A boundary corrected expansion of the moments of nearest neighbor distributions

In this paper, the moments of nearest neighbor distance distributions are examined. While the asymptotic form of such moments is well-known, the boundary effect has this far resisted a rigorous analysis. Our goal is to develop a new technique that allows a closed-form high order expansion, where the boundaries are taken into account up to the first order. The resulting theoretical predictions are tested via simulations and found to be much more accurate than the first order approximation obtained by neglecting the boundaries. While our results are of theoretical interest, they definitely also have important applications in statistics and physics. As a concrete example, we mention estimating Renyi entropies of probability distributions. Moreover, the algebraic technique developed may turn out to be useful in other, related problems including estimation of the Shannon differential entropy

Residual variance estimation using a nearest neighbor statistic

AbstractIn this paper we consider the problem of estimating E[(Y−E[Y∣X])2] based on a finite sample of independent, but not necessarily identically distributed, random variables (Xi,Yi)i=1M. We analyze the theoretical properties of a recently developed estimator. It is shown that the estimator has many theoretically interesting properties, while the practical implementation is simple

Accounting conservatism, financial reporting and stock returns

Research Question: One of the aims of this paper is to examine accounting conservatism using a robust set of data collected from the recent years to better understand how accounting conservatism affects the relations between stock returns and accounting variables. Motivation: Financial reporting is increasingly dependent on an in-depth understanding of the imperfections in the capital markets as well as the impact of the accounting standards on firm performance. Idea: The effect of accounting regulations on the firms’ reporting practices can be evaluated via a firm’s change in cash investments and its operating assets. Data: This study employs a robust set of data with different market to book ratios and corporate governance characteristics collected from Compustat North America Fundamentals Annual firm year observations for the time period of January 1998 to December 2015 fiscal years to better understand how accounting conservatism affects the relations between stock returns and accounting variables. Tools: Compared to the previous studies, any potential improvement in the research method is provided using a regression weight averaged over the years. Findings: There is an improvement in the explanatory power of the estimates of the coefficients on earnings levels and earnings changes when the variables associated with accounting conservatism are incorporated in the analysis. Contribution: Given the ample amount of research done in the international aspects of financial reporting, analyses of differences in results compared to the previous studies and future research opportunities will be provided

Comparative Study of University and Polytechnic Graduates in Finland : implications of higher education on earnings

Peer reviewe

Advances in the theory of nearest neighbor distributions

A large part of non-parametric statistical techniques are in one way or another related to the geometric properties of random point sets. This connection is present both in the design of estimators and theoretical convergence studies. One such relation between geometry and probability occurs in the application of non-parametric techniques for computing information theoretic entropies: it has been shown that the moments of the nearest neighbor distance distributions for a set of independent identically distributed random variables are asymptotically characterized by the Rényi entropies of the underlying probability density. As entropy estimation is a problem of major importance, this connection motivates an extensive study of nearest neighbor distances and distributions. In this thesis, new results in the theory of nearest neighbor distributions are derived using both geometric and probabilistic proof techniques. The emphasis is on results that are useful for finite samples and not only in the asymptotic limit of an infinite sample. Previously, in the literature it has been shown that after imposing sufficient regularity assumptions, the moments of the nearest neighbor distances can be approximated by invoking a Taylor series argument providing the connection to the Rényi entropies. However, the theoretical results provide limited understanding to the nature of the error in the approximation. As a central result of the thesis, it is shown that if the random points take values in a compact set (e.g. according to the uniform distribution), then under sufficient regularity, a higher order moment expansion is possible. Asymptotically, the result completely characterizes the error for the original low order approximation. Instead of striving for exact computation of the moments through a Taylor series expansion, in some cases inequalities are more useful. In the thesis, it is shown that concrete upper and lower bounds can be established under general assumptions. In fact, the upper bounds rely only on a geometric analysis. The thesis also contains applications to two problems in nonparametric statistics, residual variance and Rényi entropy estimation. A well-established nearest neighbor entropy estimator is analyzed and it is shown that by taking the boundary effect into account, estimation bias can be significantly reduced. Secondly, the convergence properties of a recent residual variance estimator are analyzed

Stochastic Nonlinear Filtering in Continuous Time

Tilastollinen epälineaarinen suodatus on tärkeä ongelma monella alalla. Epälineaarisen suodatuksen teorian sovelluksia ovat mm. rahoitusteoria, koneoppiminen ja signaalinkäsittely. Tässä diplomityössä tarkastellaan tilastollista epälineaarista suodatusta jatkuvassa ajassa. Työn ensimmäisessä osassa tehdään kirjallisuuskatsaus. Kaksi perustyökalua, Kushner-Stratonovitch yhtälö ja Kallianpur-Striebel kaava, käydään läpi. Teoreettinen lähestymistapa perustuu martingaalien teoriaan. Kirjallisuuskatsauksen jälkeen käydään läpi kolme numeerista menetelmää suodatusongelman ratkaisemiseksi. Nämä menetelmät tekevät erilaisia kompromisseja laskennallisen kompleksisuuden ja tarkkuuden välillä. Kokeellisessa osuudessa numeerisia menetelmiä tarkastellaan neljän simulaation avulla. Tämän lisäksi näytetään, että monissa ongelmissa Extended Kalman suodin voidaan korvata tehokkaammalla lineaariseen regressioon perustuvalla suotimella. Tällaisia ongelmia löytyy esimerkiksi signaalinkäsittelyn alalta

Residual variance estimation using a nearest neighbor statistic

In this paper we consider the problem of estimating E[(Y-E[Y|X])2] based on a finite sample of independent, but not necessarily identically distributed, random variables . We analyze the theoretical properties of a recently developed estimator. It is shown that the estimator has many theoretically interesting properties, while the practical implementation is simple.Residual variance estimation Noise variance estimation Nearest neighbors Nonparametric