A new reproducibility index is developed and studied. This index is the correlation between the two readings that fall on the 45 degree line through the origin. It is simple to use and possesses desirable properties. The statistical properties of this estimate can be satisfactorily evaluated using an inverse hyperbolic tangent transformation. A Monte Carlo experiment with 5,000 runs was performed to confirm the estimate's validity. An application using actual data is given.

A concordance correlation coefficient to evaluate reproducibility.

Asymptotic distribution theory is the primary method used to examine the properties of econometric estimators and tests We present conditions for obtaining cosistency and asymptotic normality of a very general class of estimators (extremum estimators) Consistent asymptotic variance estimators are given to enable approximation of the asymptotic distribution Asymptotic efficiency is another desirable property then considered Throughout the chapter, the general results are also specialized to common econometric estimators (eg MLE and GMM), and in specific examples we work through the conditions for the various results in detail The results are also extended to two-step estimators (with finite-dimensional parameter estimation in the first step), estimators derived from nonsmooth objective functions, and semiparametric two-step estimators (with nonparametric estimation of an infinite-dimensional parameter in the first step) Finally, the trinity of test statistics is considered within the quite general setting of GMM estimation, and numerous examples are given

Chapter 36 Large sample estimation and hypothesis testing

We extend the jackknife and the bootstrap method of estimating standard errors to the case where the observations form a general stationary sequence. We do not attempt a reduction to i.i.d. values. The jackknife calculates the sample variance of replicates of the statistic obtained by omitting each block of $l$ consecutive data once. In the case of the arithmetic mean this is shown to be equivalent to a weighted covariance estimate of the spectral density of the observations at zero. Under appropriate conditions consistency is obtained if $l = l(n) \rightarrow \infty$ and $l(n)/n \rightarrow 0$. General statistics are approximated by an arithmetic mean. In regular cases this approximation determines the asymptotic behavior. Bootstrap replicates are constructed by selecting blocks of length $l$ randomly with replacement among the blocks of observations. The procedures are illustrated by using the sunspot numbers and some simulated data.

https://projecteuclid.org/download/pdf_1/euclid.aos/1176347265

The Jackknife and the Bootstrap for General Stationary Observations

We propose two statistical tests to determine if two samples are from different distributions. Our test statistic is in both cases the distance between the means of the two samples mapped into a reproducing kernel Hilbert space (RKHS). The first test is based on a large deviation bound for the test statistic, while the second is based on the asymptotic distribution of this statistic. The test statistic can be computed in O(m2) time. We apply our approach to a variety of problems, including attribute matching for databases using the Hungarian marriage method, where our test performs strongly. We also demonstrate excellent performance when comparing distributions over graphs, for which no alternative tests currently exist.

/pdf/a-kernel-method-for-the-two-sample-problem-4qw54tjjow.pdf

A Kernel Method for the Two-Sample-Problem

Simple diagnostic tests for spatial dependence

Approximation Theorems of Mathematical Statistics

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Approximation Theorems of Mathematical Statistics