Subsampling realised kernels

In a recent paper we have introduced the class of realised kernel estimators of the increments of quadratic variation in the presence of noise. We showed that this estimator is consistent and derived its limit distribution under various assumptions on the kernel weights. In this paper we extend our analysis, looking at the class of subsampled realised kernels and we derive the limit theory for this class of estimators. We find that subsampling is highly advantageous for estimators based on discontinuous kernels, such as the truncated kernel. For kinked kernels, such as the Bartlett kernel, we show that subsampling is impotent, in the sense that subsampling has no effect on the asymptotic distribution. Perhaps surprisingly, for the efficient smooth kernels, such as the Parzen kernel, we show that subsampling is harmful as it increases the asymptotic variance. We also study the performance of subsampled realised kernels in simulations and in empirical work.     

Variance estimation for unequal probability sampling

In this paper, we discuss the optimality of the variance estimator of the Horvitz-Thompson estimator proposed by Kott (1988) in the class of model-unbiased quadratic estimators. We also propose some improved estimators over Kott's estimator in the class of general quadratic estimators. Received: February 1999     

Record values of the Lomax distribution

In this paper, firstly an introduction to the idea of record values for a sequence of independent and identically (Lomax or Pareto II) distributed random variables is given. Some of the distributional properties of these record values and moments up to second order are derived. These moments clearly depend on the location, scale and shape parameter of the Lomax distribution and two types of estlmators of these parameters, based on a series of observed record values are presented.     

Minimax estimators of a normal variance

In the estimation problem of unknown variance of a multivariate normal distribution, a new class of minimax estimators is obtained. It is noted that a sequence of estimators in our class converges to the Stein's truncated estimator. Received: March 1998     

Information in generalized method of moments estimation and entropy-based moment selection

In this paper, we make five contributions to the literature on information and entropy in generalized method of moments (GMM) estimation. First, we introduce the concept of the long run canonical correlations (LRCCs) between the true score vector and the moment function f(_vt,_θ0)$f(v_t,{\theta }_0)$ and show that they provide a metric for the information contained in the population moment condition E[f(_vt,_θ0)]=0$\mathrm{E}[f(v_t,{\theta }_0)]=0$. Second, we show that the entropy of the limiting distribution of the GMM estimator can be written in terms of these LRCCs. Third, motivated by the above results, we introduce an information criterion based on this entropy that can be used as a basis for moment selection. Fourth, we introduce the concept of nearly redundant moment conditions and use it to explore the connection between redundancy and weak identification. Fifth, we analyse the behaviour of the aforementioned entropy-based moment selection method in two scenarios of interest; these scenarios are: (i) nonlinear dynamic models where the parameter vector is identified by all the combinations of moment conditions considered; (ii) linear static models where the parameter vector may be weakly identified for some of the combinations considered. The first of these contributions rests on a generalized information equality that is proved in the paper, and may be of interest in its own right.     

Sampling with probabilities proportional to the variable of interest

To estimate the mean sojourn time, a sample of Tilburg fair visitors was asked for the duration of their stay on the fair grounds. The longer a visitor's sojourn, the larger his/her probability of being interviewed will be; therefore, longer sojourn times will be overrepresented in the sample. As a consequence, the arithmetic sample mean is not a good estimator.
The paper places this problem against a theoretical background. Sampling with unequal probabilities is considered in a general context. The special case that the sampling probabilities are a function of the variable under investigation, is discussed in detail. As a better estimator the harmonic mean of the observations is presented. Most properties of this estimator are difficult to derive analytically, but a suitable variance estimator is derived. The behavior of estimator and variance estimator is studied in a number of quite different examples.     

On two properties of an unequal probability sampling scheme

Summary For an inclusion probability proportional to size (IPPS) sampling scheme recently proposed by Saxena, Singh and Srivastava (1986), it is shown that under certain simple verifiable conditions (1) the Horvitz-Thompson (1952) estimator based on it has a smaller variance than the variance of the Hansen-Hurwitz (1943) estimator based on probability proportional to size (PPS) sampling with replacement (WR) both involving the same size-measures and the expected sample size in the former being equal to the number of draws in the latter and (2) the Yates-Grundy (1953) estimator for the variance of the Horvitz-Thompson estimator based on this IPPS scheme is uniformly non-negative.     

Distribution of stock ratings and analyst recommendation revision

With the implementation of NASD Rule 2711 in 2002, each brokerage firm is now required to publicly disseminate the distribution of stock ratings in each research report. Hence, this paper investigates the relationship between the percentage of buy recommendations and probability of deciding to downgrade or drop coverage of stocks. Our findings suggest that the percentage of buy recommendations can enhance the probability of deciding to downgrade stock ratings and drop coverage of stocks. Furthermore, we find that analysts tend to revise their recommendations downward to hold instead of an unfavorable level. In addition, we find the market tends to heed downgrade decisions of analysts with a higher percentage of buy ratings. This finding is consistent with Barber, Lehavy, McNichols, and Trueman (2006) by applying data at the broker level.This study further investigates the changing dynamic in buy ratio of analysts by partitioning pre and post regulatory reform period. We show that analysts are more likely to revise their ratings to hold and less likely to revise their ratings to sell; in particular after post regulatory reform. Moreover, we observe one key coefficient in the post-Rule period with superior performance in contrast to the pre-Rule period. Compared to the results in the pre-Rule period, the results show that analysts are more likely to revise their ratings to hold and less likely to revise ratings to sell, and more likely to drop coverage of stocks in the post-Rule period. Overall, our findings suggest that the implementation of Rule 2711 will contribute to reduce analysts’ optimistic stock ratings.     

CHOOSING AMONG ALTERNATIVE LONG‐RUN EVENT‐STUDY TECHNIQUES

This paper reviews the long‐run event‐study debate by outlining the strengths and weakness of the most commonly used alternative techniques. The fist part of the discussion highlights that prior literature has failed to provide a single risk‐adjusted model of long‐run abnormal returns with no biases. Subsequently, the paper provides guidance on how one can choose among pertinent alternative techniques. As a conclusion, researchers ought to choose among alternative techniques after considering issues such as (i) the nature of dataset and market of interest, (ii) the event type (regulatory or corporate), (iii) returns’ time‐interval, (iv) association of the event with accounting data, (v) sample characteristics and prior evidence regarding similar events, as well as (vi) risk changes following the event. Robustness tests are essential, while the road for further research regarding the appropriate technique(s) is open.     

Mixed random systematic sampling designs

In this paper, an alternative sampling procedure that is a mixture of simple random sampling and systematic sampling is proposed. It results in uniform inclusion probabilities for all individual units and positive inclusion probabilities for all pairs of units. As a result, the proposed sampling procedure enables us to estimate the population mean unbiasedly using the ordinary sample mean, and to provide an unbiased estimator of its sampling variance. It is also found that the suggested sampling procedure performs well especially when the size of simple random sample is small. Received August 2001     

Contamination in linear regression models and its influence on estimators

The consequences of the omission of possibly contaminated observations in a linear regression model for the performance of the ordinary least squares ( LS- ) estimator are discussed. We compare the ordinary L Sestimator with the corresponding 'never pooled' LS -estimator with respect to the matrix-valued mean squared error. Necessary and sufficient conditions are derived for the superiority of an estimator to another one and tests are proposed to check these conditions. Finally the resulting preliminary-test-estimators are investigated.     

Model assisted survey sampling strategy in two phases

Postulating a super-population regression model connecting a size variable, a cheaply measurable variable and an expensively observable variable of interest, an asymptotically optimal double sampling strategy to estimate the survey population total of the third variable is specified. To render it practicable, unknown model-parameters in the optimal estimator are replaced by appropriate statistics. The resulting generalized regression estimator is then shown to have a model-cum-asymptotic design based expected square error equal to that of the asymptotically optimum estimator itself. An estimator for design variance of the estimator is also proposed.