, skewness and kurtosis.

Determination of Xanthates, Dithiocarbamates, and Some Fungicides by Titration with Electrogenerated Iodine in Anhydrous Acetonitrile

1983 ◽  
Vol 66 (3) ◽  
pp. 646-650
Author(s):  
Dale D Clyde
Keyword(s):  
Dimethyl Sulfoxide ◽  
Cross Section ◽  
Relative Error ◽  
Potassium Iodide ◽  
Anhydrous Acetonitrile ◽  
Platinum Electrodes ◽  
Cell Compartment ◽  
End Point ◽  
Relative Errors

Abstract Xanthates, dithiocarbamates, and the fungicides maneb and zineb were determined by titration with electrogenerated iodine in anhydrous acetonitrile. The electrolyte was potassium iodide. The generating electrode was a platinum spiral (2.5 cm diameter, 2 mm cross section). The enclosed cell compartment was continuously flushed with dry nitrogen, and sample solutions (0.20-0.40 mL) were introduced by syringe. With the aid of 2 platinum electrodes, the end point was indicated amperometrically. Ten minutes was required for each determination. The compounds were determined at ≥5 μequiv. with relative errors of 0.21-9%. Precision is 0.60-5.7%. Thiourea, sulfur, and urea did not interfere, but thioacetamide did. Solutions of maneb and zineb in dimethyl sulfoxide are stable enough that μequiv. amounts of each compound can be determined with a relative error of 7% or less.

scholarly journals The exact asymptotics of the large deviation probabilities in the multivariate boundary crossing problem

2019 ◽  
Vol 51 (03) ◽  
pp. 835-864 ◽  
Author(s):  
Yuqing Pan ◽  
Konstantin A. Borovkov
Keyword(s):  
Large Deviation ◽  
Risk Process ◽  
Boundary Crossing ◽  
Moment Condition ◽  
Two Dimensional ◽  
Exact Asymptotics ◽  
Negative Component ◽  
Positive Orthant ◽  
Mean Vector ◽  
Target Sets

AbstractFor a multivariate random walk with independent and identically distributed jumps satisfying the Cramér moment condition and having mean vector with at least one negative component, we derive the exact asymptotics of the probability of ever hitting the positive orthant that is being translated to infinity along a fixed vector with positive components. This problem is motivated by and extends results of Avram et al. (2008) on a two-dimensional risk process. Our approach combines the large deviation techniques from a series of papers by Borovkov and Mogulskii from around 2000 with new auxiliary constructions, enabling us to extend their results on hitting remote sets with smooth boundaries to the case of boundaries with a ‘corner’ at the ‘most probable hitting point’. We also discuss how our results can be extended to the case of more general target sets.

scholarly journals Large deviations in non-uniformly hyperbolic dynamical systems

2008 ◽  
Vol 28 (2) ◽  
pp. 587-612 ◽  
Author(s):  
LUC REY-BELLET ◽  
LAI-SANG YOUNG
Keyword(s):  
Dynamical Systems ◽  
Generating Functions ◽  
Limit Theorems ◽  
Large Deviation ◽  
Return Times ◽  
Hyperbolic Diffeomorphisms ◽  
Large Deviation Principles ◽  
Hyperbolic Dynamical Systems ◽  
Rank One ◽  
Dispersing Billiards

AbstractWe prove large deviation principles for ergodic averages of dynamical systems admitting Markov tower extensions with exponential return times. Our main technical result from which a number of limit theorems are derived is the analyticity of logarithmic moment generating functions. Among the classes of dynamical systems to which our results apply are piecewise hyperbolic diffeomorphisms, dispersing billiards including Lorentz gases, and strange attractors of rank one including Hénon-type attractors.

Economies of scale in queues with sources having power-law large deviation scalings

1996 ◽  
Vol 33 (3) ◽  
pp. 840-857 ◽  
Author(s):  
N. G. Duffield
Keyword(s):  
Power Law ◽  
Generating Functions ◽  
Economies Of Scale ◽  
Shape Function ◽  
Large Deviation ◽  
Rate Function ◽  
Uhlenbeck Process ◽  
Asymptotic Decay ◽  
Potential Structure ◽  
Asymptotic Decay Rate

We analyse the queue QL at a multiplexer with L sources which may display long-range dependence. This includes, for example, sources modelled by fractional Brownian motion (FBM). The workload processes W due to each source are assumed to have large deviation properties of the form P[Wt/a(t) > x] ≈ exp[– v(t)K(x)] for appropriate scaling functions a and v, and rate-function K. Under very general conditions limL→xL–1 log P[QL > Lb] = – I(b), provided the offered load is held constant, where the shape function I is expressed in terms of the cumulant generating functions of the input traffic. For power-law scalings v(t) = tv, a(t) = ta (such as occur in FBM) we analyse the asymptotics of the shape function limb→xb–u/a(I(b) – δbv/a) = vu for some exponent u and constant v depending on the sources. This demonstrates the economies of scale available though the multiplexing of a large number of such sources, by comparison with a simple approximation P[QL > Lb] ≈ exp[−δLbv/a] based on the asymptotic decay rate δ alone. We apply this formula to Gaussian processes, in particular FBM, both alone, and also perturbed by an Ornstein–Uhlenbeck process. This demonstrates a richer potential structure than occurs for sources with linear large deviation scalings.

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