Relative performance of the grid, nearest neighbor, and OLS estimators

This article provides various paradigms for the grid estimator, the most useful being a representation of the grid estimator as a combination of the nonparametric nearest neighbor estimator and a parametric estimator. Hence, the grid estimator falls into the class of semiparametric estimators. The article used this representation to derive the relative efficiency of the nearest neighbor, grid, and OLS estimators. Under statistically perfect conditions, the OLS estimator dominated the grid estimator, which in turn dominated the nearest neighbor estimator. A Monte Carlo experiment verified the theoretical results. A second Monte Carlo experiment showed the fragility of the OLS superiority to misspecification. The results cast light upon appraisal practice.     

Nonparametric methods with applications to hedonic models

Current real estate statistical valuation involves the estimation of parameters within a posited specification. Suchparametric estimation requires judgment concerning model (1) variables; and (2) functional form. In contrast,nonparametric regression estimation requires attention to (1) but permits greatly reduced attention to (2). Parametric estimators functionally model the parameters and variables affectingE(y¦x) while nonparametric estimators directly modelpdf(y, x) and henceE(y¦x).This article applies the kernel nonparametric regression estimator to two different data sets and specifications. The article shows the nonparametric estimator outperforms the standard parametric estimator (OLS) across variable transformations and across data subsets differing in quality. In addition, the article reviews properties of nonparametric estimators, presents the history of nonparametric estimators in real estate, and discusses a representation of the kernel estimator as a nonparametric grid method.     

Estimating Systematic Risk with Daily Security Returns: A Note on the Relative Efficiency of Selected Estimators

This paper utilizes asymptotic analysis and daily security returns to examine the estimation efficiency of two unbiased robust estimators compared with ordinary least squares. Our results demonstrate a relative efficiency gain for a nonparametric rank estimator and a relative efficiency loss for the minimum absolute deviation estimator when estimating the systematic risk of securities using daily security returns.     

Semiparametric estimation of multinomial discrete‐choice models using a subset of choices

Nonlogit maximum‐likelihood estimators are inconsistent when using data on a subset of the choices available to agents. I show that the semiparametric, multinomial maximum‐score estimator is consistent when using data on a subset of choices. No information is required for choices outside of the subset. The required conditions about the error terms are the same conditions as for using all the choices. Estimation can proceed under additional restrictions if agents have unobserved, random consideration sets. A solution exists for instrumenting endogenous continuous variables. Monte Carlo experiments show the estimator performs well using small subsets of choices.     

Aggregation of Nonparametric Estimators for Volatility Matrix

An aggregated method of nonparametric estimators based on time-domainand state-domain estimators is proposed and studied. To attenuatethe curse of dimensionality, we propose a factor modeling strategy.We first investigate the asymptotic behavior of nonparametricestimators of the volatility matrix in the time domain and inthe state domain. Asymptotic normality is separately establishedfor nonparametric estimators in the time domain and state domain.These two estimators are asymptotically independent. Hence,they can be combined, through a dynamic weighting scheme, toimprove the efficiency of volatility matrix estimation. Theoptimal dynamic weights are derived, and it is shown that theaggregated estimator uniformly dominates volatility matrix estimatorsusing time-domain or state-domain smoothing alone. A simulationstudy, based on an essentially affine model for the term structure,is conducted, and it demonstrates convincingly that the newlyproposed procedure outperforms both time- and state-domain estimators.Empirical studies further endorse the advantages of our aggregatedmethod.     

Land Value and Parcel Size: A Semiparametric Analysis

We use a semiparametric estimator to analyze the relationship between land values and parcel size in a sample of 158 undeveloped parcels in the Portland, Oregon, metropolitan area. The semiparametric estimator combines the benefits of parametric and nonparametric estimation. The value-size relationship is estimated nonparametrically, which permits the function to be linear, convex, and concave in different regions. A simple log-linear parametric relationship is assumed for the rest of the model, which conserves degrees of freedom and simplifies hypothesis testing. Our semiparametric estimates do not reject log-linearity for the value-size relationship.     

Estimating and testing beta pricing models: Alternative methods and their performance in simulations

We conduct a simulation analysis of the Fama and MacBeth[1973. Risk, returns and equilibrium: empirical tests. Journal of Political Economy 71, 607–636.] two-pass procedure, as well as maximum likelihood (ML) and generalized method of moments estimators of cross-sectional expected return models. We also provide some new analytical results on computational issues, the relations between estimators, and asymptotic distributions under model misspecification. The generalized least squares estimator is often much more precise than the usual ordinary least squares (OLS) estimator, but it displays more bias as well. A “truncated” form of ML performs quite well overall in terms of bias and precision, but produces less reliable inferences than the OLS estimator.     

Modeling daily price limits

This paper characterizes the behavior of observed asset prices under price limits and proposes the use of two-limit truncated and Tobit regression models to analyze regression models whose dependent variable is subject to price limits. Through a proper arrangement of the sample, these two models, the estimation of which is easy to implement, are applied only to subsets of the sample under study, rather than the full sample. Using the estimation of simple linear regression model as an example, several Monte Carlo experiments are conducted to compare the performance of the maximum likelihood estimators (MLEs) based on these two models and a generalized method of moments (GMM) estimator developed by K. C. John Wei and R. Chiang. The results show that under different price limits and various distributional assumptions for the error terms, the MLEs based on the two-limit Tobit and truncated regression models and the GMM estimator perform reasonably well, while the naive OLS estimator is downward biased. Overall, the MLE based on the two-limit Tobit model outperforms the other estimators.     

Measuring consumption smoothing in CEX data

A new method of measuring the degree of consumption smoothing is proposed and implemented using data from the Consumer Expenditure Survey. The structure of this Survey is such that estimators previously used in the literature are inconsistent, simply because income is measured annually and consumption is measured quarterly. An AR(1) structure is imposed on the income process to obtain a proxy for quarterly income through a projection on annual income. By construction, this proxy gives rise to a measurement error which is orthogonal to the proxy itself—as opposed to the unobserved regressor—leading to a consistent estimator. Our estimates are contrasted with the output of two estimators used in the literature. This comparison shows that while the first (OLS) estimator tends to overstate the degree of risk sharing, the second (IV) estimator grossly understates it.     

Nonparametric correlation models for portfolio allocation

This article proposes time-varying nonparametric and semiparametric estimators of the conditional cross-correlation matrix in the context of portfolio allocation. Simulations results show that the nonparametric and semiparametric models are best in DGPs with substantial variability or structural breaks in correlations. Only when correlations are constant does the parametric DCC model deliver the best outcome. The methodologies are illustrated by evaluating two interesting portfolios. The first portfolio consists of the equity sector SPDRs and the S&P 500, while the second one contains major currencies. Results show the nonparametric model generally dominates the others when evaluating in-sample. However, the semiparametric model is best for out-of-sample analysis.     

Alternative beta risk estimators and asset pricing tests in emerging markets: The case of Pakistan

This paper tests and compares the applicability of two asset pricing models specifically, the CAPM and the Fama–French three factor models for an emerging stock market namely, Pakistan. The paper analyses a number of beta risk estimators, including OLS, the Dimson thin trading estimator, a trade-to-trade estimator and a sample selectivity estimator. To uncover any possible influence of the return interval and the type of the market index, the analysis is carried out on three data frequencies namely daily, weekly and monthly as well as for a value and an equally weighted market index. The alternative beta estimators appear to correct thin trading bias but their effects on asset pricing tests are not visible. Moreover contrary to the expectations the test results for monthly and weekly frequencies are not promising. Instead for daily data the cross-section of returns are explained by a number of risk factors and trading volume.     

Optimal linear estimators of location and scale parameters using order statistics and related empirical Bayes estimation

Summary

An estimator which is a linear function of the observations and which minimises the expected square error within the class of linear estimators is called an “optimal linear” estimator. Such an estimator may also be regarded as a “linear Bayes” estimator in the spirit of Hartigan (1969). Optimal linear estimators of the unknown mean of a given data distribution have been described by various authors; corresponding “linear empirical Bayes” estimators have also been developed.

The present paper exploits the results of Lloyd (1952) to obtain optimal linear estimators based on order statistics of location or/and scale parameter (s) of a continuous univariate data distribution. Related “linear empirical Bayes” estimators which can be applied in the absence of the exact knowledge of the optimal estimators are also developed. This approach allows one to extend the results to the case of censored samples.     

Robust and Efficient Estimation of the Tail Index of a Single-Parameter Pareto Distribution

Abstract

Estimation of the tail index parameter of a single-parameter Pareto model has wide application in actuarial and other sciences. Here we examine various estimators from the standpoint of two competing criteria: efficiency and robustness against upper outliers. With the maximum likelihood estimator (MLE) being efficient but nonrobust, we desire alternative estimators that retain a relatively high degree of efficiency while also being adequately robust. A new generalized median type estimator is introduced and compared with the MLE and several well-established estimators associated with the methods of moments, trimming, least squares, quantiles, and percentile matching. The method of moments and least squares estimators are found to be relatively deficient with respect to both criteria and should become disfavored, while the trimmed mean and generalized median estimators tend to dominate the other competitors. The generalized median type performs best overall. These findings provide a basis for revision and updating of prevailing viewpoints. Other topics discussed are applications to robust estimation of upper quantiles, tail probabilities, and actuarial quantities, such as stop-loss and excess-of-loss reinsurance premiums that arise concerning solvency of portfolios. Robust parametric methods are compared with empirical nonparametric methods, which are typically nonrobust.     

SYSTEMATIC RISK IN A PURELY RANDOM MARKET MODEL: SOME EMPIRICAL EVIDENCE FOR INDIVIDUAL PUBLIC UTILITIES

A minimum norm quadratic (MINQU-) type of OLS estimator is derived. The estimator is used to test if the betas of the single factor market (SFM) model are random for a sample of utilities for two contiguous periods. The estimated betas for individual utilities vary considerably over time. The statistical significance of such nonstationarity depends on both the utilities and period studied. The relative reduction in the mean square error (MSE) from using a GLS (and not OLS) estimator of beta, when beta is purely random, can be substantial for some utilities but is modest on average.     

Constructing Commercial Indices: A Semiparametric Adaptive Estimator Approach

Constant-quality commercial indices generated by ordinary least squares may suffer an efficiency loss due to leptokurtosis caused by outliers in transactions data. When the subsequent nonnormality occurs, substantial improvement in index precision is obtained by estimating the hedonic model using a semiparametric adaptive estimator technique. When this method was applied to 1,846 office transactions that occurred in the Phoenix metropolitan area from January 1997 through June 2004, a substantial standard error reduction of approximately 9% was realized relative to ordinary least squares estimates. The difference in average returns between the semiparametric method and ordinary least squares was about 0.25% in each period, which represents a substantial increase in commercial property index precision. JEL Classification C4 R0     

Risk and performance estimation in hedge funds revisited: Evidence from errors in variables

This paper revisits the performance of hedge funds in the presence of errors in variables. To reduce the bias induced by measurement error, we introduce an estimator based on cross sample moments of orders three and four. This Higher Moment Estimation (HME) technique has significant consequences on the measure of factor loadings and the estimation of abnormal performance. Large changes in alphas can be attributed to measurement errors at the level of explanatory variables, while we emphasize some shifts in the economic contents of the equity risk premiums by switching from OLS to HME.     

Seasonals,price adjustment delays and estimated systematic risk

This article analyzed potential interactions between seasonals and price adjustment delays on estimated systematic risk. It was shown that seasonals in unobservable true security returns can induce inconsistencies into the generalized Scholes and Williams estimator of systematic risk. An alternative estimator was proposed that is consistent in the presence of seasonals in the unobservable true returns. The direction of induced bias is unpredictable a priori, thereby representing a potentially important research consideration in market efficiency tests using abnormal returns. NASDAQ and Dow Jones 30 Industrial return data for the period 1983–87 were used to evaluate the proposed estimator against the OLS and generalized Scholes and Williams (GSW) alternatives. The absolute difference between the GSW and our estimator, that is the seasonal-induced bias, for NASDAQ stocks was negatively correlated with market capitalization. Moreover, seasonal-induced bias was larger for NASDAQ stocks than more highly capitalized Dow stocks. These empirical findings indicate that seasonals and price adjustment delays can interact to bias estimated systematic risk, where price adjustment delays would be projected to be more acute for smaller capitalization stocks.     

Nonparametric realized volatility estimation in the international equity markets

Using high-frequency intraday data, we construct, test and model seven new realized volatility estimators for six international equity indices. We detect jumps in these estimators, construct the jump components of volatility and perform various tests on their properties. Then we use the class of heterogeneous autoregressive (HAR) models for assessing the relevant effects of jumps on volatility. Our results expand and complement the previous literature on the nonparametric realized volatility estimation in terms of volatility jumps being examined and modeled for the international equity market, using such a variety of new realized volatility estimators. The selection of realized volatility estimator greatly affects jump detection, magnitude and modeling. The properties each volatility estimator tries to incorporate affect the detection, magnitude and properties of jumps. These volatility-estimation and jump properties are also evident in jump modeling based on statistical and economic terms.     

Covariance complexity and rates of return on assets

This paper considers the estimation of the expected rate of return on a set of risky assets. The approach to estimation focuses on the covariance matrix for the returns. The structure in the covariance matrix determines shared information which is useful in estimating the mean return for each asset. An empirical Bayes estimator is developed using the covariance structure of the returns distribution. The estimator is an improvement on the maximum likelihood and Bayes–Stein estimators in terms of mean squared error. The effect of reduced estimation error on accumulated wealth is analyzed for the portfolio choice model with constant relative risk aversion utility.