We find the asymptotic distribution of the OLS estimator of the parameters $% \beta$ and $\rho$ in the mixed spatial model with exogenous regressors $% Y_n=X_n\beta+\rho W_nY_n+V_n$. The exogenous regressors may be bounded or growing, like polynomial trends. The assumption about the spatial...

The housing market is special in that houses are immobile, costly and durable. In this paper we look at the determinants of prices of the housing market of Almaty. What affects the prices of houses and apartments? How was the housing market developing during the economic boom and after the...

In this paper we propose a new nonparametric kernel based estimator for a density function $f$ which achieves bias reduction relative to the classical Rosenblatt-Parzen estimator. Contrary to some existing estimators that provide for bias reduction, our estimator has a full asymptotic...

We derive the asymptotics of the OLS estimator for a purely autoregressive spatial model. Only low-level conditions are used. As the sample size increases, the spatial matrix is assumed to approach a square-integrable function on the square $(0,1)^2$. The asymptotic distribution is a ratio of...

We propose a general method of modeling deterministic trends for autoregressions. The method relies on the notion of $L_2$-approximable regressors previously developed by the author. Some facts from the theory of functions play an important role in the proof. In its present form, the method...

The properties of $L_2$-approximable sequences established here form a complete toolkit for statistical results concerning weighted sums of random variables, where the weights are nonstochastic sequences approximated in some sense by square-integrable functions and the random variables are...

We find the asymptotics of the OLS estimator of the parameters $\beta$ and $\rho$ in the spatial autoregressive model with exogenous regressors $Y_n = X_n\beta+\rho W_nY_n+V_n$. Only low-level conditions are imposed. Exogenous regressors may be bounded or growing, like polynomial trends. The...

The most part of the paper is about modeling (or approximating) nonstochastic regressors. Examples of regressors which are (not) L2-approximable are given. Applications to central limit theory and OLS estimator asymptotics are provided.

If the output market is perfectly competitive and the firm’s production function is not concave, an increase in the output price may lead to an explosive increase in firm’s profits at some point. We explore the properties of this point, called a threshold price. We derive the formula for the...

This is a mathematical companion for “Statistics for Business and Economics” by Paul Newbold, William L. Carlson and Betty Thorne, London: Prentice-Hall, 2003, 6th edition. It contains derivations of most formulas from the first 12 chapters of that textbook. Most importantly, the companion...