Some asymptotic results of a non‐parametric conditional mode estimator for functional time‐series data

We consider the estimation of the conditional mode function when the covariates take values in some abstract function space. The main goal of this paper was to establish the almost complete convergence and the asymptotic normality of the kernel estimator of the conditional mode when the process is assumed to be strongly mixing and under the concentration property over the functional regressors. Some applications are given. This approach can be applied in time‐series analysis to the prediction and confidence band building. We illustrate our methodology by using El Nio data.     

A J–function for inhomogeneous point processes

We propose new summary statistics for intensity‐reweighted moment stationary point processes, that is, point processes with translation invariant n‐point correlation functions for all , that generalise the well known J‐, empty space, and spherical Palm contact distribution functions. We represent these statistics in terms of generating functionals and relate the inhomogeneous J‐function to the inhomogeneous reduced second moment function. Extensions to space time and marked point processes are briefly discussed.     

Partially varying coefficient instrumental variables models

In this article, we study a new class of semiparametric instrumental variables models, in which the structural function has a partially varying coefficient functional form. Under this specification, the model is linear in the endogenous/exogenous components with unknown constant or functional coefficients. As a result, the ill‐posed inverse problem in a general non‐parametric model with continuous endogenous variables can be avoided. We propose a three‐step estimation procedure for estimating both constant and functional coefficients and establish their asymptotic properties such as consistency and asymptotic normality. We develop consistent estimators for their error variances. We demonstrate that the constant coefficient estimators achieve the optimal ‐convergence rate, and the functional coefficient estimators are oracle. In addition, efficiency issue of the parameter estimation is discussed and a simple efficient estimator is proposed. The proposed procedure is illustrated via a Monte Carlo simulation and an application to returns to education.     

Gumbel’s Identity,Binomial Moments,and Bonferroni Sums

Gumbel’s Identity equates the Bonferroni sum with the k ‐ th binomial moment of the number of events M_n which occur, out of n arbitrary events. We provide a unified treatment of familiar probability bounds on a union of events by Bonferroni, Galambos–Rényi, Dawson–Sankoff, and Chung–Erdös, as well as less familiar bounds by Fréchet and Gumbel, all of which are expressed in terms of Bonferroni sums, by showing that all these arise as bounds in a more general setting in terms of binomial moments of a general non‐negative integer‐valued random variable. Use of Gumbel’s Identity then gives the inequalities in familiar Bonferroni sum form. This approach simplifies existing proofs. It also allows generalization of the results of Fréchet and Gumbel to give bounds on the probability that at least t of n events occur for any A further consequence of the approach is an improvement of a recent bound of Petrov which itself generalizes the Chung–Erdös bound.     

A Note on the Regularized Approach to Biased 2SLS Estimation with Weak Instruments

The presence of weak instruments is translated into a nearly singular problem in a control function representation. Therefore, the ‐norm type of regularization is proposed to implement the 2SLS estimation for addressing the weak instrument problem. The ‐norm regularization with a regularized parameter O(n) allows us to obtain the Rothenberg (1984) type of higher‐order approximation of the 2SLS estimator in the weak instrument asymptotic framework. The proposed regularized parameter yields the regularized concentration parameter O(n), which is used as a standardized factor in the higher‐order approximation. We also show that the proposed ‐norm regularization consequently reduces the finite sample bias. A number of existing estimators that address finite sample bias in the presence of weak instruments, especially Fuller's limited information maximum likelihood estimator, are compared with our proposed estimator in a simple Monte Carlo exercise.     

Testing for Exogeneity in Cointegrated Panels

This paper proposes a test for the null that, in a cointegrated panel, the long‐run correlation between the regressors and the error term is different from zero. As is well known, in such case the OLS estimator is T‐consistent, whereas it is ‐consistent when there is no endogeneity. Other estimators can be employed, such as the FM‐OLS, that are ‐consistent irrespective of whether exogeneity is present or not. Using the difference between the former and the latter estimator, we construct a test statistic which diverges at a rate under the null of endogeneity, whilst it is bounded under the alternative of exogeneity, and employ a randomization approach to carry out the test. Monte Carlo evidence shows that the test has the correct size and good power.     

Stable Asymptotics for M‐estimators

We review some first‐order and higher‐order asymptotic techniques for M‐estimators, and we study their stability in the presence of data contaminations. We show that the estimating function (ψ) and its derivative with respect to the parameter play a central role. We discuss in detail the first‐order Gaussian density approximation, saddlepoint density approximation, saddlepoint test, tail area approximation via the Lugannani–Rice formula and empirical saddlepoint density approximation (a technique related to the empirical likelihood method). For all these asymptotics, we show that a bounded ψ (in the Euclidean norm) and a bounded (e.g. in the Frobenius norm) yield stable inference in the presence of data contamination. We motivate and illustrate our findings by theoretical and numerical examples about the benchmark case of one‐dimensional location model.     

Unification of some multivariate process capability indices for asymmetric specification region

In manufacturing industries, it is often seen that the bilateral specification limits corresponding to a particular quality characteristic are not symmetric with respect to the stipulated target. A unified superstructure of univariate process capability indices was specially designed for processes with asymmetric specification limits. However, as in most of the practical situations a process consists of a number of inter‐related quality characteristics, subsequently, a multivariate analogue of , which is called C_M(u,v), was developed. In the present paper, we study some properties of C_M(u,v) like threshold value and compatibility with the asymmetry in loss function. We also discuss estimation procedures for plug‐in estimators of some of the member indices of C_M(u,v). Finally, the superstructure is applied to a numerical example to supplement the theory developed in this article.     

Connecting Distributions with Power Tails on the Real Line, the Half Line and the Interval

Univariate continuous distributions have three possible types of support exemplified by: the whole real line , , the semi‐finite interval and the bounded interval (0,1). This paper is about connecting distributions on these supports via ‘natural’ simple transformations in such a way that tail properties are preserved. In particular, this work is focussed on the case where the tails (at ±∞) of densities are heavy, decreasing as a (negative) power of their argument; connections are then especially elegant. At boundaries (0 and 1), densities behave conformably with a directly related dependence on power of argument. The transformation from (0,1) to is the standard odds transformation. The transformation from to is a novel identity‐minus‐reciprocal transformation. The main points of contact with existing distributions are with the transformations involved in the Birnbaum–Saunders distribution and, especially, the Johnson family of distributions. Relationships between various other existing and newly proposed distributions are explored.     

Exponent of Cross‐Sectional Dependence: Estimation and Inference

This paper provides a characterisation of the degree of cross‐sectional dependence in a two dimensional array, {x_it,i = 1,2,...N;t = 1,2,...,T} in terms of the rate at which the variance of the cross‐sectional average of the observed data varies with N. Under certain conditions this is equivalent to the rate at which the largest eigenvalue of the covariance matrix of x _t=(x_1t,x_2t,...,x_Nt)′ rises with N. We represent the degree of cross‐sectional dependence by α, which we refer to as the ‘exponent of cross‐sectional dependence’, and define it by the standard deviation, , where is a simple cross‐sectional average of x_it. We propose bias corrected estimators, derive their asymptotic properties for α > 1/2 and consider a number of extensions. We include a detailed Monte Carlo simulation study supporting the theoretical results. We also provide a number of empirical applications investigating the degree of inter‐linkages of real and financial variables in the global economy. Copyright © 2015 John Wiley & Sons, Ltd.     

On Families of Distributions with Shape Parameters

Univariate continuous distributions are one of the fundamental components on which statistical modelling, ancient and modern, frequentist and Bayesian, multi‐dimensional and complex, is based. In this article, I review and compare some of the main general techniques for providing families of typically unimodal distributions on with one or two, or possibly even three, shape parameters, controlling skewness and/or tailweight, in addition to their all‐important location and scale parameters. One important and useful family is comprised of the ‘skew‐symmetric’ distributions brought to prominence by Azzalini. As these are covered in considerable detail elsewhere in the literature, I focus more on their complements and competitors. Principal among these are distributions formed by transforming random variables, by what I call ‘transformation of scale’—including two‐piece distributions—and by probability integral transformation of non‐uniform random variables. I also treat briefly the issues of multi‐variate extension, of distributions on subsets of and of distributions on the circle. The review and comparison is not comprehensive, necessarily being selective and therefore somewhat personal. © 2014 The Authors. International Statistical Review © 2014 International Statistical Institute     

Estimation of nonlinear models with mismeasured regressors using marginal information

We consider the estimation of nonlinear models with mismeasured explanatory variables, when information on the marginal distribution of the true values of these variables is available. We derive a semi‐parametric MLE that is shown to be $\sqrt{n}$ consistent and asymptotically normally distributed. In a simulation experiment we find that the finite sample distribution of the estimator is close to the asymptotic approximation. The semi‐parametric MLE is applied to a duration model for AFDC welfare spells with misreported welfare benefits. The marginal distribution of the correctly measured welfare benefits is obtained from an administrative source. Copyright © 2010 John Wiley & Sons, Ltd.     

Afschatting van verdelingen van kwadratische vormen met toepassingen op aanpassingstoetsen voor normaliteit en exponentialiteit

Summary In this paper a simple approximation is given for the distribution of the quadratic form being a weighted sum of squares of independent, identically distributed standardized normal variates. Using the formulae, the Monte Carlo results concerning some goodness of fit tests for normality and exponentiality are verified and extended.     

Een indelingsprobleem

Summary A branch and bound algorithm is given to solve the following problem: To each pair of elements (i,j) from a set X={l,…, n} a number r_ij with r_ij≥ 0, r_ij=r_ij and r_ij= 0 has been assigned. Find a prescribed number of disjoint subsets P₁…,P_m from X, such that Experiments indicate that an optimal solution is usually found in a small number of iterations, but the verification may be rather time consuming. The algorithm may be used to find the minimum value of m for which a partitioning of X with z= 0 exists. The algorithm appears to be efficient for finding this ‘chromatic number of a graph’.     

Employee ownership and firm performance: a meta‐analysis

Employee ownership has been an area of significant practitioner and academic interest for the past four decades. Yet, empirical results on the relationship between employee ownership and firm performance remain mixed. To aggregate findings and provide potential direction for future theoretical development, we conducted a meta‐analysis of 102 samples representing 56,984 firms. Employee ownership has a small, but positive and statistically significant relation to firm performance ( = 0.04). The effect is generally positive for studies with different sampling designs (samples assessing change in performance pre‐employee–post‐employee ownership adoption or samples on firms with employee ownership), different performance operationalisation (efficiency or growth) and firm type (publicly held or privately held). Suggesting benefits of employee ownership in a variety of contexts, we found no differences in effects on performance in publicly held versus privately held firms, stock or stock option‐based ownership plans or differences in effects across different firm sizes (i.e. number of employees). We do find that the effect of employee ownership on performance has increased in studies over time and that studies with samples from outside the USA report stronger effects than those within. We also find little to no evidence of publication bias.     

Strong uniform convergence of the recursive regression estimator under φ-mixing conditions

Suppose the observations (X_i, Y_i) taking values in R^d×R, are -mixing. Compared with the i.i.d. case, some known strong uniform convergence results for the estimators of the regression function r(x)=E(Y_i|X_i=x) need strong moment conditions under -mixing setting. We consider the following improved kernel estimators of r(x) suggested by Cheng (1983): Qian and Mammitzsch (2000) investigated the strong uniform convergence and convergence rate for to r(x) under weaker moment conditions than those of the others in the literature, and the optimal convergence rate can be attained under almost the same conditions as stated in Theorem 3.3.2 of Györfi et al. (1989). In this paper, under the similar conditions of Qian and Mammitzsch (2000), we study the strong uniform convergence and convergence rates for (j=2,3) to r(x), which have not been discussed by Qian and Mammitzsch (2000). In contrast to , our estimators and are recursive, which is highly desirable for practical computation.     

Euromind‐ : A Density Estimate of Monthly Gross Domestic Product for the Euro Area

EuroMInd‐ is a density estimate of monthly gross domestic product (GDP) constructed according to a bottom‐up approach, pooling the density estimates of 11 GDP components, by output and expenditure type. The components' density estimates are obtained from a medium‐size dynamic factor model handling mixed frequencies of observation and ragged‐edged data structures. They reflect both parameter and filtering uncertainty and are obtained by implementing a bootstrap algorithm for simulating from the distribution of the maximum likelihood estimators of the model parameters, and conditional simulation filters for simulating from the predictive distribution of GDP. Both algorithms process the data sequentially as they become available in real time. The GDP density estimates for the output and expenditure approach are combined using alternative weighting schemes and evaluated with different tests based on the probability integral transform and by applying scoring rules. Copyright © 2016 John Wiley & Sons, Ltd.     

Een toepassing van “importance sampling”

Summary This paper describes an experiment with “importance sampling”, to show how much reduction of the computation time and sample size can be achieved in comparison with the usual Monte Carlo method. A comparison is made between each of the three methods of “importance sampling” and the usual Monte Carlo method by the determination of the expression Of the three methods A, B and C the first one uses the shifted exponential distribution, the second one uses the gamma distribution, and the third one uses the exponential distribution with modified parameter. These three methods have all smaller variances, ranges and sample sizes than the usual Monte Carlo method. Their order of preference is A, B, C. With respect to computing time only the method A is significantly better. So only the method A is an improvement in respect of both the sample size and the computing time.     

Residual‐based IV estimation of dynamic panel data models with fixed effects

In dynamic panel regression, when the variance ratio of individual effects to disturbance is large, the system‐GMM estimator will have large asymptotic variance and poor finite sample performance. To deal with this variance ratio problem, we propose a residual‐based instrumental variables (RIV) estimator, which uses the residual from regressing Δy_i,t?1 on as the instrument for the level equation. The RIV estimator proposed is consistent and asymptotically normal under general assumptions. More importantly, its asymptotic variance is almost unaffected by the variance ratio of individual effects to disturbance. Monte Carlo simulations show that the RIV estimator has better finite sample performance compared to alternative estimators. The RIV estimator generates less finite sample bias than difference‐GMM, system‐GMM, collapsing‐GMM and Level‐IV estimators in most cases. Under RIV estimation, the variance ratio problem is well controlled, and the empirical distribution of its t‐statistic is similar to the standard normal distribution for moderate sample sizes.     

Het verdelen van steekproeven over subpopulaties bij accountantscontroles

Summary “Stratificationprocedures for a typical auditing problem”. During the past ten years, much experience was gained in The Netherlands in using random sampling methods for typical auditing problems. Especially, a method suggested by VAN. HEERDEN [2] turned out to be very fruitful. In this method a register of entries is considered to be a population of T guilders, if all entries total up to T guilders. The sample size n₀ is determined in such a way that the probability β not to find any mistake in the sample, if a fraction p₀ or more of T is incorrect, is smaller than a preassigned value β₀. So n₀ should satisfy (l-p)ⁿ⁰≤β₀ for p≥p₀. A complication arises if it is not possible to postpone sampling until the whole population T is available. One then wants to take samples from a population which is growing up to T. Suppose one is going to take samples n_i from e.g. r subpopulations Using the minimax procedure, it is shown, that in this case one should choose the sizes n_i equal to (T_i/T)n₀. The minimax-value of the probability not to find any incorrect guilder in the r samples, taken together is equal to β₀.